@article {2023, title = {Benjamin-Feir Instability of Stokes Waves in Finite Depth}, journal = {ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS}, volume = {247}, year = {2023}, month = {OCT}, pages = {91}, type = {Article}, abstract = {

Whitham and Benjamin predicted in 1967 that small-amplitude periodic traveling Stokes waves of the 2d-gravity water waves equations are linearly unstable with respect to long-wave perturbations, if the depth h is larger than a critical threshold h(WB) approximate to 1.363. In this paper, we completely describe, for any finite value of h \> 0, the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent mu is turned on. We prove, in particular, the existence of a unique depth h(WB), which coincides with the one predicted by Whitham and Benjamin, such that, for any 0 \< h \< h(WB), the eigenvalues close to zero are purely imaginary and, for any h \> h(WB), a pair of non-purely imaginary eigenvalues depicts a closed figure {\textquoteleft}{\textquoteleft}8{\textquoteright}{\textquoteright}, parameterized by the Floquet exponent. As h -\> h(WB)(+) the {\textquoteleft}{\textquoteleft}8{\textquoteright}{\textquoteright} collapses to the origin of the complex plane. The complete bifurcation diagram of the spectrum is not deduced as in deep water, since the limits h -\> +infinity (deep water) and mu -\> 0 (long waves) do not commute. In finite depth, the four eigenvalues have all the same size O(mu), unlike in deep water, and the analysis of their splitting is much more delicate, requiring, as a new ingredient, a non-perturbative step of block-diagonalization. Along the whole proof, the explicit dependence of the matrix entries with respect to the depth h is carefully tracked.

}, issn = {0003-9527}, doi = {10.1007/s00205-023-01916-2}, author = {Berti, Massimiliano and Maspero, Alberto and Ventura, Paolo} } @article {2023, title = {On the distribution of the van der Corput sequences}, journal = {Archiv der Mathematik}, year = {2023}, month = {2023/01/13}, abstract = {For an integer $p\ge 2$, let $\{x_n\}_{n\in {\mathbb {N}}}\subset {\mathbb {T}}$ be the p-adic van der Corput sequence. For intervals $[0,\alpha )\subset {\mathbb {T}}$ and for positive integers N, consider the geometrically-shifted discrepancy function $D_{p,N,\alpha }(t)=\sum _{n=0}^{N-1}\mathcal {X}_{[0,\alpha )}(x_n+t)-N\alpha$. In this paper, we give a characterization of the asymptotic behavior of $\Vert D_{p,N,\alpha }(\cdot )\Vert _{L^2({\mathbb {T}})}$ for $N\rightarrow \infty$that depends on the p-adic expansion of $\alpha$.}, keywords = {Diaphony, Discrepancy, Uniform distribution, Van der Corput sequence}, isbn = {1420-8938}, doi = {https://doi.org/10.1007/s00013-022-01811-4}, author = {Beretti, Thomas} } @article {noselli_2023, title = {Flutter instability in solids and structures, with a view on biomechanics and metamaterials}, journal = {Proceedings of the Royal Society A}, volume = {479}, year = {2023}, pages = {20230523}, abstract = {The phenomenon of oscillatory instability called {\textquoteleft}flutter{\textquoteright} was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.}, doi = {10.1098/rspa.2023.0523}, url = {https://royalsocietypublishing.org/doi/10.1098/rspa.2023.0523}, author = {Davide Bigoni and Francesco Dal Corso and Oleg N. Kirillov and Diego Misseroni and Giovanni Noselli and Andrea Piccolroaz} } @article {2023, title = {An optimisation{\textendash}based domain{\textendash}decomposition reduced order model for the incompressible Navier-Stokes equations}, volume = {151}, year = {2023}, month = {2023/12/01/}, pages = {172 - 189}, abstract = {

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain{\textendash}decomposition (DD) methods and reduced{\textendash}order modelling (ROM). In particular, we consider an optimisation{\textendash}based domain{\textendash}decomposition algorithm for the parameter{\textendash}dependent stationary incompressible Navier{\textendash}Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal{\textendash}control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward{\textendash}facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain{\textendash}decomposition algorithm.

}, keywords = {Computational fluid dynamics, Domain decomposition, Optimal control, Proper orthogonal decomposition, Reduced order modelling}, isbn = {0898-1221}, url = {https://www.sciencedirect.com/science/article/pii/S0898122123004248}, author = {Ivan Prusak and Monica Nonino and Davide Torlo and Francesco Ballarin and Gianluigi Rozza} } @article {2023, title = {Properties of Mixing BV Vector Fields}, journal = {Communications in Mathematical Physics}, volume = {402}, year = {2023}, month = {jul}, pages = {1953{\textendash}2009}, doi = {10.1007/s00220-023-04780-z}, url = {https://doi.org/10.1007\%2Fs00220-023-04780-z}, author = {Stefano Bianchini and Martina Zizza} } @booklet {2023, title = {Relaxed area of graphs of piecewise Lipschitz maps in the strict $BV$-convergence}, year = {2023}, author = {Bellettini, Giovanni and Carano, Simone and Scala, Riccardo} } @article {2023, title = {Stokes waves at the critical depth are modulational unstable}, year = {2023}, author = {Berti, Massimiliano and Maspero, Alberto and Ventura, Paolo} } @article {2022, title = {On the analyticity of the Dirichlet-Neumann operator and Stokes waves}, journal = {RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI}, volume = {33}, year = {2022}, pages = {611-650}, type = {Article}, abstract = {

We prove an analyticity result for the Dirichlet-Neumann operator under space periodic boundary conditions in any dimension in an unbounded domain with infinite depth. We derive an analytic bifurcation result of analytic Stokes waves-i.e., space periodic traveling solutions-of the water waves equations in deep water.

}, keywords = {Bifurcation theory, Dirichlet-Neumann operator, traveling waves, water waves}, issn = {1120-6330}, doi = {10.4171/RLM/983}, author = {Berti, Massimiliano and Maspero, Alberto and Ventura, Paolo} } @article {2022, title = {A behavioral change model to assess vaccination-induced relaxation of social distancing during an epidemic}, journal = {Journal of Biological Systems}, volume = {30}, year = {2022}, month = {2022/03/01}, pages = {1-25}, abstract = {

The success of mass vaccination campaigns may be jeopardized by human risky behaviors. For example, high level of vaccination coverage may induce early relaxation of social distancing. In this paper, we focus on the mutual influence between the decline in prevalence, due to the rise in the overall immunization coverage, and the consequent decrease in the compliance to social distancing measures. We consider an epidemic model where both the vaccination rate and the disease transmission rate are influenced by human behavior, which in turn depends on the current and past information about the spread of the disease. We highlight the impact of the information-related parameters on the transient and asymptotic behavior of the system that is on the early stage of the epidemic and its final outcome. Among the main results, we evidence that sustained oscillations may be triggered by the behavioral memory in the prevalence-dependent vaccination rate. However, the relaxation of social distancing may induce a switch from a cyclic regime to damped oscillations.

}, isbn = {0218-3390}, url = {https://doi.org/10.1142/S0218339022500085}, author = {Buonomo, Bruno and Della Marca, Rossella and Sintayehu Sharbayta, Sileshi} } @article {2022, title = {Benjamin-Feir instability of Stokes waves}, journal = {RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI}, volume = {33}, year = {2022}, pages = {399-412}, type = {Article}, abstract = {

We present the recent results in Berti et al. [Invent. Math. (2022), to appear] regarding the Benjamin-Feir instability of small amplitude Stokes waves in deep water. We completely describe the behavior of the four eigenvalues close to zero of the linearized water waves equations at the Stokes solution, as the Floquet exponent is turned on, proving the conjecture that a pair of non-purely imaginary eigenvalues depicts a closed figure {\textquoteleft}{\textquoteleft}8{\textquoteright}{\textquoteright}, in full agreement with numerical simulations.

}, keywords = {Kato perturbation theory, modulational instability, traveling waves, water waves}, issn = {1120-6330}, doi = {10.4171/RLM/975}, author = {Berti, Massimiliano and Maspero, Alberto and Ventura, Paolo} } @article {2022, title = {Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier{\textendash}Stokes equations with model order reduction}, journal = {ESAIM: M2AN}, volume = {56}, year = {2022}, month = {2022///}, pages = {1361 - 1400}, url = {https://doi.org/10.1051/m2an/2022044}, author = {Federico Pichi and Maria Strazzullo and F. Ballarin and Gianluigi Rozza} } @article {2022, title = {Full description of Benjamin-Feir instability of stokes waves in deep water}, volume = {230}, year = {2022}, month = {2022/11/01}, pages = {651 - 711}, abstract = {

Small-amplitude, traveling, space periodic solutions {\textendash}called Stokes waves{\textendash} of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to long-wave perturbations, as predicted by Benjamin and Feir in 1967. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent is turned on. We prove in particular the conjecture that a pair of non-purely imaginary eigenvalues depicts a closed figure {\textquotedblleft}8{\textquotedblright}, parameterized by the Floquet exponent, in full agreement with numerical simulations. Our new spectral approach to the Benjamin-Feir instability phenomenon uses a symplectic version of Kato{\textquoteright}s theory of similarity transformation to reduce the problem to determine the eigenvalues of a $ 4 \times 4 $ complex Hamiltonian and reversible matrix. Applying a procedure inspired by KAM theory, we block-diagonalize such matrix into a pair of $2 \times 2 $ Hamiltonian and reversible matrices, thus obtaining the full description of its eigenvalues.

}, isbn = {1432-1297}, url = {https://doi.org/10.1007/s00222-022-01130-z}, author = {Berti, Massimiliano and Maspero, Alberto and Ventura, Paolo} } @booklet {2022, title = {Projection based semi{\textendash}implicit partitioned Reduced Basis Method for non parametrized and parametrized Fluid{\textendash}Structure Interaction problems}, year = {2022}, abstract = {

The goal of this manuscript is to present a partitioned Model Order Reduction method that is based on a semi-implicit projection scheme to solve multiphysics problems. We implement a Reduced Order Method based on a Proper Orthogonal Decomposition, with the aim of addressing both time-dependent and time-dependent, parametrized Fluid-Structure Interaction problems, where the fluid is incompressible and the structure is thick and two dimensional.

}, author = {Monica Nonino and Francesco Ballarin and Gianluigi Rozza and Yvon Maday} } @article {2022, title = {The relaxed area of $S^1$-valued singular maps in the strict $BV$-convergence}, journal = {ESAIM: Control, Optimization and Calculus of Variations}, volume = {28}, year = {2022}, pages = {38}, url = {http://cvgmt.sns.it/paper/5440/}, author = {Bellettini, Giovanni and Carano, Simone and Scala, Riccardo} } @article {bonito2021approximation, title = {Approximation of the spectral fractional powers of the Laplace-Beltrami Operator}, journal = {arXiv preprint arXiv:2101.05141}, year = {2021}, author = {Bonito, Andrea and Wenyu Lei} } @unpublished {2021, title = {An artificial neural network approach to bifurcating phenomena in computational fluid dynamics}, year = {2021}, author = {Federico Pichi and Francesco Ballarin and Gianluigi Rozza and Jan S Hesthaven} } @unpublished {2021, title = {A CERTIFIED REDUCED BASIS Method FOR LINEAR PARAMETRIZED PARABOLIC OPTIMAL CONTROL PROBLEMS IN SPACE-TIME FORMULATION}, year = {2021}, author = {Maria Strazzullo and Francesco Ballarin and Gianluigi Rozza} } @unpublished {2021, title = {Consistency of the full and reduced order models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows}, year = {2021}, author = {Maria Strazzullo and Michele Girfoglio and Francesco Ballarin and T. Iliescu and Gianluigi Rozza} } @article {ArndtBangerthBlais-2021-h, title = {The deal.II Library, Version 9.3}, journal = {Journal of Numerical Mathematics}, year = {2021}, url = {https://doi.org/10.1515/jnma-2021-0081}, author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Marc Fehling and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Uwe K{\"o}cher and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Sebastian Proell and Konrad Simon and Bruno Turcksin and David Wells and Jiaqi Zhang} } @article {BacDeRFraLan21, title = {Exactness of Linear Response in the Quantum Hall Effect}, journal = {Annales Henri Poincar{\'e}}, volume = {22}, number = {4}, year = {2021}, month = {Jan}, pages = {1113{\textendash}1132}, publisher = {Springer Science and Business Media LLC}, issn = {1424-0661}, doi = {10.1007/s00023-020-00989-z}, url = {http://dx.doi.org/10.1007/s00023-020-00989-z}, author = {Sven Bachmann and De Roeck, Wojciech and Fraas, Martin and Markus Lange} } @article {2021, title = {Hierarchical model reduction techniques for flow modeling in a parametrized setting}, journal = {Multiscale Modeling and Simulation}, volume = {19}, year = {2021}, pages = {267-293}, abstract = {

In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases.

}, doi = {10.1137/19M1285330}, author = {Matteo Zancanaro and F. Ballarin and Simona Perotto and Gianluigi Rozza} } @article {2021, title = {Local Well Posedness of the Euler{\textendash}Korteweg Equations on $${{\mathbb {T}}^d}$$}, volume = {33}, year = {2021}, month = {2021/09/01}, pages = {1475 - 1513}, abstract = {

We consider the Euler{\textendash}Korteweg system with space periodic boundary conditions $$ x \in {\mathbb {T}}^d$$. We prove a local in time existence result of classical solutions for irrotational velocity fields requiring natural minimal regularity assumptions on the initial data.

}, isbn = {1572-9222}, url = {https://doi.org/10.1007/s10884-020-09927-3}, author = {Massimiliano Berti and Alberto Maspero and Federico Murgante} } @article {2021, title = {A Monolithic and a Partitioned, Reduced Basis Method for Fluid{\textendash}Structure Interaction Problems}, journal = {Fluids}, volume = {6}, year = {2021}, pages = {229}, abstract = {

The aim of this work is to present an overview about the combination of the Reduced Basis Method (RBM) with two different approaches for Fluid{\textendash}Structure Interaction (FSI) problems, namely a monolithic and a partitioned approach. We provide the details of implementation of two reduction procedures, and we then apply them to the same test case of interest. We first implement a reduction technique that is based on a monolithic procedure where we solve the fluid and the solid problems all at once. We then present another reduction technique that is based on a partitioned (or segregated) procedure: the fluid and the solid problems are solved separately and then coupled using a fixed point strategy. The toy problem that we consider is based on the Turek{\textendash}Hron benchmark test case, with a fluid Reynolds number Re=100.

}, issn = {2311-5521}, doi = {10.3390/fluids6060229}, url = {https://www.mdpi.com/2311-5521/6/6/229}, author = {Monica Nonino and F. Ballarin and Gianluigi Rozza} } @article {2021, title = {Non-intrusive data-driven ROM framework for hemodynamics problems}, journal = {Acta Mechanica Sinica}, volume = {37}, year = {2021}, pages = {1183{\textendash}1191}, author = {Michele Girfoglio and Leonardo Scandurra and Francesco Ballarin and Giuseppe Infantino and Francesca Nicol{\`o} and Andrea Montalto and Gianluigi Rozza and Roberto Scrofani and Marina Comisso and Francesco Musumeci} } @article {StarStabileBelloniRozzaDegroote2019, title = {A novel iterative penalty method to enforce boundary conditions in Finite Volume POD-Galerkin reduced order models for fluid dynamics problems}, journal = {Communications in Computational Physics}, volume = {30}, number = {1}, year = {2021}, pages = {34{\textendash}66}, publisher = {Global Science Press}, abstract = {A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamic problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the control function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation. The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the speedup ratio between the reduced order models and the full order model is of the order 1000 for the lid driven cavity case and of the order 100 for the Y-junction test case.}, doi = {https://doi.org/10.4208/cicp.OA-2020-0059}, author = {Kelbij Star and Giovanni Stabile and Francesco Belloni and Gianluigi Rozza and Joris Degroote} } @article {MorelliBarralQuintelaRozzaStabile2021, title = {A numerical approach for heat flux estimation in thin slabs continuous casting molds using data assimilation}, journal = {International Journal for Numerical Methods in Engineering}, volume = {122}, number = {17}, year = {2021}, pages = {4541{\textendash}4574}, publisher = {Wiley}, doi = {10.1002/nme.6713}, url = {https://doi.org/10.1002/nme.6713}, author = {Umberto Emil Morelli and Patricia Barral and Peregrina Quintela and Gianluigi Rozza and Giovanni Stabile} } @article {HeltaiBangerthKronbichler-2021, title = {Propagating geometry information to finite element computations}, journal = {Transactions on Mathematical Software}, volume = {47}, year = {2021}, pages = {1--30}, chapter = {1}, doi = {https://dx.doi.org/10.1145/3468428}, author = {Luca Heltai and Wolfgang Bangerth and Martin Kronbichler and Andrea Mola} } @article {2021, title = {Quadratic Life Span of Periodic Gravity-capillary Water Waves}, volume = {3}, year = {2021}, month = {2021/04/01}, pages = {85 - 115}, abstract = {

We consider the gravity-capillary water waves equations for a bi-dimensional fluid with a periodic one-dimensional free surface. We prove a rigorous reduction of this system to Birkhoff normal form up to cubic degree. Due to the possible presence of three-wave resonances for general values of gravity, surface tension, and depth, such normal form may be not trivial and exhibit a chaotic dynamics (Wilton ripples). Nevertheless, we prove that for all the values of gravity, surface tension, and depth, initial data that are of size $$ \varepsilon $$in a sufficiently smooth Sobolev space leads to a solution that remains in an $$ \varepsilon $$-ball of the same Sobolev space up times of order $$ \varepsilon ^{-2}$$. We exploit that the three-wave resonances are finitely many, and the Hamiltonian nature of the Birkhoff normal form.

}, isbn = {2523-3688}, url = {https://doi.org/10.1007/s42286-020-00036-8}, author = {Massimiliano Berti and Roberto Feola and Luca Franzoi} } @article {2021, title = {A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier{\textendash}Stokes problems}, journal = {Computer \& Mathematics With Applications}, year = {2021}, month = {2021/08/12/}, abstract = {

We focus on steady and unsteady Navier{\textendash}Stokes flow systems in a reduced-order modeling framework based on Proper Orthogonal Decomposition within a levelset geometry description and discretized by an unfitted mesh Finite Element Method. This work extends the approaches of [1], [2], [3] to nonlinear CutFEM discretization. We construct and investigate a unified and geometry independent reduced basis which overcomes many barriers and complications of the past, that may occur whenever geometrical morphings are taking place. By employing a geometry independent reduced basis, we are able to avoid remeshing and transformation to reference configurations, and we are able to handle complex geometries. This combination of a fixed background mesh in a fixed extended background geometry with reduced order techniques appears beneficial and advantageous in many industrial and engineering applications, which could not be resolved efficiently in the past.

}, keywords = {Cut Finite Element Method, Navier{\textendash}Stokes equations, Parameter{\textendash}dependent shape geometry, Reduced Order Models, Unfitted mesh}, isbn = {0898-1221}, url = {https://www.sciencedirect.com/science/article/pii/S0898122121002790}, author = {Efthymios N Karatzas and Monica Nonino and F. Ballarin and Gianluigi Rozza} } @conference { 20.500.11767_123375, title = {Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, volume = {139}, year = {2021}, pages = {841{\textendash}850}, publisher = {Springer}, organization = {Springer}, isbn = {978-3-030-55873-4}, doi = {10.1007/978-3-030-55874-1_83}, url = {https://arxiv.org/abs/1912.07886}, author = {Maria Strazzullo and Zakia Zainib and F. Ballarin and Gianluigi Rozza} } @conference {2021, title = {Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2019}, year = {2021}, month = {2021//}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (1) time dependent Stokes equations and (2) steady non-linear Navier-Stokes equations.

}, isbn = {978-3-030-55874-1}, doi = {https://doi.org/10.1007/978-3-030-55874-1_83}, url = {https://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676}, author = {Maria Strazzullo and Zakia Zainib and F. Ballarin and Gianluigi Rozza}, editor = {Fred J Vermolen and Cornelis Vuik} } @article {2021, title = {Traveling Quasi-periodic Water Waves with Constant Vorticity}, volume = {240}, year = {2021}, month = {2021/04/01}, pages = {99 - 202}, abstract = {

We prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.

}, isbn = {1432-0673}, url = {https://doi.org/10.1007/s00205-021-01607-w}, author = {Massimiliano Berti and Luca Franzoi and Alberto Maspero} } @booklet {BacLan21, title = {Trotter product formulae for $*$-automorphisms of quantum lattice systems}, year = {2021}, author = {Sven Bachmann and Markus Lange} } @article {2021, title = {A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences}, journal = {Computers and Mathematics with Applications}, volume = {102}, year = {2021}, pages = {261-276}, doi = {10.1016/j.camwa.2021.10.020}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85117948561\&doi=10.1016\%2fj.camwa.2021.10.020\&partnerID=40\&md5=cb57d59a6975a35315b2cf5d0e3a6001}, author = {G. Carere and Maria Strazzullo and Francesco Ballarin and Gianluigi Rozza and R. Stevenson} } @inbook {RozzaHessStabileTezzeleBallarin2020, title = {Basic ideas and tools for projection-based model reduction of parametric partial differential equations}, booktitle = {Model Order Reduction, Volume 2 Snapshot-Based Methods and Algorithms}, year = {2020}, pages = {1 - 47}, publisher = {De Gruyter}, organization = {De Gruyter}, address = {Berlin, Boston}, isbn = {9783110671490}, doi = {https://doi.org/10.1515/9783110671490-001}, url = {https://www.degruyter.com/view/book/9783110671490/10.1515/9783110671490-001.xml}, author = {Gianluigi Rozza and Martin W. Hess and Giovanni Stabile and Marco Tezzele and F. Ballarin} } @article {2020, title = {Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height}, journal = {Computers and Mathematics with Applications}, volume = {80}, year = {2020}, pages = {973-989}, abstract = {

In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that lets us obtain an affine decomposition with respect to the parameters. We construct an a posteriori error estimator, based upon the Brezzi{\textendash}Rappaz{\textendash}Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for different parameter configuration.

}, doi = {10.1016/j.camwa.2020.05.013}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085843368\&doi=10.1016\%2fj.camwa.2020.05.013\&partnerID=40\&md5=7c6596865ec89651319c7dd97159dd77}, author = {F. Ballarin and Rebollo, T.C. and E.D. {\'A}vila and Marmol, M.G. and Gianluigi Rozza} } @article {ArndtBangerthDavydov-2020-a, title = {The deal.II finite element library: Design, features, and insights}, journal = {Computers and Mathematics with Applications}, year = {2020}, url = {https://doi.org/10.1016/j.camwa.2020.02.022}, author = {Daniel Arndt and Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {ArndtBangerthBlais-2020-a, title = {The deal.II library, Version 9.2}, journal = {Journal of Numerical Mathematics}, volume = {28}, number = {3}, year = {2020}, pages = {131{\textendash}146}, author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and Thomas C. Clevenger and Marc Fehling and Alexander V. Grayver and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Reza Rastak and Ignacio Tomas and Bruno Turcksin and Zhuoran Wang and David Wells} } @conference {HijaziAliStabileBallarinRozza2020, title = {The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows}, booktitle = {Lecture Notes in Computational Science and Engineering}, year = {2020}, pages = {245{\textendash}264}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

We present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

}, isbn = {978-3-030-30705-9}, doi = {10.1007/978-3-030-30705-9_22}, author = {Saddam Hijazi and Shafqat Ali and Giovanni Stabile and F. Ballarin and Gianluigi Rozza} } @article {bonito2020finite, title = {Finite element approximation of an obstacle problem for a class of integro{\textendash}differential operators}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis}, volume = {54}, number = {1}, year = {2020}, pages = {229{\textendash}253}, publisher = {EDP Sciences}, author = {Bonito, Andrea and Wenyu Lei and Salgado, Abner J} } @article {Bonelli:2020xps, title = {Gauge theories on compact toric manifolds}, year = {2020}, month = {7}, doi = {10.1007/s11005-021-01419-9}, author = {Giulio Bonelli and Francesco Fucito and Morales, Jose Francisco and Massimiliano Ronzani and Sysoeva, Ekaterina and Alessandro Tanzini} } @article {2020, title = {A hybrid reduced order method for modelling turbulent heat transfer problems}, journal = {Computers \& Fluids}, volume = {208}, year = {2020}, pages = {104615}, abstract = {

A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation. For high Reynolds numbers, the eddy viscosity and eddy diffusivity are incorporated into the reduced order model with a Proper Orthogonal Decomposition (nested and standard) with Interpolation (PODI), where the interpolation is performed using Radial Basis Functions. The reduced order solver, obtained using a k-ω SST URANS full order model, is tested against the full order solver in a 3D T-junction pipe with parametric velocity inlet boundary conditions.

}, doi = {10.1016/j.compfluid.2020.104615}, url = {https://arxiv.org/abs/1906.08725}, author = {Sokratia Georgaka and Giovanni Stabile and Kelbij Star and Gianluigi Rozza and Michael J. Bluck} } @unpublished {2020, title = {POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations}, year = {2020}, abstract = {

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

}, author = {Maria Strazzullo and F. Ballarin and Gianluigi Rozza} } @article {2020, title = {POD{\textendash}Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation}, journal = {Journal of Scientific Computing}, volume = {83}, year = {2020}, abstract = {

In this work we deal with parametrized time dependent optimal control problems governed by partial differential equations. We aim at extending the standard saddle point framework of steady constraints to time dependent cases. We provide an analysis of the well-posedness of this formulation both for parametrized scalar parabolic constraint and Stokes governing equations and we propose reduced order methods as an effective strategy to solve them. Indeed, on one hand, parametrized time dependent optimal control is a very powerful mathematical model which is able to describe several physical phenomena, on the other, it requires a huge computational effort. Reduced order methods are a suitable approach to have rapid and accurate simulations. We rely on POD{\textendash}Galerkin reduction over the physical and geometrical parameters of the optimality system in a space-time formulation. Our theoretical results and our methodology are tested on two examples: a boundary time dependent optimal control for a Graetz flow and a distributed optimal control governed by time dependent Stokes equations. With these two test cases the convenience of the reduced order modelling is further extended to the field of time dependent optimal control.

}, doi = {10.1007/s10915-020-01232-x}, author = {Maria Strazzullo and F. Ballarin and Gianluigi Rozza} } @article {2020, title = {POD{\textendash}Galerkin reduced order methods for combined Navier{\textendash}Stokes transport equations based on a hybrid FV-FE solver}, journal = {Computers and Mathematics with Applications}, volume = {79}, year = {2020}, pages = {256-273}, abstract = {

The purpose of this work is to introduce a novel POD{\textendash}Galerkin strategy for the semi-implicit hybrid high order finite volume/finite element solver introduced in Berm{\'u}dez et al. (2014) and Busto et al. (2018). The interest is into the incompressible Navier{\textendash}Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.

}, doi = {10.1016/j.camwa.2019.06.026}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068068567\&doi=10.1016\%2fj.camwa.2019.06.026\&partnerID=40\&md5=a8dcce1b53b8ee872d174bbc4c20caa3}, author = {S. Busto and Giovanni Stabile and Gianluigi Rozza and M.E. V{\'a}zquez-Cend{\'o}n} } @article {2020, title = {Projection-based reduced order models for a cut finite element method in parametrized domains}, journal = {Computers and Mathematics with Applications}, volume = {79}, year = {2020}, pages = {833-851}, abstract = {

This work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail.

}, doi = {10.1016/j.camwa.2019.08.003}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85070900852\&doi=10.1016\%2fj.camwa.2019.08.003\&partnerID=40\&md5=2d222ab9c7832955d155655d3c93e1b1}, author = {Efthymios N Karatzas and F. Ballarin and Gianluigi Rozza} } @article {2020, title = {Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation}, journal = {International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng}, volume = {n/a}, year = {2020}, month = {2020/05/27}, pages = {e3367}, abstract = {

Abstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

}, keywords = {coronary artery bypass grafts, data assimilation, flow control, Galerkin methods, hemodynamics modeling, Optimization, patient-specific simulations, Proper orthogonal decomposition, reduced order methods}, isbn = {2040-7939}, doi = {https://doi.org/10.1002/cnm.3367}, url = {https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R}, author = {Zakia Zainib and F. Ballarin and Stephen E. Fremes and Piero Triverio and Laura Jim{\'e}nez-Juan and Gianluigi Rozza} } @article {2020, title = {Stabilized reduced basis methods for parametrized steady Stokes and Navier{\textendash}Stokes equations}, journal = {Computers and Mathematics with Applications}, volume = {80}, year = {2020}, pages = {2399-2416}, abstract = {

It is well known in the Reduced Basis approximation of saddle point problems that the Galerkin projection on the reduced space does not guarantee the inf{\textendash}sup approximation stability even if a stable high fidelity method was used to generate snapshots. For problems in computational fluid dynamics, the lack of inf{\textendash}sup stability is reflected by the inability to accurately approximate the pressure field. In this context, inf{\textendash}sup stability is usually recovered through the enrichment of the velocity space with suitable supremizer functions. The main goal of this work is to propose an alternative approach, which relies on the residual based stabilization techniques customarily employed in the Finite Element literature, such as Brezzi{\textendash}Pitkaranta, Franca{\textendash}Hughes, streamline upwind Petrov{\textendash}Galerkin, Galerkin Least Square. In the spirit of offline{\textendash}online reduced basis computational splitting, two such options are proposed, namely offline-only stabilization and offline{\textendash}online stabilization. These approaches are then compared to (and combined with) the state of the art supremizer enrichment approach. Numerical results are discussed, highlighting that the proposed methodology allows to obtain smaller reduced basis spaces (i.e., neglecting supremizer enrichment) for which a modified inf{\textendash}sup stability is still preserved at the reduced order level.

}, doi = {10.1016/j.camwa.2020.03.019}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083340115\&doi=10.1016\%2fj.camwa.2020.03.019\&partnerID=40\&md5=7ace96eee080701acb04d8155008dd7d}, author = {Shafqat Ali and F. Ballarin and Gianluigi Rozza} } @article {bogluk, title = {Stable vector bundles on the families of curves}, year = {2020}, abstract = {We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.}, author = {Fedor Bogomolov and Elena Lukzen} } @article {RICCOBELLI2020103745, title = {Surface tension controls the onset of gyrification in brain organoids}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {134}, year = {2020}, pages = {103745}, abstract = {

Understanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e.\ the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length generated by surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.

}, keywords = {Buckling, Embryogenesis, Morpho-elasticity, Post-buckling analysis, Surface tension}, issn = {0022-5096}, doi = {https://doi.org/10.1016/j.jmps.2019.103745}, url = {http://www.sciencedirect.com/science/article/pii/S0022509619304065}, author = {Davide Riccobelli and Giulia Bevilacqua} } @article {ArndtBangerthClevenger-2019-a, title = {The deal.II Library, Version 9.1}, journal = {Journal of Numerical Mathematics}, year = {2019}, author = {Daniel Arndt and Wolfgang Bangerth and Thomas C. Clevenger and Denis Davydov and Marc Fehling and Garcia-Sanchez, Daniel and Harper, Graham and Timo Heister and Luca Heltai and Martin Kronbichler and Maguire Kynch, Ross and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {ArndtBangerthClevenger-2019-a, title = {The deal.II Library, Version 9.1}, journal = {Journal of Numerical Mathematics}, year = {2019}, abstract = {This paper provides an overview of the new features of the finite element library deal.II, version 9.1.}, issn = {15702820}, doi = {10.1515/jnma-2019-0064}, author = {Daniel Arndt and Wolfgang Bangerth and Thomas C. Clevenger and Denis Davydov and Marc Fehling and Garcia-Sanchez, Daniel and Harper, Graham and Timo Heister and Luca Heltai and Martin Kronbichler and Maguire Kynch, Ross and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {Bawane:2017gjf, title = {N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts}, journal = {JHEP}, volume = {07}, year = {2019}, pages = {040}, doi = {10.1007/JHEP07(2019)040}, url = {http://inspirehep.net/record/1631219/}, author = {Aditya Bawane and Benvenuti, Sergio and Giulio Bonelli and Muteeb, Nouman and Alessandro Tanzini} } @article {BLP2019, title = {Numerical approximation of the integral fractional Laplacian}, journal = {Numerische Mathematik}, volume = {142}, number = {2}, year = {2019}, pages = {235{\textendash}278}, abstract = {We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem. The numerical approximation of the action of the corresponding stiffness matrix consists of three steps: (1) apply a sinc quadrature scheme to approximate the integral representation by a finite sum where each term involves the solution of an elliptic partial differential equation defined on the entire space, (2) truncate each elliptic problem to a bounded domain, (3) use the finite element method for the space approximation on each truncated domain. The consistency error analysis for the three steps is discussed together with the numerical implementation of the entire algorithm. The results of computations are given illustrating the error behavior in terms of the mesh size of the physical domain, the domain truncation parameter and the quadrature spacing parameter.}, isbn = {0945-3245}, doi = {10.1007/s00211-019-01025-x}, url = {https://doi.org/10.1007/s00211-019-01025-x}, author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak} } @article {2019, title = {Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems}, journal = {Communications in Computational Physics}, volume = {27}, year = {2019}, pages = {1{\textendash}32}, abstract = {

A parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume approximation. Two different paramet- ric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model.

}, issn = {1991-7120}, doi = {10.4208/cicp.OA-2018-0207}, url = {https://arxiv.org/abs/1808.05175}, author = {Sokratia Georgaka and Giovanni Stabile and Gianluigi Rozza and Michael J. Bluck} } @conference {StarStabileGeorgakaBelloniRozzaDegroote2019, title = {POD-Galerkin Reduced Order Model of the Boussinesq Approximation for Buoyancy-Driven Enclosed Flows}, booktitle = {International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2019}, year = {2019}, isbn = {9780894487699}, author = {Kelbij Star and Giovanni Stabile and Sokratia Georgaka and Francesco Belloni and Gianluigi Rozza and Joris Degroote} } @article {2019, title = {A POD-selective inverse distance weighting method for fast parametrized shape morphing}, journal = {International Journal for Numerical Methods in Engineering}, volume = {117}, year = {2019}, pages = {860-884}, abstract = {

Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency.

}, doi = {10.1002/nme.5982}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85056396233\&doi=10.1002\%2fnme.5982\&partnerID=40\&md5=6aabcbdc9a0da25e36575a0ebfac034f}, author = {F. Ballarin and A. D{\textquoteright}Amario and Simona Perotto and Gianluigi Rozza} } @article {Beltr{\'a}n2019, title = {The Real Polynomial Eigenvalue Problem is Well Conditioned on the Average}, journal = {Foundations of Computational Mathematics}, year = {2019}, month = {May}, abstract = {

We study the average condition number for polynomial eigenvalues of collections of matrices drawn from some random matrix ensembles. In particular, we prove that polynomial eigenvalue problems defined by matrices with random Gaussian entries are very well conditioned on the average.

}, issn = {1615-3383}, doi = {10.1007/s10208-019-09414-2}, url = {https://doi.org/10.1007/s10208-019-09414-2}, author = {Carlos Beltr{\'a}n and Khazhgali Kozhasov} } @article {2019, title = {A reduced order variational multiscale approach for turbulent flows}, journal = {Advances in Computational Mathematics}, volume = {45}, year = {2019}, pages = {2349-2368}, abstract = {

The purpose of this work is to present different reduced order model strategies starting from full order simulations stabilized using a residual-based variational multiscale (VMS) approach. The focus is on flows with moderately high Reynolds numbers. The reduced order models (ROMs) presented in this manuscript are based on a POD-Galerkin approach. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case, the VMS stabilization method is used at both the full order and the reduced order levels. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM, while the latter is named non-consistent ROM, in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark.

}, doi = {10.1007/s10444-019-09712-x}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068076665\&doi=10.1007\%2fs10444-019-09712-x\&partnerID=40\&md5=af0142e6d13bbc2e88c6f31750aef6ad}, author = {Giovanni Stabile and F. Ballarin and G. Zuccarino and Gianluigi Rozza} } @article {Bellettini2019, title = {On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, year = {2019}, month = {Jul}, abstract = {

In this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to {\textquoteleft}{\textquoteleft}fill the hole{\textquoteright}{\textquoteright} in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

}, issn = {1618-1891}, doi = {10.1007/s10231-019-00887-0}, url = {https://doi.org/10.1007/s10231-019-00887-0}, author = {Giovanni Bellettini and Alaa Elshorbagy and Maurizio Paolini and Riccardo Scala} } @inbook {2019, title = {A Spectral Element Reduced Basis Method in Parametric CFD}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2017}, volume = {126}, year = {2019}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, chapter = {A Spectral Element Reduced Basis Method in Parametric CFD}, abstract = {

We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

}, doi = {10.1007/978-3-319-96415-7_64 pages = 693{\textendash}701}, url = {https://arxiv.org/abs/1712.06432}, author = {Martin W. Hess and Gianluigi Rozza}, editor = {Radu, Florin Adrian and Kumar, Kundan and Berre, Inga and Nordbotten, Jan Martin and Pop, Iuliu Sorin} } @article {2019, title = {On the square distance function from a manifold with boundary}, year = {2019}, abstract = {

We characterize arbitrary codimensional smooth manifolds $\mathcal{M}$ with boundary embedded in $\mathbb{R}^n$ using the square distance function and the signed distance function from $\mathcal{M}$ and from its boundary. The results are localized in an open set.

}, url = {http://cvgmt.sns.it/media/doc/paper/4260/manif_with_bound_dist.pdf}, author = {Giovanni Bellettini and Alaa Elshorbagy} } @article {2019, title = {Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras}, journal = {arXiv e-prints}, year = {2019}, month = {May}, pages = {arXiv:1905.07730}, abstract = {

We strengthen a result of Hanke{\textendash}Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

}, keywords = {Mathematics - K-Theory and Homology, Mathematics - Operator Algebras}, author = {Paolo Antonini and Buss, Alcides and Engel, Alexander and Siebenand , Timo} } @article {Natphys_2019, title = {Swimming Euglena respond to confinement with a behavioural change enabling effective crawling}, journal = {Nature Physics}, volume = {15}, number = {5}, year = {2019}, pages = {496{\textendash}502}, abstract = {Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modelling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells.}, doi = {10.1038/s41567-019-0425-8}, url = {https://doi.org/10.1038/s41567-019-0425-8}, author = {Giovanni Noselli and Alfred Beran and Marino Arroyo and Antonio DeSimone} } @article {2019, title = {A Weighted POD Method for Elliptic PDEs with Random Inputs}, journal = {Journal of Scientific Computing}, volume = {81}, year = {2019}, pages = {136-153}, abstract = {

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems. The algorithm is introduced alongside the weighted greedy method. Our proposed method aims to minimize the error in a L2 norm and, in contrast to the weighted greedy approach, it does not require the availability of an error bound. Moreover, we consider sparse discretization of the input space in the construction of the reduced model; for high-dimensional problems, provided the sampling is done accordingly to the parameters distribution, this enables a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We provide many numerical tests to assess the performance of the proposed method compared to an equivalent reduced order model without weighting, as well as to the weighted greedy approach, in both low and high dimensional problems.

}, doi = {10.1007/s10915-018-0830-7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053798049\&doi=10.1007\%2fs10915-018-0830-7\&partnerID=40\&md5=5cad501b6ef1955da55868807079ee5d}, author = {L.Venturi and F. Ballarin and Gianluigi Rozza} } @article {2019, title = {Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs}, journal = {PoliTO Springer Series}, year = {2019}, pages = {27-40}, abstract = {

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.

}, doi = {10.1007/978-3-030-04870-9_2}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379\&doi=10.1007\%2f978-3-030-04870-9_2\&partnerID=40\&md5=446bcc1f331167bbba67bc00fb170150}, author = {L. Venturi and D. Torlo and F. Ballarin and Gianluigi Rozza} } @article {BraHasLan18, title = {On asymptotic expansions in spin-boson models}, journal = {Ann. Henri Poincar{\'e}}, volume = {19}, number = {2}, year = {2018}, pages = {515{\textendash}564}, issn = {1424-0637}, doi = {10.1007/s00023-017-0625-7}, url = {https://doi.org/10.1007/s00023-017-0625-7}, author = {Br{\"a}unlich, Gerhard and Hasler, David and Markus Lange} } @article {2018, title = {Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations}, number = {SISSA;45/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.}, url = {http://preprints.sissa.it/handle/1963/35325}, author = {Stefano Bianchini and Laura Spinolo} } @inbook {tezzele2018combined, title = {Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods}, booktitle = {Mathematical and Numerical Modeling of the Cardiovascular System and Applications}, year = {2018}, pages = {185{\textendash}207}, publisher = {Springer}, organization = {Springer}, author = {Marco Tezzele and F. Ballarin and Gianluigi Rozza} } @article {20.500.11767_83906, title = {deal2lkit: A toolkit library for high performance programming in deal.II}, journal = {SOFTWAREX}, volume = {7}, year = {2018}, pages = {318{\textendash}327}, doi = {10.1016/j.softx.2018.09.004}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {20.500.11767_81694, title = {The deal.II Library, Version 9.0}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, year = {2018}, doi = {10.1515/jnma-2018-0054}, url = {https://doi.org/10.1515/jnma-2018-0054}, author = {Giovanni Alzetta and Daniel Arndt and Wolfgang Bangerth and Boddu, Vishal and Brands, Benjamin and Denis Davydov and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Kormann, Katharina and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {MR3871555, title = {Discriminant circle bundles over local models of Strebel graphs and Boutroux curves}, journal = {Teoret. Mat. Fiz.}, volume = {197}, number = {2}, year = {2018}, pages = {163{\textendash}207}, issn = {0564-6162}, doi = {10.4213/tmf9513}, url = {https://doi.org/10.4213/tmf9513}, author = {Marco Bertola and Korotkin, D. A.} } @inbook {20.500.11767_86398, title = {A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids}, booktitle = {Mathematical and Numerical Modeling of the Cardiovascular System and Applications}, volume = {16}, year = {2018}, pages = {1{\textendash}21}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, doi = {10.1007/978-3-319-96649-6_1}, url = {https://arxiv.org/abs/1712.02545v1}, author = {Boffi, Daniele and Gastaldi, Lucia and Luca Heltai} } @inbook {Bianchini2018, title = {Failure of the Chain Rule in the Non Steady Two-Dimensional Setting}, booktitle = {Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg}, year = {2018}, pages = {33{\textendash}60}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-89800-1}, doi = {10.1007/978-3-319-89800-1_2}, url = {https://doi.org/10.1007/978-3-319-89800-1_2}, author = {Stefano Bianchini and Paolo Bonicatto}, editor = {Rassias, Themistocles M.} } @article {20.500.11767_86219, title = {Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments}, journal = {ASTRONOMY \& ASTROPHYSICS}, volume = {618}, year = {2018}, pages = {1{\textendash}14}, doi = {10.1051/0004-6361/201832710}, url = {https://arxiv.org/abs/1801.08937}, author = {Puglisi, Giuseppe and Poletti, Davide and Fabbian, Giulio and Baccigalupi, Carlo and Luca Heltai and Stompor, Radek} } @article {BELLETTINI20181, title = {Minimizing movements for mean curvature flow of droplets with prescribed contact angle}, journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, volume = {117}, year = {2018}, pages = {1 - 58}, abstract = {

We study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the solutions constructed as a limit of an approximation algorithm of Almgren{\textendash}Taylor{\textendash}Wang and Luckhaus{\textendash}Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. R{\'e}sum{\'e} Nous {\'e}tudions le mouvement par courbure moyenne d{\textquoteright}une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit {\'e}ventuellement non constant. En utilisant les solutions construites comme limites d{\textquoteright}un algorithme d{\textquoteright}approximation d{\^u} {\`a} Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l{\textquoteright}existence d{\textquoteright}une {\'e}volution faible, et sa compatibilit{\'e} avec une solution au sens des distributions. Nous d{\'e}montrons {\'e}galement plusieurs r{\'e}sultats de comparaison.

}, keywords = {Capillary functional, Mean curvature flow with prescribed contact angle, Minimizing movements, Sets of finite perimeter}, issn = {0021-7824}, doi = {https://doi.org/10.1016/j.matpur.2018.06.003}, url = {http://www.sciencedirect.com/science/article/pii/S0021782418300825}, author = {Giovanni Bellettini and Matteo Novaga and Shokhrukh Kholmatov} } @article {doi:10.1137/17M1159294, title = {Minimizing Movements for Mean Curvature Flow of Partitions}, journal = {SIAM Journal on Mathematical Analysis}, volume = {50}, number = {4}, year = {2018}, pages = {4117-4148}, abstract = {

We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some consistency results for a minimizing movement solution with smooth and viscosity solutions when the evolution starts from a partition made by a union of bounded sets at a positive distance. In addition, the motion starting from the union of convex sets at a positive distance agrees with the classical mean curvature flow and is stable with respect to the Hausdorff convergence of the initial partitions.

}, doi = {10.1137/17M1159294}, url = {https://doi.org/10.1137/17M1159294}, author = {Giovanni Bellettini and Shokhrukh Kholmatov} } @article {doi:10.1137/17M1150591, title = {Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering}, journal = {SIAM Journal on Scientific Computing}, volume = {40}, number = {4}, year = {2018}, pages = {B1055-B1079}, doi = {10.1137/17M1150591}, url = {https://doi.org/10.1137/17M1150591}, author = {Maria Strazzullo and F. Ballarin and Mosetti, R. and Gianluigi Rozza} } @article {BeCaRu, title = {Noncommutative Painlev{\'e} Equations and Systems of Calogero Type}, journal = {Comm. Math. Phys}, year = {2018}, author = {Marco Bertola and Mattia Cafasso and V. Rubtsov} } @article {Stabile2018, title = {A novel reduced order model for vortex induced vibrations of long flexible cylinders}, volume = {156}, year = {2018}, month = {may}, pages = {191{\textendash}207}, publisher = {Elsevier {BV}}, doi = {10.1016/j.oceaneng.2018.02.064}, url = {https://doi.org/10.1016/j.oceaneng.2018.02.064}, author = {Giovanni Stabile and Hermann G. Matthies and Claudio Borri} } @article {2018, title = {Observables in the equivariant A-model}, number = {arXiv:1807.08659}, year = {2018}, url = {https://arxiv.org/abs/1807.08659}, author = {Bonechi, F. and Cattaneo, A.S. and Riccardo Iraso and Maxim Zabzine} } @article {bertola2018painleve, title = {Painlev{\'e} IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane}, journal = {Symmetry, Integrability and Geometry. Methods and Applications}, volume = {14}, year = {2018}, publisher = {National Academy of Sciences of Ukraine}, abstract = {

We study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a transition for a special value of the parameter, where it develops a corner-type singularity. In the double scaling limit near the transition we determine the asymptotic behaviour of the orthogonal polynomials in terms of a solution of the Painlev{\textasciiacute}e IV equation. We determine the Fredholm determinant associated to such solution and we compute it numerically on the real line, showing also that the corresponding Painlev{\textasciiacute}e transcendent is pole-free on a semiaxis.

}, doi = {10.3842/SIGMA.2018.091}, author = {Marco Bertola and Jos{\'e} Gustavo Elias Rebelo and Tamara Grava} } @article {12166, title = {Positive solutions for super-sublinear indefinite problems: high multiplicity results via coincidence degree}, journal = {Trans. Amer. Math. Soc.}, number = {Transactions of the American Mathematical Society;}, year = {2018}, note = {AMS Subject Classification: 34B15, 34B18, 34C25, 34C28, 47H11.}, publisher = {American Mathematical Society}, abstract = {

We study the periodic boundary value problem associated with the second order nonlinear equation u{\textquoteright}{\textquoteright}+(λa+(t)-μa-(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m-1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35264}, author = {Alberto Boscaggin and Guglielmo Feltrin and Fabio Zanolin} } @article {doi:10.1142/S0219199717500213, title = {Positive subharmonic solutions to nonlinear ODEs with indefinite weight}, journal = {Communications in Contemporary Mathematics}, volume = {20}, number = {01}, year = {2018}, pages = {1750021}, abstract = {

We prove that the superlinear indefinite equation u" + a(t)up = 0, where p \> 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt \< 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467{\textendash}477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincar{\'e}{\textendash}Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

}, doi = {10.1142/S0219199717500213}, url = {https://doi.org/10.1142/S0219199717500213}, author = {Alberto Boscaggin and Guglielmo Feltrin} } @article {BLP18, title = {On sinc quadrature approximations of fractional powers of regularly accretive operators}, journal = {Journal of Numerical Mathematics}, year = {2018}, publisher = {De Gruyter}, doi = {10.1515/jnma-2017-0116}, author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak} } @article {doi:10.1063/1.5026311, title = {Spectral triples on the Jiang-Su algebra}, journal = {Journal of Mathematical Physics}, volume = {59}, number = {5}, year = {2018}, pages = {053507}, doi = {10.1063/1.5026311}, url = {https://doi.org/10.1063/1.5026311}, author = {Jacopo Bassi and Ludwik Dabrowski} } @conference {2018, title = {SRTP 2.0 - The evolution of the safe return to port concept}, booktitle = {Technology and Science for the Ships of the Future - Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research}, year = {2018}, abstract = {

In 2010 IMO (International Maritime Organisation) introduced new rules in SOLAS with the aim of intrinsically increase the safety of passenger ships. This requirement is achieved by providing safe areas for passengers and essential services for allowing ship to Safely Return to Port (SRtP). The entry into force of these rules has changed the way to design passenger ships. In this respect big effort in the research has been done by industry to address design issues related to the impact on failure analysis of the complex interactions among systems. Today the research activity is working to bring operational matters in the design stage. This change of research focus was necessary because human factor and the way to operate the ship itself after a casualty on board may have a big impact in the design of the ship/systems. Also the management of the passengers after a casualty is becoming a major topic for safety. This paper presents the state of the art of Italian knowledge in the field of system engineering applied to passenger ship address to safety improvement and design reliability. An overview of present tools and methodologies will be offered together with future focuses in the research activity.

}, doi = {10.3233/978-1-61499-870-9-665}, author = {D. Cangelosi and A. Bonvicini and M. Nardo and Andrea Mola and A. Marchese and Marco Tezzele and Gianluigi Rozza} } @article {2018, title = {Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs}, journal = {SIAM-ASA Journal on Uncertainty Quantification}, volume = {6}, year = {2018}, pages = {1475-1502}, abstract = {

In this work, we propose viable and eficient strategies for stabilized parametrized advection dominated problems, with random inputs. In particular, we investigate the combination of the wRB (weighted reduced basis) method for stochastic parametrized problems with the stabilized RB (reduced basis) method, which is the integration of classical stabilization methods (streamline/upwind Petrov-Galerkin (SUPG) in our case) in the ofine-online structure of the RB method. Moreover, we introduce a reduction method that selectively enables online stabilization; this leads to a sensible reduction of computational costs, while keeping a very good accuracy with respect to high-fdelity solutions. We present numerical test cases to assess the performance of the proposed methods in steady and unsteady problems related to heat transfer phenomena.

}, doi = {10.1137/17M1163517}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058246502\&doi=10.1137\%2f17M1163517\&partnerID=40\&md5=6c54e2f0eb727cb85060e988486b8ac8}, author = {D. Torlo and F. Ballarin and Gianluigi Rozza} } @article {doi:10.1098/rsta.2017.0424, title = {Symplectic invariants for parabolic orbits and cusp singularities of integrable systems}, journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {376}, number = {2131}, year = {2018}, pages = {20170424}, abstract = {

We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type. This article is part of the theme issue {\textquoteleft}Finite dimensional integrable systems: new trends and methods{\textquoteright}.

}, doi = {10.1098/rsta.2017.0424}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2017.0424}, author = {Alexey Bolsinov and Lorenzo Guglielmi and Elena Kudryavtseva} } @conference {10.1007/978-3-319-91545-6_15, title = {On Uniqueness of Weak Solutions to Transport Equation with Non-smooth Velocity Field}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, year = {2018}, pages = {191{\textendash}203}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-91545-6}, doi = {10.1007/978-3-319-91545-6_15}, url = {https://link.springer.com/chapter/10.1007/978-3-319-91545-6_15}, author = {Paolo Bonicatto}, editor = {Klingenberg, Christian and Westdickenberg, Michael} } @article {2017, title = {Almost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions}, number = {arXiv;1702.04674}, year = {2017}, abstract = {The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ-N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.}, url = {http://preprints.sissa.it/handle/1963/35285}, author = {Massimiliano Berti and Jean-Marc Delort} } @article {BLP16, title = {The approximation of parabolic equations involving fractional powers of elliptic operators}, journal = {J. Comput. Appl. Math.}, volume = {315}, year = {2017}, pages = {32{\textendash}48}, issn = {0377-0427}, doi = {10.1016/j.cam.2016.10.016}, url = {http://dx.doi.org/10.1016/j.cam.2016.10.016}, author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak} } @article {2017, title = {On a certified smagorinsky reduced basis turbulence model}, journal = {SIAM Journal on Numerical Analysis}, volume = {55}, year = {2017}, pages = {3047-3067}, doi = {10.1137/17M1118233}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218\&doi=10.1137\%2f17M1118233\&partnerID=40\&md5=221d9cd2bcc74121fcef93efd9d3d76c}, author = {Rebollo, T.C. and E.D. {\'A}vila and Marmol, M.G. and F. Ballarin and Gianluigi Rozza} } @article {2017, title = {Complex Friedrichs systems and applications}, number = {SISSA;03/2017/MATE}, year = {2017}, abstract = {We provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper.}, url = {http://urania.sissa.it/xmlui/handle/1963/35270}, author = {Nenad Antoni{\'c} and Kre{\v s}imir Burazin and Ivana Crnjac and Marko Erceg} } @article {GiustiStabileMarinoBorri2017, title = {Coupling effects on the dynamic response of moored floating platforms for offshore wind energy plants}, journal = {Procedia engineering}, volume = {199}, year = {2017}, pages = {3194{\textendash}3199}, publisher = {Elsevier}, doi = {10.1016/j.proeng.2017.09.527}, author = {Giusti, Alessandro and Giovanni Stabile and Marino, Enzo and Claudio Borri} } @article {BARILARI2017118, title = {Curvature terms in small time heat kernel expansion for a model class of hypoelliptic H{\"o}rmander operators}, journal = {Nonlinear Analysis}, volume = {164}, year = {2017}, pages = {118 - 134}, abstract = {

We consider the heat equation associated with a class of second order hypoelliptic H{\"o}rmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

}, keywords = {Curvature, Hypoelliptic heat equation, Small time asymptotics}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2017.09.002}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X17302298}, author = {Davide Barilari and Elisa Paoli} } @article {20.500.11767_47950, title = {The deal.II Library, Version 8.5}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {25}, year = {2017}, pages = {137{\textendash}145}, doi = {10.1515/jnma-2017-0058}, url = {https://www.dealii.org/deal85-preprint.pdf}, author = {Daniel Arndt and Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Jean-Paul Pelteret and Bruno Turcksin and David Wells} } @article {BERSHTEIN201740, title = {Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants}, journal = {Journal of Geometry and Physics}, volume = {118}, year = {2017}, note = {Interactions between Geometry and Physics. A Special Issue in Honor of Ugo Bruzzo{\textquoteright}s 60th Birthday}, pages = {40 - 50}, abstract = {

We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$\ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics {\textemdash} in honor of Ugo Bruzzo{\textquoteright}s 60th birthday 17{\textendash}22 August 2015, Guaruj{\'a}, S{\~a}o Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

}, keywords = {AGT, Donaldson invariants, Equivariant localization, Exact partition function, Supersymmetry, Virasoro conformal blocks}, issn = {0393-0440}, doi = {https://doi.org/10.1016/j.geomphys.2017.01.012}, url = {http://www.sciencedirect.com/science/article/pii/S0393044017300165}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {Agrachev2017, title = {Homotopically invisible singular curves}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {56}, number = {4}, year = {2017}, month = {Jul}, pages = {105}, issn = {1432-0835}, doi = {10.1007/s00526-017-1203-z}, url = {https://doi.org/10.1007/s00526-017-1203-z}, author = {Andrei A. Agrachev and Francesco Boarotto and Antonio Lerario} } @article {boarotto2017homotopy, title = {Homotopy properties of horizontal path spaces and a theorem of Serre in subriemannian geometry}, journal = {Communications in Analysis and Geometry}, volume = {25}, number = {2}, year = {2017}, pages = {269{\textendash}301}, publisher = {International Press of Boston}, doi = {10.4310/CAG.2017.v25.n2.a1}, author = {Francesco Boarotto and Antonio Lerario} } @article {rossi13085, title = {Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes}, journal = {Proceedings of the National Academy of Sciences}, volume = {114}, number = {50}, year = {2017}, pages = {13085-13090}, abstract = {Active flagella provide the propulsion mechanism for a large variety of swimming eukaryotic microorganisms, from protists to sperm cells. Planar and helical beating patterns of these structures are recurrent and widely studied. The fast spinning motion of the locomotory flagellum of the alga Euglena gracilis constitutes a remarkable exception to these patterns. We report a quantitative description of the 3D flagellar beating in swimming E. gracilis. Given their complexity, these shapes cannot be directly imaged with current microscopy techniques. We show how to overcome these limitations by developing a method to reconstruct in full the 3D kinematics of the cell from conventional 2D microscopy images, based on the exact characterization of the helical motion of the cell body.The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement.}, doi = {10.1073/pnas.1708064114}, url = {https://www.pnas.org/content/114/50/13085}, author = {Massimiliano Rossi and Giancarlo Cicconofri and Alfred Beran and Giovanni Noselli and Antonio DeSimone} } @article {Bertola:2016nr, title = {The Kontsevich matrix integral: convergence to the Painlev{\'e} hierarchy and Stokes{\textquoteright} phenomenon}, journal = {Comm. Math. Phys}, volume = {DOI 10.1007/s00220-017-2856-3}, year = {2017}, url = {http://arxiv.org/abs/1603.06420}, author = {Marco Bertola and Mattia Cafasso} } @article {2017, title = {A Lagrangian approach for scalar multi-d conservation laws}, number = {SISSA;36/2017/MATE}, year = {2017}, url = {http://preprints.sissa.it/handle/1963/35290}, author = {Stefano Bianchini and Paolo Bonicatto and Elio Marconi} } @article {bianchini2017lagrangian, title = {Lagrangian representations for linear and nonlinear transport}, journal = {Contemporary Mathematics. Fundamental Directions}, volume = {63}, number = {3}, year = {2017}, pages = {418{\textendash}436}, publisher = {Peoples{\textquoteright} Friendship University of Russia}, abstract = {

In this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

}, doi = {10.22363/2413-3639-2017-63-3-418-436}, url = {http://www.mathnet.ru/php/archive.phtml?wshow=paper\&jrnid=cmfd\&paperid=327\&option_lang=eng}, author = {Stefano Bianchini and Paolo Bonicatto and Elio Marconi} } @article {MR3665212, title = {The Malgrange form and Fredholm determinants}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, volume = {13}, year = {2017}, pages = {Paper No. 046, 12}, issn = {1815-0659}, doi = {10.3842/SIGMA.2017.046}, url = {http://dx.doi.org/10.3842/SIGMA.2017.046}, author = {Marco Bertola} } @article {MR3663616, title = {Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schr{\"o}dinger Equation}, journal = {Comm. Math. Phys.}, volume = {354}, number = {2}, year = {2017}, pages = {525{\textendash}547}, issn = {0010-3616}, doi = {10.1007/s00220-017-2895-9}, url = {http://dx.doi.org/10.1007/s00220-017-2895-9}, author = {Marco Bertola and Alexander Tovbis} } @article {1534-0392_2017_4_1427, title = {Minimizers of anisotropic perimeters with cylindrical norms}, journal = {Communications on Pure \& Applied Analysis}, volume = {16}, number = {1534-0392_2017_4_142}, year = {2017}, pages = {1427}, abstract = {

We study various regularity properties of minimizers of the Φ{\textendash}perimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

}, keywords = {anisotropic Bernstein problem;, minimal cones, Non parametric minimal surfaces, Sets of finite perimeter}, issn = {1534-0392}, doi = {10.3934/cpaa.2017068}, url = {http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d}, author = {Giovanni Bellettini and Matteo Novaga and Shokhrukh Kholmatov} } @article {BLP17a, title = {Numerical approximation of space-time fractional parabolic equations}, journal = {Comput. Methods Appl. Math.}, volume = {17}, number = {4}, year = {2017}, pages = {679{\textendash}705}, issn = {1609-4840}, doi = {10.1515/cmam-2017-0032}, url = {https://doi.org/10.1515/cmam-2017-0032}, author = {Bonito, Andrea and Wenyu Lei and Joseph E Pasciak} } @article {2017, title = {Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts}, journal = {Biomechanics and Modeling in Mechanobiology}, volume = {16}, year = {2017}, pages = {1373-1399}, doi = {10.1007/s10237-017-0893-7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851\&doi=10.1007\%2fs10237-017-0893-7\&partnerID=40\&md5=c388f20bd5de14187bad9ed7d9affbd0}, author = {F. Ballarin and Elena Faggiano and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza and Sonia Ippolito and Roberto Scrofani} } @article {1711.08253, title = {Random spectrahedra}, year = {2017}, author = {Paul Breiding and Khazhgali Kozhasov and Antonio Lerario} } @inbook {BallarinRozzaMaday2017, title = {Reduced-order semi-implicit schemes for fluid-structure interaction problems}, booktitle = {Model Reduction of Parametrized Systems}, year = {2017}, pages = {149{\textendash}167}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, chapter = {Reduced-order semi-implicit schemes for fluid-structure interaction problems}, abstract = {

POD{\textendash}Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

}, doi = {10.1007/978-3-319-58786-8_10}, author = {F. Ballarin and Gianluigi Rozza and Yvon Maday}, editor = {Peter Benner and Mario Ohlberger and Anthony Patera and Gianluigi Rozza and Karsten Urban} } @article {2017, title = {Semistable Higgs Bundles on Calabi-Yau Manifolds}, number = {SISSA;40/2017/MATE;}, year = {2017}, abstract = {We provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.}, url = {http://preprints.sissa.it/handle/1963/35295}, author = {Ugo Bruzzo and Valeriano Lanza and Alessio Lo Giudice} } @article {2017, title = {Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions}, number = {SISSA;61/2017/MATE}, year = {2017}, note = {Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and Mathematical Physics" code RBFR13WAET (S.B., A.M., A.O.), by the DAAD International Trainership Programme (S.B.), and by a 2017 visiting research fellowship at the International Center for Mathematical Research CIRM, Trento (A.M.).}, publisher = {SISSA}, abstract = {We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise and prove the finiteness of the discrete spectrum, qualify the angular symmetry of the eigenfunctions, and prove the monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence of bound states in a physically relevant regime of masses.}, url = {http://preprints.sissa.it/handle/1963/35303}, author = {Simon Becker and Alessandro Michelangeli and Andrea Ottolini} } @article {Bertola:2015tg, title = {Symplectic geometry of the moduli space of projective structures in homological coordinates}, journal = {Inventiones Mathematicae}, year = {2017}, month = {06}, pages = {1{\textendash}56}, url = {https://arxiv.org/abs/1506.07918}, author = {Marco Bertola and Dmitry Korotkin and Chaya Norton} } @article {2017, title = {Time quasi-periodic gravity water waves in finite depth}, number = {arXiv;1708.01517}, year = {2017}, abstract = {We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.}, url = {http://preprints.sissa.it/handle/1963/35296}, author = {P Baldi and Massimiliano Berti and Emanuele Haus and Riccardo Montalto} } @article {2017, title = {A uniqueness result for the decomposition of vector fields in Rd}, number = {SISSA;15/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {

Given a vector field $\rho (1,\b) \in L^1_\loc(\R^+\times \R^{d},\R^{d+1})$ such that $\dive_{t,x} (\rho (1,\b))$ is a measure, we consider the problem of uniqueness of the representation $\eta$ of $\rho (1,\b) \mathcal L^{d+1}$ as a superposition of characteristics $\gamma : (t^-_\gamma,t^+_\gamma) \to \R^d$, $\dot \gamma (t)= \b(t,\gamma(t))$. We give conditions in terms of a local structure of the representation $\eta$ on suitable sets in order to prove that there is a partition of $\R^{d+1}$ into disjoint trajectories $\wp_\a$, $\a \in \A$, such that the PDE \begin{equation*} \dive_{t,x} \big( u \rho (1,\b) \big) \in \mathcal M(\R^{d+1}), \qquad u \in L^\infty(\R^+\times \R^{d}), \end{equation*} can be disintegrated into a family of ODEs along $\wp_\a$ with measure r.h.s.. The decomposition $\wp_\a$ is essentially unique. We finally show that $\b \in L^1_t(\BV_x)_\loc$ satisfies this local structural assumption and this yields, in particular, the renormalization property for nearly incompressible $\BV$ vector fields.

}, url = {http://preprints.sissa.it/handle/1963/35274}, author = {Stefano Bianchini and Paolo Bonicatto} } @article {MR3686488, title = {Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles}, journal = {Random Matrices Theory Appl.}, volume = {6}, number = {3}, year = {2017}, pages = {1750010, 22}, issn = {2010-3263}, doi = {10.1142/S2010326317500101}, url = {http://dx.doi.org/10.1142/S2010326317500101}, author = {Marco Bertola and Mattia Cafasso} } @article {PhysRevLett.119.033901, title = {Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schr{\"o}dinger Equation}, journal = {Phys. Rev. Lett.}, volume = {119}, year = {2017}, month = {Jul}, pages = {033901}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.119.033901}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.033901}, author = {Tikan, Alexey and Billet, Cyril and Gennady El and Alexander Tovbis and Marco Bertola and Sylvestre, Thibaut and Gustave, Francois and Randoux, Stephane and Genty, Go{\"e}ry and Suret, Pierre and Dudley, John M.} } @conference {2016, title = {Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives}, booktitle = {Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering,}, year = {2016}, month = {06/2016}, publisher = {ECCOMAS}, organization = {ECCOMAS}, address = {Crete, Greece}, abstract = {

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

}, author = {Filippo Salmoiraghi and F. Ballarin and Giovanni Corsi and Andrea Mola and Marco Tezzele and Gianluigi Rozza}, editor = {Papadrakakis, M. and Papadopoulos, V. and Stefanou, G. and Plevris, V.} } @article {2013, title = {On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity}, journal = {ESAIM: COCV}, volume = {22}, number = {arXiv:1310.2443;}, year = {2016}, pages = {29-63}, abstract = {

In this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau{\textquoteright}s problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

}, keywords = {Area functional}, doi = {10.1051/cocv/2014065}, url = {https://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html}, author = {Giovanni Bellettini and Lucia Tealdi and Maurizio Paolini} } @article {MR3589917, title = {On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight}, journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, volume = {12}, year = {2016}, pages = {Paper No. 118, 50 pages}, issn = {1815-0659}, doi = {10.3842/SIGMA.2016.118}, url = {http://dx.doi.org/10.3842/SIGMA.2016.118}, author = {Marco Bertola and Alexander Tovbis} } @article {Bonechi2016, title = {Comparing Poisson Sigma Model with A-model}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {10}, year = {2016}, month = {Oct}, pages = {133}, abstract = {

We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

}, issn = {1029-8479}, doi = {10.1007/JHEP10(2016)133}, url = {https://doi.org/10.1007/JHEP10(2016)133}, author = {Bonechi, F. and Cattaneo, A.S. and Riccardo Iraso} } @article {1937-1632_2016_1_73, title = {On the concentration of entropy for scalar conservation laws}, journal = {Discrete \& Continuous Dynamical Systems - S}, volume = {9}, number = {1937-1632_2016_1_7}, year = {2016}, pages = {73}, abstract = {

We prove that the entropy for an $L^$\infty$$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

}, keywords = {concentration, Conservation laws, entropy solutions, Lagrangian representation, shocks}, issn = {1937-1632}, doi = {10.3934/dcdss.2016.9.73}, url = {http://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae}, author = {Stefano Bianchini and Elio Marconi} } @article {Boarotto2016, title = {Conformal Equivalence of 3D Contact Structures on Lie Groups}, journal = {Journal of Dynamical and Control Systems}, volume = {22}, number = {2}, year = {2016}, month = {Apr}, pages = {251{\textendash}283}, abstract = {

In this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

}, issn = {1573-8698}, doi = {10.1007/s10883-015-9273-8}, url = {https://doi.org/10.1007/s10883-015-9273-8}, author = {Francesco Boarotto} } @article {MR3505204, title = {Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$}, journal = {Phys. D}, volume = {327}, year = {2016}, pages = {30{\textendash}57}, issn = {0167-2789}, doi = {10.1016/j.physd.2016.04.008}, url = {http://dx.doi.org/10.1016/j.physd.2016.04.008}, author = {Marco Bertola and Boris Dubrovin and Di Yang} } @article {BertolaCorrection, title = {CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function}, year = {2016}, month = {01}, url = {http://arxiv.org/abs/1601.04790}, author = {Marco Bertola} } @article {20.500.11767_14497, title = {The deal.II Library, Version 8.3}, journal = {ARCHIVE OF NUMERICAL SOFTWARE}, volume = {4}, year = {2016}, pages = {1{\textendash}11}, doi = {10.11588/ans.2016.100.23122}, url = {http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-231226}, author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin} } @article {20.500.11767_14498, title = {The deal.II library, Version 8.4}, journal = {JOURNAL OF NUMERICAL MATHEMATICS}, volume = {24}, year = {2016}, pages = {135{\textendash}141}, doi = {10.1515/jnma-2016-1045}, url = {https://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf}, author = {Wolfgang Bangerth and Denis Davydov and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and David Wells} } @article {2016, title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I}, journal = {Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337}, number = {Journal of Differential Equations;261}, year = {2016}, publisher = {Elsevier}, doi = {10.1016/j.jde.2016.06.026}, url = {http://urania.sissa.it/xmlui/handle/1963/35207}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {2016, title = {Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II}, number = {SISSA;32/2016/MATE}, year = {2016}, url = {http://urania.sissa.it/xmlui/handle/1963/35197}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {Bershtein2016, title = {Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {7}, year = {2016}, month = {Jul}, pages = {23}, abstract = {

We provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2016)023}, url = {https://doi.org/10.1007/JHEP07(2016)023}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {BATTAGLIA20163750, title = {Existence and non-existence results for the SU(3) singular Toda system on compact surfaces}, journal = {Journal of Functional Analysis}, volume = {270}, number = {10}, year = {2016}, pages = {3750 - 3807}, abstract = {

We consider the SU(3) singular Toda system on a compact surface (Σ,g)-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑m=1Mα1m(δpm-1)-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑m=1Mα2m(δpm-1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim\>-1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Poho{\v z}aev-type identities."

}, keywords = {Liouville-type equations, Min{\textendash}max solutions, Non-existence results, Toda system}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2015.12.011}, url = {http://www.sciencedirect.com/science/article/pii/S0022123615004942}, author = {Luca Battaglia and Andrea Malchiodi} } @article {2016, title = {A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts}, year = {2016}, institution = {Submitted}, abstract = {A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.}, url = {http://urania.sissa.it/xmlui/handle/1963/35240}, author = {F. Ballarin and Elena Faggiano and Andrea Manzoni and Gianluigi Rozza and Alfio Quarteroni and Sonia Ippolito and Roberto Scrofani and Carlo Antona} } @article {arici2016gysin, title = {The Gysin sequence for quantum lens spaces}, journal = {Journal of Noncommutative Geometry}, volume = {9}, number = {4}, year = {2016}, pages = {1077{\textendash}1111}, abstract = {

We define quantum lens spaces as {\textquoteleft}direct sums of line bundles{\textquoteright} and exhibit them as {\textquoteleft}total spaces{\textquoteright} of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as {\textquoteleft}line bundles{\textquoteright} over quantum lens spaces and generically define {\textquoteleft}torsion classes{\textquoteright}. We work out explicit examples of these classes.

}, doi = {10.4171/JNCG/216}, author = {Francesca Arici and Simon Brain and Giovanni Landi} } @article {BertoBothBalogh, title = {Hankel determinant approach to generalized Vorob{\textquoteright}ev-Yablonski polynomials and their roots}, journal = {Constr. Approx.}, volume = {44}, number = {3}, year = {2016}, pages = {417{\textendash}453}, issn = {0176-4276}, doi = {10.1007/s00365-016-9328-4}, url = {http://dx.doi.org/10.1007/s00365-016-9328-4}, author = {Ferenc Balogh and Marco Bertola and Thomas Bothner} } @article {2016, title = {Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes}, number = {AMOS Advanced Modelling and Simulation in Engineering Sciences}, year = {2016}, institution = {Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences}, abstract = {In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.}, url = {http://urania.sissa.it/xmlui/handle/1963/35199}, author = {Filippo Salmoiraghi and F. Ballarin and Luca Heltai and Gianluigi Rozza} } @article {2016, title = {Large KAM tori for perturbations of the dNLS equation}, number = {arXiv;1603.09252}, year = {2016}, abstract = {We prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2{\texttimes}2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues.}, url = {http://preprints.sissa.it/handle/1963/35284}, author = {Massimiliano Berti and Thomas Kappeler and Riccardo Montalto} } @article {20.500.11767_11950, title = {LinearOperator {\textendash} a generic, high-level expression syntax for linear algebra}, journal = {COMPUTERS \& MATHEMATICS WITH APPLICATIONS}, volume = {72}, year = {2016}, pages = {1{\textendash}24}, doi = {10.1016/j.camwa.2016.04.024}, author = {Matthias Maier and Mauro Bardelloni and Luca Heltai} } @article {Battaglia2016, title = {Moser{\textendash}Trudinger inequalities for singular Liouville systems}, journal = {Mathematische Zeitschrift}, volume = {282}, number = {3}, year = {2016}, month = {Apr}, pages = {1169{\textendash}1190}, abstract = {

In this paper we prove a Moser{\textendash}Trudinger inequality for the Euler{\textendash}Lagrange functional of general singular Liouville systems on a compact surface. We characterize the values of the parameters which yield coercivity for the functional, hence the existence of energy-minimizing solutions for the system, and we give necessary conditions for boundedness from below. We also provide a sharp inequality under assuming the coefficients of the system to be non-positive outside the diagonal. The proofs use a concentration-compactness alternative, Poho{\v z}aev-type identities and blow-up analysis.

}, issn = {1432-1823}, doi = {10.1007/s00209-015-1584-7}, url = {https://doi.org/10.1007/s00209-015-1584-7}, author = {Luca Battaglia} } @article {2016, title = {Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 449{\textendash}474.}, number = {Proceedings of the Royal Society of Edinburgh. Section A. Mathematics;volume 146; issue 3; pages 449-474;}, year = {2016}, note = {AMS Subject Classification: Primary 34B18; 34C25; Secondary 34B15; 47H11;}, publisher = {Cambridge University Press}, abstract = {

We study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u{\textquoteright}{\textquoteright}+cu{\textquoteright}+λa(t)g(u)=0, where g:[0,+$\infty$[{\textrightarrow}[0,+$\infty$[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin{\textquoteright}s coincidence degree theory and index computations.

}, doi = {10.1017/S0308210515000621}, url = {http://urania.sissa.it/xmlui/handle/1963/35262}, author = {Alberto Boscaggin and Guglielmo Feltrin and Fabio Zanolin} } @article {11943, title = {POD{\textendash}Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems}, journal = {International Journal Numerical Methods for Fluids}, year = {2016}, publisher = {Wiley}, abstract = {In this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD){\textendash}Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD{\textendash}Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances}, doi = {10.1002/fld.4252}, author = {F. Ballarin and Gianluigi Rozza} } @article {doi:10.1137/15M1007380, title = {Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions}, journal = {SIAM Journal on Mathematical Analysis}, volume = {48}, number = {1}, year = {2016}, pages = {1-33}, abstract = {

Given a bounded autonomous vector field $b \colon \mathbb{R}^d \to \mathbb{R}^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio{\textquoteright}s superposition principle [4].

}, doi = {10.1137/15M1007380}, url = {https://doi.org/10.1137/15M1007380}, author = {Stefano Bianchini and Paolo Bonicatto and N.A. Gusev} } @article {MR3592329, title = {Rogue waves in multiphase solutions of the focusing nonlinear Schr{\"o}dinger equation}, journal = {Proc. A.}, volume = {472}, number = {2194}, year = {2016}, pages = {20160340, 12}, issn = {1364-5021}, doi = {10.1098/rspa.2016.0340}, url = {http://dx.doi.org/10.1098/rspa.2016.0340}, author = {Marco Bertola and Gennady El and Alexander Tovbis} } @article {2016, title = {Second-order structured deformations}, year = {2016}, institution = {SISSA}, author = {Ana Cristina Barroso and Jose Matias and Marco Morandotti and David R. Owen} } @conference {mola2016ship, title = {Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model}, booktitle = {The 26th International Ocean and Polar Engineering Conference}, volume = {3}, year = {2016}, pages = {511{\textendash}518}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {BertoDiDub, title = {Simple Lie Algebras and Topological ODEs}, journal = {Int. Math. Res. Not.}, volume = {2016}, number = {rnw285}, year = {2016}, author = {Marco Bertola and Boris Dubrovin and Di Yang} } @article {BKT-sobolev, title = {On Sobolev instability of the interior problem of tomography}, journal = {Journal of Mathematical Analysis and Applications}, year = {2016}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @article {doi:10.1080/03605302.2015.1095766, title = {Spectral analysis and the Aharonov-Bohm effect on certain almost-Riemannian manifolds}, journal = {Communications in Partial Differential Equations}, volume = {41}, number = {1}, year = {2016}, pages = {32-50}, publisher = {Taylor \& Francis}, abstract = {

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl{\textquoteright}s law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalized Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

}, doi = {10.1080/03605302.2015.1095766}, url = {https://doi.org/10.1080/03605302.2015.1095766}, author = {Ugo Boscain and Dario Prandi and M. Seri} } @article {2016, title = {On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension}, year = {2016}, institution = {SISSA}, abstract = {

We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the characteristics. In particular the characteristic curves are segments outside a countably 1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f{\textquoteright}{\textquoteright}=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

}, url = {http://urania.sissa.it/xmlui/handle/1963/35209}, author = {Stefano Bianchini and Elio Marconi} } @article {Benvenuti2016, title = {Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {9}, year = {2016}, month = {Sep}, pages = {53}, abstract = {

We explore $\mathcal{N}=(1,0)$ superconformal six-dimensional theories arising from M5 branes probing a transverse $A_k$ singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $q\mathcal{W}$ algebrae.

}, issn = {1029-8479}, doi = {10.1007/JHEP09(2016)053}, url = {https://doi.org/10.1007/JHEP09(2016)053}, author = {Benvenuti, Sergio and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {agrachev2016volume, title = {Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics}, journal = {arXiv preprint arXiv:1602.08745}, year = {2016}, author = {Andrei A. Agrachev and Davide Barilari and Elisa Paoli} } @article {2015, title = {Anisotropic mean curvature on facets and relations with capillarity}, number = {Geometric Flows;1}, year = {2015}, publisher = {de Gruyter}, abstract = {

We discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

}, doi = {10.1515/geofl-2015-0005}, url = {http://urania.sissa.it/xmlui/handle/1963/34481}, author = {Stefano Amato and Lucia Tealdi and Giovanni Bellettini} } @article {MR3346719, title = {Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlev{\'e} equation}, journal = {Constr. Approx.}, volume = {41}, number = {3}, year = {2015}, pages = {529{\textendash}587}, issn = {0176-4276}, doi = {10.1007/s00365-015-9288-0}, url = {http://dx.doi.org/10.1007/s00365-015-9288-0}, author = {Marco Bertola and Alexander Tovbis} } @article {2015, title = {A bridging mechanism in the homogenisation of brittle composites with soft inclusions}, number = {SISSA;02/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.}, url = {http://urania.sissa.it/xmlui/handle/1963/7492}, author = {Marco Barchiesi and Giuliano Lazzaroni and Caterina Ida Zeppieri} } @article {2014, title = {Constrained BV functions on double coverings for Plateau{\textquoteright}s type problems}, journal = {Adv. Calc. Var.}, year = {2015}, abstract = {

We link Brakke{\textquoteright}s "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau{\textquoteright}s problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n - 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

}, author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini} } @article {modena2015convergence, title = {Convergence rate of the Glimm scheme}, journal = {Bulletin of the Institute of Mathematics of Academia Sinica (New Series)}, year = {2015}, author = {Stefano Modena and Stefano Bianchini} } @article {2015, title = {Deal2lkit: a Toolkit Library for High Performance Programming in deal.II}, year = {2015}, publisher = {SISSA}, abstract = {We present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit.}, url = {http://urania.sissa.it/xmlui/handle/1963/35006}, author = {Alberto Sartori and Nicola Giuliani and Mauro Bardelloni and Luca Heltai} } @article {2015, title = {The deal.II Library, Version 8.2}, journal = {Archive of Numerical Software, vol. 3, n. 100, (2015), pages : 1-8}, year = {2015}, abstract = {This paper provides an overview of the new features of the finite element library deal.II version 8.2}, doi = {10.11588/ans.2015.100.18031}, url = {http://urania.sissa.it/xmlui/handle/1963/34464}, author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and T. D. Young} } @article {MR3369874, title = {A degeneration of two-phase solutions of the focusing nonlinear Schr{\"o}dinger equation via Riemann-Hilbert problems}, journal = {J. Math. Phys.}, volume = {56}, number = {6}, year = {2015}, pages = {061507, 17}, issn = {0022-2488}, doi = {10.1063/1.4922362}, url = {http://dx.doi.org/10.1063/1.4922362}, author = {Marco Bertola and Giavedoni, Pietro} } @article {2015, title = {Dynamics of screw dislocations: a generalised minimising-movements scheme approach}, number = {SISSA;38/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalization of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric.}, url = {http://urania.sissa.it/xmlui/handle/1963/34495}, author = {Giovanni A. Bonaschi and Patrick Van Meurs and Marco Morandotti} } @article {BATTAGLIA201549, title = {Existence and multiplicity result for the singular Toda system}, journal = {Journal of Mathematical Analysis and Applications}, volume = {424}, number = {1}, year = {2015}, pages = {49 - 85}, abstract = {

We consider the Toda system on a compact surface (Σ,g)-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑j=1Jα1j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑j=1Jα2j(δpj-1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than -1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij{\textquoteright}s are allowed to be negative."

}, keywords = {Existence result, Liouville-type equations, Multiplicity result, PDEs on compact surfaces, Toda system}, issn = {0022-247X}, doi = {https://doi.org/10.1016/j.jmaa.2014.10.081}, url = {http://www.sciencedirect.com/science/article/pii/S0022247X14010191}, author = {Luca Battaglia} } @article {2015, title = {Explicit formulas for relaxed disarrangement densities arising from structured deformations}, number = {SISSA;37/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g-G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca{\textquoteright}s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)-, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)-, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni{\textquoteright}s results, and we establish additional explicit formulas for other measures of disarrangements.}, url = {http://urania.sissa.it/xmlui/handle/1963/34492}, author = {Ana Cristina Barroso and Jose Matias and Marco Morandotti and David R. Owen} } @article {2015, title = {Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization}, year = {2015}, abstract = {In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD{\textendash}Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach.}, url = {http://urania.sissa.it/xmlui/handle/1963/34623}, author = {F. Ballarin and Elena Faggiano and Sonia Ippolito and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza and Roberto Scrofani} } @article {BATTAGLIA2015937, title = {A general existence result for the Toda system on compact surfaces}, journal = {Advances in Mathematics}, volume = {285}, year = {2015}, pages = {937 - 979}, abstract = {

In this paper we consider the following Toda system of equations on a compact surface:-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-Δu1=-4π∑j=1mα1,j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-Δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern{\textendash}Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation-Δu=ρ1(heu∫ΣheudVg-1)-ρ2(he-u∫Σhe-udVg-1), which arises in fluid dynamics."

}, keywords = {Geometric PDEs, Min{\textendash}max schemes, Variational methods}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2015.07.036}, url = {http://www.sciencedirect.com/science/article/pii/S0001870815003072}, author = {Luca Battaglia and Aleks Jevnikar and Andrea Malchiodi and David Ruiz} } @article {2015, title = {Hilbert schemes of points of OP1(-n) as quiver varieties}, year = {2015}, publisher = {arXiv:1504.02987 [math.AG]}, abstract = {Relying on a representation of framed torsion-free sheaves on Hirzebruch surfaces in terms of monads, we construct ADHM data for the Hilbert scheme of points of the total space of the line bundle $\mathcal O(-n)$ on $\mathbb P^1$. This ADHM description is then used to realize these Hilbert schemes as quiver varieties.}, url = {http://urania.sissa.it/xmlui/handle/1963/34487}, author = {Ugo Bruzzo} } @article {MR3305428, title = {Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves}, journal = {Anal. Math. Phys.}, volume = {5}, number = {1}, year = {2015}, pages = {1{\textendash}22}, issn = {1664-2368}, doi = {10.1007/s13324-014-0088-7}, url = {http://dx.doi.org/10.1007/s13324-014-0088-7}, author = {Marco Bertola and Alexander Tovbis} } @article {BennerOhlbergerPateraRozzaSorensenUrban2015, title = {Model order reduction of parameterized systems ({MoRePaS}): Preface to the special issue of advances in computational mathematics}, journal = {Advances in Computational Mathematics}, volume = {41}, number = {5}, year = {2015}, pages = {955{\textendash}960}, doi = {10.1007/s10444-015-9443-y}, author = {Peter Benner and Mario Ohlberger and Anthony Patera and Gianluigi Rozza and Sorensen, D.C. and Karsten Urban} } @article {Bawane2015, title = {N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity}, journal = {Journal of High Energy Physics}, volume = {2015}, number = {7}, year = {2015}, month = {Jul}, pages = {54}, abstract = {

We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2015)054}, url = {https://doi.org/10.1007/JHEP07(2015)054}, author = {Aditya Bawane and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @article {2015, title = {A note on compactness properties of the singular Toda system}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. }, volume = {26}, number = {Rendiconti Lincei. Mathematics and Applications;vol. 26, Issue 3}, year = {2015}, pages = {299-307}, abstract = {

In this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

}, doi = {10.4171/RLM/708}, author = {Luca Battaglia and Gabriele Mancini} } @article {MR3342766, title = {The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy}, journal = {J. Phys. A}, volume = {48}, number = {19}, year = {2015}, pages = {195205, 20}, issn = {1751-8113}, doi = {10.1088/1751-8113/48/19/195205}, url = {http://dx.doi.org/10.1088/1751-8113/48/19/195205}, author = {Marco Bertola and Di Yang} } @article {bianchini2015quadratic, title = {Quadratic Interaction Functional for General Systems of Conservation Laws}, journal = {Communications in Mathematical Physics}, volume = {338}, year = {2015}, pages = {1075{\textendash}1152}, abstract = {

For the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

}, doi = {10.1007/s00220-015-2372-2}, author = {Stefano Bianchini and Stefano Modena} } @conference {StabileMatthiesBorri2015, title = {A Reduced Order Model for the Simulation of Mooring Cable Dynamics}, booktitle = {Computational Methods in Marine Engineering VI {\textendash} MARINE2015}, year = {2015}, pages = {387{\textendash}400}, publisher = {Salvatore, Francesco; Broglia, Riccardo; Muscari, Roberto}, organization = {Salvatore, Francesco; Broglia, Riccardo; Muscari, Roberto}, author = {Giovanni Stabile and Hermann G. Matthies and Claudio Borri} } @article {2015, title = {Results on the minimization of the Dirichlet functional among semicartesian parametrizations}, year = {2015}, note = {The article is compsed of 18 pages and is recorded in PDF format}, abstract = {

We start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau{\textquoteright}s problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34488}, author = {Lucia Tealdi and Giovanni Bellettini and Maurizio Paolini} } @article {2015, title = {Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity}, year = {2015}, note = {The preprint is compsed of 37 pages and is recorded in PDF format}, abstract = {

We address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34483}, author = {Lucia Tealdi and Giovanni Bellettini and Maurizio Paolini} } @article {2013, title = {Stable regular critical points of the Mumford-Shah functional are local minimizers}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {32}, number = {SISSA preprint;SISSA 33/2013/MATE}, year = {2015}, pages = {533-570}, publisher = {SISSA}, chapter = {533}, abstract = {

In this paper it is shown that any regular critical point of the Mumford{\textendash}Shah functional, with positive definite second variation, is an isolated local minimizer with respect to competitors which are sufficiently close in the $L^1$
-topology. A global\ minimality\ result in small tubular neighborhoods of the\ discontinuity\ set is also established.

}, keywords = {Mumford-Shah functional}, doi = {10.1016/j.anihpc.2014.01.006}, url = {https://www.sciencedirect.com/science/article/pii/S0294144914000171}, author = {Marco Bonacini and Massimiliano Morini} } @article {MR3280250, title = {Strong asymptotics of the orthogonal polynomials with respect to a measure supported on the plane}, journal = {Comm. Pure Appl. Math.}, volume = {68}, number = {1}, year = {2015}, pages = {112{\textendash}172}, issn = {0010-3640}, doi = {10.1002/cpa.21541}, url = {http://dx.doi.org/10.1002/cpa.21541}, author = {Ferenc Balogh and Marco Bertola and Lee, Seung-Yeop and Kenneth McLaughlin} } @article {2015, title = {Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations}, number = {International Journal for Numerical Methods in Engineering;Volume 102, issue 5; pp.1136-1161;}, year = {2015}, publisher = {Wiley}, abstract = {In this work, we present a stable proper orthogonal decomposition{\textendash}Galerkin approximation for parametrized steady incompressible Navier{\textendash}Stokes equations with low Reynolds number.}, doi = {10.1002/nme.4772}, url = {http://urania.sissa.it/xmlui/handle/1963/34701}, author = {F. Ballarin and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {Bertola-Bothner-MeijerG, title = {Universality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices}, journal = {Commun. Math. Phys.}, volume = {337}, number = {3}, year = {2015}, month = {08}, pages = {1077{\textendash}1141}, doi = {10.1007/s00220-015-2327-7}, url = {http://link.springer.com/article/10.1007/s00220-015-2327-7}, author = {Marco Bertola and Thomas Bothner} } @mastersthesis {2015, title = {Variational aspects of singular Liouville systems}, year = {2015}, school = {SISSA}, abstract = {I studied singular Liouville systems on compact surfaces from a variational point of view. I gave sufficient and necessary conditions for the existence of globally minimizing solutions, then I found min-max solutions for some particular systems. Finally, I also gave some non-existence results.}, keywords = {Variational methods, Liouville systems, Moser-Trudinger inequalities, min-max methods}, author = {Luca Battaglia} } @article {2014, title = {An Abstract Nash{\textendash}Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds}, number = {Communications in mathematical physics;volume 334; issue 3; pages 1413-1454;}, year = {2014}, publisher = {Springer}, abstract = {We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups.}, doi = {10.1007/s00220-014-2128-4}, url = {http://urania.sissa.it/xmlui/handle/1963/34651}, author = {Massimiliano Berti and Livia Corsi and Michela Procesi} } @article {2014, title = {Approximate Hermitian{\textendash}Yang{\textendash}Mills structures on semistable principal Higgs bundles}, number = {Annals of global analysis and geometry;volume 47; issue 1; pp 1-11}, year = {2014}, publisher = {Springer}, abstract = {We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.}, doi = {10.1007/s10455-014-9433-1}, url = {http://urania.sissa.it/xmlui/handle/1963/34645}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2014, title = {Approximate Hitchin-Kobayashi correspondence for Higgs G-bundles}, number = {International Journal of Geometric Methods in Modern Physics;volume 11; issue 7; article number 1460015;}, year = {2014}, publisher = {World Scientific Publishing}, abstract = {We announce a result about the extension of the Hitchin-Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact K{\"a}hler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.}, doi = {10.1142/S0219887814600159}, url = {http://urania.sissa.it/xmlui/handle/1963/35095}, author = {Ugo Bruzzo and Beatriz Gra{\~n}a Otero} } @article {MR3162486, title = {Cauchy-Laguerre two-matrix model and the Meijer-G random point field}, journal = {Comm. Math. Phys.}, volume = {326}, number = {1}, year = {2014}, pages = {111{\textendash}144}, issn = {0010-3616}, doi = {10.1007/s00220-013-1833-8}, url = {http://dx.doi.org/10.1007/s00220-013-1833-8}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {2014, title = {Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics}, journal = {Annals of Nuclear Energy}, volume = {71}, number = {Annals of Nuclear Energy;volume 71; pages 217-229;}, year = {2014}, month = {09/2014}, pages = {229}, publisher = {Elsevier}, chapter = {217}, abstract = {

In this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

}, doi = {10.1016/j.anucene.2014.03.043}, url = {http://urania.sissa.it/xmlui/handle/1963/35039}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Davide Chiesa and Lelio Luzzi and Roberto R. Ponciroli and Ezio Previtali and Marco E. Ricotti and Gianluigi Rozza and Monica Sisti} } @conference {MarinoLugniStabileBorriManuel2014, title = {Coupled dynamic simulations of offshore wind turbines: influence of wave modelling on the fatigue load assesment}, booktitle = {XIII Conference of the Italian Association for Wind Engineering (In-Vento 2014)}, year = {2014}, author = {Marino, Enzo and Lugni, Claudio and Giovanni Stabile and Claudio Borri and Manuel, Lance} } @conference {MarinoLugniStabileBorri2014, title = {Coupled dynamic simulations of offshore wind turbines using linear, weakly and fully nonlinear wave models: the limitations of the second-order wave theory}, booktitle = {9th International Conference on Structural Dynamics (EURODYN 2014)}, year = {2014}, author = {Marino, Enzo and Lugni, Claudio and Giovanni Stabile and Claudio Borri} } @article {BertolaCafasso5, title = {Darboux Transformations and Random Point Processes}, journal = {IMRN}, volume = {rnu122}, year = {2014}, pages = {56}, author = {Marco Bertola and Mattia Cafasso} } @mastersthesis {2014, title = {The decomposition of optimal transportation problems with convex cost}, year = {2014}, school = {SISSA}, keywords = {Optimal Transportation}, url = {http://urania.sissa.it/xmlui/handle/1963/7475}, author = {Mauro Bardelloni} } @article {2014, title = {The decomposition of optimal transportation problems with convex cost}, number = {SISSA;45/2014/MATE}, year = {2014}, institution = {SISSA}, url = {http://hdl.handle.net/1963/7433}, author = {Stefano Bianchini and Mauro Bardelloni} } @article {2014, title = {Donagi{\textendash}Markman cubic for the generalised Hitchin system}, year = {2014}, abstract = {Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi{\textendash}Pantev formula holds on maximal rank symplectic leaves of the G-generalised Hitchin system.}, keywords = {Generalized Hitchin system, Donagi-Markman cubic, algebraically completely integrable systems, moduli space of Higgs G-bundles}, url = {http://hdl.handle.net/1963/7253}, author = {Ugo Bruzzo and Peter Dalakov} } @article {2014, title = {Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures}, number = {Rendiconti dell{\textquoteright}Istituto di Matematica dell{\textquoteright}Universita di Trieste;Volume 46; issue 1; pp. 43-70;}, year = {2014}, note = {This paper resumes the main part of the Bachelor thesis of the second author, discussed in 2013 at the University of Trieste.}, publisher = {EUT Edizioni Universita di Trieste}, abstract = {After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below.}, url = {http://urania.sissa.it/xmlui/handle/1963/34693}, author = {Stefano Bianchini and Alexander Dabrowski} } @article {2014, title = {Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians}, number = {Journal of Mathematical Physics;volume 55; issue 8; article number 1.4890818;}, year = {2014}, publisher = {American Institute of Physics Inc.}, abstract = {We study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Pl{\"u}cker coordinates appearing as coefficients in the Schur function expansion of the τ-function.}, doi = {10.1063/1.4890818}, url = {http://urania.sissa.it/xmlui/handle/1963/34952}, author = {Ferenc Balogh and Tiago Fonseca and John P. Harnad} } @article {2014, title = {Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension}, number = {Communications in Partial Differential Equations;Volume 39; issue 2; pp. 244-273;}, year = {2014}, publisher = {Taylor \& Francis}, abstract = {

The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

}, doi = {10.1080/03605302.2013.775153}, url = {http://urania.sissa.it/xmlui/handle/1963/34694}, author = {Stefano Bianchini and Lei Yu} } @article {Baldi20141, title = {KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation}, journal = {Mathematische Annalen}, year = {2014}, note = {cited By (since 1996)0; Article in Press}, pages = {1-66}, abstract = {We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients. {\textcopyright} 2014 Springer-Verlag Berlin Heidelberg.}, issn = {00255831}, doi = {10.1007/s00208-013-1001-7}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @article {2014, title = {KAM for quasi-linear KdV}, journal = {C. R. Math. Acad. Sci. Paris}, volume = {352}, number = {Comptes Rendus Mathematique;volume 352; issue 7-8; pages 603-607;}, year = {2014}, pages = {603-607}, publisher = {Elsevier}, abstract = {

We prove the existence and stability of Cantor families of quasi-periodic, small-amplitude solutions of quasi-linear autonomous Hamiltonian perturbations of KdV.

}, doi = {10.1016/j.crma.2014.04.012}, url = {http://urania.sissa.it/xmlui/handle/1963/35067}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @article {2014, title = {KAM for Reversible Derivative Wave Equations}, journal = {Arch. Ration. Mech. Anal.}, volume = {212}, number = {Archive for rational mechanics and analysis;volume 212; issue 3; pages 905-955;}, year = {2014}, pages = {905-955}, publisher = {Springer}, abstract = {

We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.

}, doi = {10.1007/s00205-014-0726-0}, url = {http://urania.sissa.it/xmlui/handle/1963/34646}, author = {Massimiliano Berti and Luca Biasco and Michela Procesi} } @article {2013, title = {Local and global minimality results for a nonlocal isoperimetric problem on R^N}, journal = { SIAM Journal on Mathematical Analysis}, volume = {46}, number = {Siam journal on mathematical analysis}, year = {2014}, pages = {2310-2349}, publisher = {SIAM Publications}, abstract = {

We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

}, keywords = {Nonlocal isoperimetric problem}, doi = {10.1137/130929898}, url = {http://hdl.handle.net/1963/6984}, author = {Marco Bonacini and Riccardo Cristoferi} } @article {2014, title = {On the Lp-differentiability of certain classes of functions}, number = {Revista Matematica Iberoamericana;Volume 30; issue 1; pp. 349-367;}, year = {2014}, publisher = {European Mathematical Society}, abstract = {We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.}, doi = {10.4171/rmi/782}, url = {http://urania.sissa.it/xmlui/handle/1963/34695}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {2014, title = {Minimal Liouville gravity correlation numbers from Douglas string equation}, number = {Journal of high energy physics;volume 2014; issue 1; article number 156;}, year = {2014}, publisher = {Springer}, abstract = {We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of \cite{Moore:1991ir}, \cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to $(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that there exist such coordinates $\tau_{m,n}$ on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates $\tau_{m,n}$ are related in a non-linear fashion to the natural coupling constants $\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the physical operators $O_{m,n}$. We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj}, \cite{Belavin:2006ex}.}, doi = {10.1007/JHEP01(2014)156}, url = {http://urania.sissa.it/xmlui/handle/1963/34588}, author = {Alexander Belavin and Boris Dubrovin and Baur Mukhametzhanov} } @article {battaglia2013moser, title = {A Moser-Trudinger inequality for the singular Toda system}, journal = {Bull. Inst. Math. Acad. Sin.}, volume = {9}, number = {1}, year = {2014}, pages = {1{\textendash}23}, author = {Luca Battaglia and Andrea Malchiodi} } @article {2014, title = {N = 2 Quiver Gauge Theories on A-type ALE Spaces}, number = {Letters in mathematical physics;volume 105; issue 3; pages 401-445;}, year = {2014}, publisher = {Springer}, abstract = {We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg{\textendash}Witten geometry.}, doi = {10.1007/s11005-014-0734-x}, url = {http://urania.sissa.it/xmlui/handle/1963/34719}, author = {Ugo Bruzzo and Francesco Sala and Richard J. Szabo} } @conference {mola2014ship, title = {Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures}, booktitle = {The 24th International Ocean and Polar Engineering Conference}, volume = {4}, year = {2014}, pages = {815{\textendash}822}, publisher = {International Society of Offshore and Polar Engineers}, organization = {International Society of Offshore and Polar Engineers}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone and Massimiliano Berti} } @article {2014, title = {On a quadratic functional for scalar conservation laws}, journal = {Journal of Hyperbolic Differential Equations}, volume = {11}, number = {Journal of Hyperbolic Differential Equations;Volume 11; issue 2; pp. 355-435;}, year = {2014}, pages = {355-435}, publisher = {World Scientific Publishing}, abstract = {

We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme.

}, doi = {10.1142/S0219891614500118}, url = {http://arxiv.org/abs/1311.2929}, author = {Stefano Bianchini and Stefano Modena} } @article {bianchini2013quadratic, title = {Quadratic interaction functional for systems of conservation laws: a case study}, journal = {Bulletin of the Institute of Mathematics of Academia Sinica (New Series)}, volume = {9}, year = {2014}, pages = {487-546}, url = {https://w3.math.sinica.edu.tw/bulletin_ns/20143/2014308.pdf}, author = {Stefano Bianchini and Stefano Modena} } @article {2014, title = {Quantum gauge symmetries in noncommutative geometry}, number = {Journal of Noncommutative Geometry;volume 8; issue 2; pages 433-471;}, year = {2014}, publisher = {European Mathematical Society Publishing House}, abstract = {We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group).}, doi = {10.4171/JNCG/161}, url = {http://urania.sissa.it/xmlui/handle/1963/34897}, author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Biswarup Krishna Das and Ludwik Dabrowski} } @proceedings {2014, title = {A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics}, number = {International Conference on Nuclear Engineering, Proceedings, ICONE;volume 5;}, year = {2014}, note = {2014 22nd International Conference on Nuclear Engineering, ICONE 2014; Prague; Czech Republic; 7 July 2014 through 11 July 2014; Code 109131;}, month = {07/2014}, pages = {V005T17A048-V005T17A048}, publisher = {American Society of Mechanical Engineers (ASME)}, edition = {American Society Mechanical Engineering}, address = {Prague, Czech Republic}, abstract = {

In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

}, isbn = {978-079184595-0}, doi = {10.1115/ICONE22-30707}, url = {http://urania.sissa.it/xmlui/handle/1963/35123}, author = {Alberto Sartori and Davide Baroli and Antonio Cammi and Lelio Luzzi and Gianluigi Rozza} } @inbook {2013, title = {Reduction on characteristics for continuous of a scalar balance law}, booktitle = {AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406}, number = {AIMS Series on Applied Mathematics}, year = {2014}, publisher = {SISSA}, organization = {SISSA}, keywords = {Method of characteristics}, url = {http://hdl.handle.net/1963/6562}, author = {Giovanni Alberti and Stefano Bianchini and Laura Caravenna} } @article {2014, title = {SBV Regularity of Systems of Conservation Laws and Hamilton{\textendash}Jacobi Equations}, number = {Journal of Mathematical Sciences;Volume 201; issue 6; pp. 733-745;}, year = {2014}, publisher = {Springer}, abstract = {We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper.}, doi = {10.1007/s10958-014-2022-9}, url = {http://urania.sissa.it/xmlui/handle/1963/34691}, author = {Stefano Bianchini} } @article {2014, title = {Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows}, number = {Journal of scientific computing;volume 60; issue 3; pages 537-563;}, year = {2014}, publisher = {Springer}, abstract = {Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.}, doi = {10.1007/s10915-013-9807-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34698}, author = {F. Ballarin and Andrea Manzoni and Gianluigi Rozza and Sandro Salsa} } @article {berto-Tovbis-Katsevich-CPAM, title = {Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach}, journal = {Comm. Pure Appl. Math.}, year = {2014}, author = {Marco Bertola and Alexander Katsevich and Alexander Tovbis} } @article {2014, title = {Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics}, number = {Journal of high energy physics;volume 2014; issue 7; article number 141;}, year = {2014}, publisher = {Springer}, abstract = {We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.}, doi = {10.1007/JHEP07(2014)141}, url = {http://urania.sissa.it/xmlui/handle/1963/34546}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {2013, title = {Stability of equilibrium configurations for elastic films in two and three dimensions}, journal = {Advances in Calculus of Variations}, volume = {8}, number = {SISSA preprint;SISSA 38/2013/MATE}, year = {2014}, month = {01/2014}, pages = {117-153}, publisher = {SISSA}, chapter = {117}, abstract = {

We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional case and for a general class of nonlinear elastic energies. Applications to the study of the local minimality of flat morphologies are also shown.

}, keywords = {Epitaxially strained elastic films}, issn = {Online: 1864-8266; Print: 1864-8258}, doi = { https://doi.org/10.1515/acv-2013-0018}, url = {https://www.degruyter.com/view/j/acv.2015.8.issue-2/acv-2013-0018/acv-2013-0018.xml}, author = {Marco Bonacini} } @article {2014, title = {Steady nearly incompressible vector elds in 2D: chain rule and renormalization}, year = {2014}, institution = {SISSA}, author = {Stefano Bianchini and N.A. Gusev} } @article {2014, title = {The stringy instanton partition function}, number = {Journal of high energy physics;volume 2014; issue 1; article number 038;}, year = {2014}, publisher = {Springer}, abstract = {We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit C^2/Z_2 the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants of P^1 x C^2.}, doi = {10.1007/JHEP01(2014)038}, url = {http://urania.sissa.it/xmlui/handle/1963/34589}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {2014, title = {Structure of entropy solutions to general scalar conservation laws in one space dimension}, journal = {Journal of Mathematical Analysis and Applications}, volume = {428}, number = {SISSA;11/2014/MATE}, year = {2014}, month = {08/2015}, pages = {356-386}, publisher = {SISSA}, chapter = {356}, doi = {https://doi.org/10.1016/j.jmaa.2015.03.006}, url = {https://www.sciencedirect.com/science/article/pii/S0022247X15002218}, author = {Stefano Bianchini and Lei Yu} } @article {2014, title = {A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday}, number = {Journal of the European Mathematical Society;Volume 16; issue 2; pp. 201-234;}, year = {2014}, publisher = {European Mathematical Society; Springer Verlag}, abstract = {We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.}, doi = {10.4171/JEMS/431}, url = {http://urania.sissa.it/xmlui/handle/1963/34692}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {2014, title = {Vortex Partition Functions, Wall Crossing and Equivariant Gromov{\textendash}Witten Invariants}, number = {Communications in mathematical physics;volume 333; issue 2; pages 717-760;}, year = {2014}, publisher = {Springer}, abstract = {In this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov{\textendash}Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov{\textendash}Witten theory follow just by deforming the integration contour. In particular, we apply our formalism to compute Gromov{\textendash}Witten invariants of the C3/Zn orbifold, of the Uhlembeck (partial) compactification of the moduli space of instantons on C2, and of An and Dn singularities both in the orbifold and resolved phases. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algebrae.}, doi = {10.1007/s00220-014-2193-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34652}, author = {Giulio Bonelli and Antonio Sciarappa and Alessandro Tanzini and Petr Vasko} } @article {2014, title = {Weighted quantile correlation test for the logistic family}, number = {Acta Scientiarum Mathematicarum;volume 80; issue 1-2; pages 307-326;}, year = {2014}, publisher = {University of Szeged}, abstract = {We summarize the results of investigating the asymptotic behavior of the weighted quantile correlation tests for the location-scale family associated to the logistic distribution. Explicit representations of the limiting distribution are given in terms of integrals of weighted Brownian bridges or alternatively as infinite series of independent Gaussian random variables. The power of this test and the test for the location logistic family against some alternatives are demonstrated by numerical simulations.}, doi = {10.14232/actasm-013-809-8}, url = {http://urania.sissa.it/xmlui/handle/1963/35025}, author = {Ferenc Balogh and {\'E}va Krauczi} } @article {Berto-Bothner-YV, title = {Zeros of Large Degree Vorob{\textquoteright}ev-Yablonski Polynomials via a Hankel Determinant Identity}, journal = {International Mathematics Research Notices}, volume = {rnu239}, year = {2014}, author = {Marco Bertola and Thomas Bothner} } @article {MR2997471, title = {Basic principles of virtual element methods}, journal = {Math. Models Methods Appl. Sci.}, volume = {23}, number = {1}, year = {2013}, pages = {199{\textendash}214}, issn = {0218-2025}, doi = {10.1142/S0218202512500492}, url = {https://doi.org/10.1142/S0218202512500492}, author = {Beir{\~a}o da Veiga, L. and Brezzi, F. and Andrea Cangiani and Manzini, G. and Marini, L. D. and Russo, A.} } @inbook {MarinoStabileBorriLugni2013, title = {A comparative study about the effects of linear, weakly and fully nonlinear wave models on the dynamic response of offshore wind turbines}, booktitle = {Research and Applications in Structural Engineering, Mechanics and Computation}, year = {2013}, pages = {389{\textendash}390}, publisher = {CRC Press}, organization = {CRC Press}, author = {Marino, Enzo and Giovanni Stabile and Claudio Borri and Lugni, Claudio} } @article {2013, title = {The curvature: a variational approach}, number = {arXiv:1306.5318;}, year = {2013}, note = {88 pages, 10 figures, (v2) minor typos corrected, (v3) added sections on Finsler manifolds, slow growth distributions, Heisenberg group}, institution = {SISSA}, abstract = {The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.}, keywords = {Crurvature, subriemannian metric, optimal control problem}, url = {http://hdl.handle.net/1963/7226}, author = {Andrei A. Agrachev and Davide Barilari and Luca Rizzi} } @article {2013, title = {The deal.II Library, Version 8.1}, number = {arXiv:1312.2266;}, year = {2013}, note = {5 pages}, institution = {SISSA}, abstract = {This paper provides an overview of the new features of the finite element library deal.II version 8.0.}, url = {http://hdl.handle.net/1963/7236}, author = {Wolfgang Bangerth and Timo Heister and Luca Heltai and G. Kanschat and Martin Kronbichler and Matthias Maier and Bruno Turcksin and T. D. Young} } @article {2013, title = {Defect annihilation and proliferation in active nematics}, number = {arXiv:1303.4720;}, year = {2013}, note = {5 pages, 4 figures}, institution = {SISSA}, abstract = {Liquid crystals inevitably possess topological defect excitations generated\r\nthrough boundary conditions, applied fields or in quenches to the ordered\r\nphase. In equilibrium pairs of defects coarsen and annihilate as the uniform\r\nground state is approached. Here we show that defects in active liquid crystals\r\nexhibit profoundly different behavior, depending on the degree of activity and\r\nits contractile or extensile character. While contractile systems enhance the\r\nannihilation dynamics of passive systems, extensile systems act to drive\r\ndefects apart so that they swarm around in the manner of topologically\r\nwell-characterized self-propelled particles. We develop a simple analytical\r\nmodel for the defect dynamics which reproduces the key features of both the\r\nnumerical solutions and recent experiments on microtuble-kinesin assemblies.}, url = {http://hdl.handle.net/1963/6566}, author = {Luca Giomi and Mark J. Bowick and Xu Ma and M. Cristina Marchetti} } @article {2013, title = {Epitaxially strained elastic films: the case of anisotropic surface energies}, journal = {ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189}, number = {SISSA;31/2011/M}, year = {2013}, publisher = {EDP Sciences}, abstract = {

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

}, doi = {10.1051/cocv/2012003}, url = {http://hdl.handle.net/1963/4268}, author = {Marco Bonacini} } @article {2013, title = {Equilibrium measures for a class of potentials with discrete rotational symmetries}, number = {arXiv:1312.1483;}, year = {2013}, note = {23 pages, 3 figures}, institution = {SISSA}, abstract = {In this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|t_{cr}$.}, url = {http://hdl.handle.net/1963/7230}, author = {Ferenc Balogh and Dario Merzi} } @article {Berti2013199, title = {Existence and stability of quasi-periodic solutions for derivative wave equations}, journal = {Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni}, volume = {24}, number = {2}, year = {2013}, note = {cited By (since 1996)0}, pages = {199-214}, abstract = {In this note we present the new KAM result in [3] which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. In turn, this result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems*.}, keywords = {Constant coefficients, Dynamical systems, Existence and stability, Infinite dimensional, KAM for PDEs, Linearized equations, Lyapunov exponent, Lyapunov methods, Quasi-periodic solution, Small divisors, Wave equations}, issn = {11206330}, doi = {10.4171/RLM/652}, author = {Massimiliano Berti and Luca Biasco and Michela Procesi} } @article {2013, title = {Framed sheaves on projective stacks}, year = {2013}, abstract = {Given a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider {\em framed sheaves} on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent sheaf on $\mathscr X$ and $\phi_{\mathcal E}$ is a morphism from $\mathcal E$ to a fixed coherent sheaf $\mathcal F$. After introducing a suitable notion of (semi)stability, we construct a projective scheme, which is a moduli space for semistable framed sheaves with fixed Hilbert polynomial, and an open subset of it, which is a fine moduli space for stable framed sheaves. If $\mathscr X$ is a projective irreducible orbifold of dimension two and $\mathcal F$ a locally free sheaf on a smooth divisor $\mathscr D\subset \mathscr X$ satisfying certain conditions, we consider {\em $(\mathscr{D}, \mathcal{F})$-framed sheaves}, i.e., framed sheaves $(\mathcal E,\phi_{\mathcal E})$ with $\mathcal E$ a torsion-free sheaf which is locally free in a neighborhood of $\mathscr D$, and ${\phi_{\mathcal{E}}}_{\vert \mathscr{D}}$ an isomorphism. These pairs are $\mu$-stable for a suitable choice of a parameter entering the (semi)stability condition, and of the polarization of $\mathscr X$. This implies the existence of a fine moduli space parameterizing isomorphism classes of $(\mathscr{D}, \mathcal{F})$-framed sheaves on $\mathscr{X}$ with fixed Hilbert polynomial, which is a quasi-projective scheme. In an appendix we develop the example of stacky Hirzebruch surfaces. This is the first paper of a project aimed to provide an algebro-geometric approach to the study of gauge theories on a wide class of 4-dimensional Riemannian manifolds by means of framed sheaves on {\textquoteleft}{\textquoteleft}stacky" compactifications of them. In particular, in a subsequent paper \cite{art:bruzzopedrinisalaszabo2013} these results are used to study gauge theories on ALE spaces of type $A_k$.}, url = {http://urania.sissa.it/xmlui/handle/1963/7438}, author = {Ugo Bruzzo and Francesco Sala} } @article {BertolaCafasso4, title = {The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation}, journal = {Random Matrices: Theory and Applications}, volume = {02}, number = {02}, year = {2013}, pages = {1350003}, doi = {10.1142/S2010326313500032}, url = {http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032}, author = {Marco Bertola and Mattia Cafasso} } @article {2012, title = {An improved geometric inequality via vanishing moments, with applications to singular Liouville equations}, journal = {Communications in Mathematical Physics 322, nr.2 (2013): 415-452}, number = {arXiv:1206.0225;}, year = {2013}, publisher = {SISSA}, doi = {10.1007/s00220-013-1731-0}, url = {http://hdl.handle.net/1963/6561}, author = {Mauro Bardelloni and Andrea Malchiodi} } @article {BertolaKatsevichTovbis1, title = {Inversion formulae for the $\romancosh$-weighted Hilbert transform}, journal = {Proc. Amer. Math. Soc.}, volume = {141}, number = {8}, year = {2013}, pages = {2703{\textendash}2718}, issn = {0002-9939}, doi = {10.1090/S0002-9939-2013-11642-4}, url = {http://dx.doi.org/10.1090/S0002-9939-2013-11642-4}, author = {Marco Bertola and Katsevich, A. and Alexander Tovbis} } @article {Berti2013301, title = {KAM theory for the Hamiltonian derivative wave equation}, journal = {Annales Scientifiques de l{\textquoteright}Ecole Normale Superieure}, volume = {46}, number = {2}, year = {2013}, note = {cited By (since 1996)4}, pages = {301-373}, abstract = {

We prove an infinite dimensional KAM theorem which implies the existence of Can- tor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. {\textcopyright} 2013 Soci{\'e}t{\'e} Math{\'e}matique de France.

}, issn = {00129593}, author = {Massimiliano Berti and Luca Biasco and Michela Procesi} } @article {Boscain2013, title = {Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces}, journal = {Journal of Geometric Analysis}, volume = {23}, number = {1}, year = {2013}, month = {Jan}, pages = {438{\textendash}455}, abstract = {

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot{\textendash}Carath{\'e}odory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

}, issn = {1559-002X}, doi = {10.1007/s12220-011-9262-4}, url = {https://doi.org/10.1007/s12220-011-9262-4}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi and Mario Sigalotti} } @mastersthesis {2013, title = {Minimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems}, year = {2013}, school = {SISSA}, keywords = {free-discontinuity problems}, author = {Marco Bonacini} } @article {2013, title = {Monads for framed sheaves on Hirzebruch surfaces}, number = {SISSA preprint;05/2014/mate}, year = {2013}, abstract = {We define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.}, keywords = {Monads, framed sheaves, Hirzebruch surfaces}, author = {Claudio Bartocci and Ugo Bruzzo and Claudio L.S. Rava} } @article {Bianchini2013, title = {The Monge Problem for Distance Cost in Geodesic Spaces}, journal = {Communications in Mathematical Physics}, volume = {318}, number = {3}, year = {2013}, month = {Mar}, pages = {615{\textendash}673}, abstract = {

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dLis a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting dL-cyclical monotonicity is not sufficient for optimality.

}, issn = {1432-0916}, doi = {10.1007/s00220-013-1663-8}, url = {https://doi.org/10.1007/s00220-013-1663-8}, author = {Stefano Bianchini and Fabio Cavalletti} } @article {2013, title = {N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae}, number = {arXiv:1208.0790;}, year = {2013}, note = {33 pages, 1 figure; v2: discussions on U(1) gauge theory and\r\n Frenkel-Kac construction have been added in section 5.1, and typos corrected;\r\n v3: published version; v4: typos corrected}, institution = {SISSA}, abstract = {We compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories.}, url = {http://hdl.handle.net/1963/6577}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagi} } @article {modena2013, title = {A New Quadratic Potential for Scalar Conservation Laws}, journal = {Oberwolfach Reports}, volume = {29}, year = {2013}, author = {Stefano Bianchini and Stefano Modena} } @article {11011, title = {Nonabelian Lie algebroid extensions}, number = {SISSA preprint;06/2014/mate}, year = {2013}, abstract = {

We classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

}, keywords = {Lie algebroids, nonabelian extensions, spectral sequences}, author = {Ugo Bruzzo and Igor Mencattini and Pietro Tortella and Vladimir Rubtsov} } @article {2013, title = {The nonlinear multidomain model: a new formal asymptotic analysis.}, journal = {Geometry Partial Differential Equations {\textendash} proceedings, CRM Series (15), 2013.}, number = {SISSA preprint;SISSA 54/2013/MATE}, year = {2013}, abstract = {

We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

}, keywords = {bidomain model, anisotropic mean curvature, star-shaped combination}, isbn = {8876424724}, author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini} } @article {2013, title = {A note on KAM theory for quasi-linear and fully nonlinear forced KdV}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437{\textendash}450}, year = {2013}, publisher = {European Mathematical Society}, abstract = {We present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.}, keywords = {KAM for PDEs}, doi = {10.4171/RLM/660}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @article {boscaggin2013pairs, title = {Pairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions}, journal = {Advanced Nonlinear Studies}, volume = {13}, number = {1}, year = {2013}, pages = {13{\textendash}53}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2013-0103}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {Boscaggin2013, title = {Planar Hamiltonian systems at resonance: the Ahmad{\textendash}Lazer{\textendash}Paul condition}, journal = {Nonlinear Differential Equations and Applications NoDEA}, volume = {20}, number = {3}, year = {2013}, month = {Jun}, pages = {825{\textendash}843}, abstract = {

We consider the planar Hamiltonian system\$\$Ju^{\backslashprime} = \backslashnabla F(u) + \backslashnabla_u R(t,u), \backslashquad t \backslashin [0,T], \backslash,u \backslashin \backslashmathbb{R}^2,\$\$with F(u) positive and positively 2-homogeneous and \$\${\backslashnabla_{u}R(t, u)}\$\$sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman{\textendash}Lazer condition is analyzed, as well.

}, issn = {1420-9004}, doi = {10.1007/s00030-012-0181-2}, url = {https://doi.org/10.1007/s00030-012-0181-2}, author = {Alberto Boscaggin and Maurizio Garrione} } @article {Berti2013229, title = {Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential}, journal = {Journal of the European Mathematical Society}, volume = {15}, number = {1}, year = {2013}, note = {cited By (since 1996)5}, pages = {229-286}, abstract = {We prove the existence of quasi-periodic solutions for Schr{\"o}dinger equations with a multiplicative potential on Td , d >= 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C$\infty$ then the solutions are C$\infty$. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. {\textcopyright} European Mathematical Society 2013.}, issn = {14359855}, doi = {10.4171/JEMS/361}, author = {Massimiliano Berti and Philippe Bolle} } @article {11613, title = {Remarks on the Moser{\textendash}Trudinger inequality}, journal = {Advances in Nonlinear Analysis}, volume = {2}, number = {Advances in nonlinear analysis;volume 2; issue 4}, year = {2013}, note = {The article is composed of 32 pages inad recorded in PDF format}, pages = {389-425}, publisher = {Advances in Nonlinear Analysis}, abstract = {

We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincar{\'e}{\textquoteright}s inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

}, doi = {10.1515/anona-2013-0014}, url = {http://edoc.unibas.ch/43974/}, author = {Gabriele Mancini and Luca Battaglia} } @article {1305.5271, title = {Self-adjoint extensions and stochastic completeness of the Laplace-Beltrami operator on conic and anticonic surfaces}, year = {2013}, doi = {10.1016/j.jde.2015.10.011}, author = {Ugo Boscain and Dario Prandi} } @article {MR3117621, title = {Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes}, journal = {J. Stat. Phys.}, volume = {153}, number = {4}, year = {2013}, pages = {654{\textendash}697}, issn = {0022-4715}, doi = {10.1007/s10955-013-0845-2}, url = {http://dx.doi.org/10.1007/s10955-013-0845-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {doi:10.1080/00036811.2011.628173, title = {Stable determination of a body immersed in a fluid: the nonlinear stationary case}, journal = {Applicable Analysis}, volume = {92}, number = {3}, year = {2013}, pages = {460-481}, publisher = {Taylor \& Francis}, abstract = {

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier{\textendash}Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of stability of log{\textendash}log type.

}, doi = {10.1080/00036811.2011.628173}, url = {https://doi.org/10.1080/00036811.2011.628173}, author = {Andrea Ballerini} } @article {MR3088819, title = {Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model}, journal = {J. Math. Phys.}, volume = {54}, number = {4}, year = {2013}, pages = {043517, 25}, issn = {0022-2488}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {1078-0947_2013_1_89, title = {Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {33}, number = {1078-0947_2013_1_8}, year = {2013}, pages = {89}, abstract = {

We study the problem of existence and multiplicity of subharmonic solutions for a second order nonlinear ODE in presence of lower and upper solutions. We show how such additional information can be used to obtain more precise multiplicity results. Applications are given to pendulum type equations and to Ambrosetti-Prodi results for parameter dependent equations.

}, keywords = {lower and upper solutions, parameter dependent equations, Periodic solutions, Poincar{\'e}-Birkhoff twist theorem, subharmonic solutions}, issn = {1078-0947}, doi = {10.3934/dcds.2013.33.89}, url = {http://aimsciences.org//article/id/3638a93e-4f3e-4146-a927-3e8a64e6863f}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {2013, title = {On Sudakov{\textquoteright}s type decomposition of transference plans with norm costs}, number = {SISSA;51/2013/MATE}, year = {2013}, institution = {SISSA}, url = {http://hdl.handle.net/1963/7206}, author = {Stefano Bianchini and Sara Daneri} } @article {2013, title = {Symplectic instanton bundles on P3 and {\textquoteright}t Hooft instantons}, year = {2013}, note = {This preprint has been published with the title "Moduli of symplectic instanton vector bundles of higher rank on projective space P-3 " in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, Volume: 10, issue 4, Augst 2012, pages 1232-1245.}, institution = {arXiv:1312.5554 [math.AG]}, abstract = {We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of {\textquoteright}t Hooft instantons.}, url = {http://urania.sissa.it/xmlui/handle/1963/34486}, author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov} } @article {BertolaTovbisNLS2, title = {Universality for the focusing nonlinear Schr{\"o}dinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronqu{\'e}e solution to Painlev{\'e} I}, journal = {Comm. Pure Appl. Math.}, volume = {66}, number = {5}, year = {2013}, pages = {678{\textendash}752}, issn = {0010-3640}, doi = {10.1002/cpa.21445}, url = {http://dx.doi.org/10.1002/cpa.21445}, author = {Marco Bertola and Alexander Tovbis} } @article {2012, title = {On 2-step, corank 2 nilpotent sub-Riemannian metrics}, journal = {SIAM J. Control Optim., 50 (2012) 559{\textendash}582}, number = {arXiv:1105.5766;}, year = {2012}, publisher = {Society for Industrial and Applied Mathematics}, abstract = {In this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics\\r\\nthat are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.}, doi = {10.1137/110835700}, url = {http://hdl.handle.net/1963/6065}, author = {Davide Barilari and Ugo Boscain and Jean-Paul Gauthier} } @article {bonheure2012concentration, title = {Concentration on circles for nonlinear Schr{\"o}dinger{\textendash}Poisson systems with unbounded potentials vanishing at infinity}, journal = {Communications in Contemporary Mathematics}, volume = {14}, number = {02}, year = {2012}, pages = {1250009}, publisher = {World Scientific}, abstract = {

The present paper is devoted to weighted nonlinear Schr{\"o}dinger{\textendash}Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

}, doi = {10.1142/S0219199712500095}, url = {https://doi.org/10.1142/S0219199712500095}, author = {Bonheure, Denis and Di Cosmo, Jonathan and Mercuri, Carlo} } @article {2012, title = {Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis}, journal = {Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149}, year = {2012}, publisher = {SISSA}, abstract = {The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems}, doi = {10.1093/nar/gks467}, url = {http://hdl.handle.net/1963/6506}, author = {Q Beg and Mattia Zampieri and N Klitgord and S Collins and M Serres and Daniel Segr{\`e} and Claudio Altafini} } @article {2012, title = {A dynamical feedback model for adaptation in the olfactory transduction pathway}, journal = {Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686}, number = {PMID:22735517;}, year = {2012}, publisher = {Biophysical Society, Elsevier}, abstract = {Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.}, doi = {10.1016/j.bpj.2012.04.040}, url = {http://hdl.handle.net/1963/7019}, author = {Giovanna De Palo and Anna Boccaccio and Andrew Miri and Anna Menini and Claudio Altafini} } @article {2012, title = {A formula for Popp\'s volume in sub-Riemannian geometry}, journal = {Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57}, number = {arXiv:1211.2325;}, year = {2012}, note = {16 pages, minor revisions}, publisher = {SISSA}, abstract = {For an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property.}, keywords = {subriemannian, volume, Popp, control}, doi = {10.2478/agms-2012-0004}, url = {http://hdl.handle.net/1963/6501}, author = {Luca Rizzi and Davide Barilari} } @article {BertolaCafasso3, title = {Fredholm determinants and pole-free solutions to the noncommutative Painlev{\'e} II equation}, journal = {Comm. Math. Phys.}, volume = {309}, number = {3}, year = {2012}, pages = {793{\textendash}833}, issn = {0010-3616}, doi = {10.1007/s00220-011-1383-x}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x}, author = {Marco Bertola and Mattia Cafasso} } @article {2012, title = {Gauge Theories on ALE Space and Super Liouville Correlation Functions}, journal = {Lett. Math. Phys. 101 (2012) 103-124}, number = {arXiv:1107.4609v1;}, year = {2012}, note = {21 pages}, publisher = {SISSA}, abstract = {We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture.}, doi = {10.1007/s11005-012-0553-x}, url = {http://hdl.handle.net/1963/4305}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {2012, title = {On the Hausdorff volume in sub-Riemannian geometry}, journal = {Calculus of Variations and Partial Differential Equations. Volume 43, Issue 3-4, March 2012, Pages 355-388}, number = {arXiv:1005.0540;}, year = {2012}, publisher = {SISSA}, abstract = {For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative\r\nof the spherical Hausdorff measure with respect to a smooth volume. We prove\r\nthat this is the volume of the unit ball in the nilpotent approximation and it\r\nis always a continuous function. We then prove that up to dimension 4 it is\r\nsmooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4\r\non every smooth curve) but in general not C^5. These results answer to a\r\nquestion addressed by Montgomery about the relation between two intrinsic\r\nvolumes that can be defined in a sub-Riemannian manifold, namely the Popp and\r\nthe Hausdorff volume. If the nilpotent approximation depends on the point (that\r\nmay happen starting from dimension 5), then they are not proportional, in\r\ngeneral.}, doi = {10.1007/s00526-011-0414-y}, url = {http://hdl.handle.net/1963/6454}, author = {Andrei A. Agrachev and Davide Barilari and Ugo Boscain} } @article {2012, title = {Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment}, journal = {Nanoscale. 2012 Mar; 4(5):1734-41}, number = {PMID:22301788;}, year = {2012}, publisher = {Royal Society of Chemistry}, abstract = {Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters.}, doi = {10.1039/c2nr11662f}, author = {Alessandro Bosco and Fouzia Bano and Pietro Parisse and Loredana Casalis and Antonio DeSimone and Cristian Micheletti} } @article {2012, title = {Introduction to Riemannian and sub-Riemannian geometry}, number = {SISSA;09/2012/M}, year = {2012}, institution = {SISSA}, url = {http://hdl.handle.net/1963/5877}, author = {Andrei A. Agrachev and Davide Barilari and Ugo Boscain} } @article {2012, title = {On localization in holomorphic equivariant cohomology}, journal = {Central European Journal of Mathematics, Volume 10, Issue 4, August 2012, Pages 1442-1454}, number = {arXiv:0910.2019;}, year = {2012}, publisher = {Springer}, abstract = {We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu{\textquoteright}s localization formulas.}, keywords = {Lie algebroids}, doi = {10.2478/s11533-012-0054-2}, url = {http://hdl.handle.net/1963/6584}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {Bertola:P2poles, title = {On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev{\'e} equation}, journal = {Nonlinearity}, volume = {25}, number = {4}, year = {2012}, pages = {1179{\textendash}1185}, issn = {0951-7715}, doi = {10.1088/0951-7715/25/4/1179}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/1179}, author = {Marco Bertola} } @article {2011, title = {Moduli of symplectic instanton vector bundles of higher rank on projective space $\\mathbb{P}^3$}, journal = {Central European Journal of Mathematics 10, nr. 4 (2012) 1232}, number = {arXiv:1109.2292v1;}, year = {2012}, note = {14 pages}, publisher = {SISSA}, abstract = {Symplectic instanton vector bundles on the projective space $\\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\\mathbb{P}^3$ with $r\\ge2$ and second Chern class $n\\ge r,\\ n\\equiv r({\\rm mod}2)$. We give an explicit construction of an irreducible component $I^*_{n,r}$ of this space for each such value of $n$ and show that $I^*_{n,r}$ has the expected dimension $4n(r+1)-r(2r+1)$.}, doi = {10.2478/s11533-012-0062-2}, url = {http://hdl.handle.net/1963/4656}, author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov} } @article {2012, title = {Moduli spaces of noncommutative instantons: gauging away noncommutative parameters}, journal = {Quarterly Journal of Mathematics (2012) 63 (1): 41-86}, number = {SISSA;62/2009/FM}, year = {2012}, publisher = {Oxford University Press}, abstract = {Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\\\\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.}, doi = {10.1093/qmath/haq036}, url = {http://hdl.handle.net/1963/3777}, author = {Simon Brain and Giovanni Landi} } @article {boscaggin2012one, title = {One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations}, journal = {Advanced Nonlinear Studies}, volume = {12}, number = {3}, year = {2012}, pages = {445{\textendash}463}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2012-0302}, author = {Alberto Boscaggin} } @article {BOSCAGGIN20122900, title = {Pairs of positive periodic solutions of second order nonlinear equations with indefinite weight}, journal = {Journal of Differential Equations}, volume = {252}, number = {3}, year = {2012}, pages = {2900 - 2921}, abstract = {

We study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu"+λa(t)g(u)=0,λ\>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

}, keywords = {Critical points, Necessary conditions, Pairs of positive solutions, Periodic solutions}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2011.09.011}, url = {http://www.sciencedirect.com/science/article/pii/S0022039611003895}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {boscaggin2012periodic, title = {Periodic solutions to superlinear planar Hamiltonian systems}, journal = {Portugaliae Mathematica}, volume = {69}, number = {2}, year = {2012}, pages = {127{\textendash}141}, publisher = {European Mathematical Society Publishing House}, abstract = {

We prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincare-Birkhoff fixed point theorem.

}, author = {Alberto Boscaggin} } @article {BOSCAGGIN20122922, title = {Positive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics}, journal = {Journal of Differential Equations}, volume = {252}, number = {3}, year = {2012}, pages = {2922 - 2950}, abstract = {

We prove the existence of a pair of positive T-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODEu"+aλ,μ(t)g(u)=0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T-periodic and sign indefinite weight of the form λa+(t)-μa-(t), with λ,μ\>0 and large.

}, keywords = {Complex dynamics, Poincar{\'e} map, Positive periodic solutions, Subharmonics}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2011.09.010}, url = {http://www.sciencedirect.com/science/article/pii/S0022039611003883}, author = {Alberto Boscaggin and Fabio Zanolin} } @article {2011, title = {Quasistatic evolution in non-associative plasticity - the cap models}, journal = {SIAM Journal on Mathematical Analysis 44, nr. 1 (2012) 245-292}, number = {SISSA;05/2011/M}, year = {2012}, publisher = {SIAM}, abstract = {Non-associative elasto-plasticity is the working model of plasticity for soil and rocks mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plastic evolution is expressed for times that are conveniently rescaled.}, keywords = {Elasto-plasticity}, doi = {10.1137/110823511}, url = {http://hdl.handle.net/1963/4139}, author = {Jean-Francois Babadjian and Gilles A. Francfort and Maria Giovanna Mora} } @article {BertolaCafasso2, title = {Riemann{\textendash}Hilbert approach to multi-time processes: The Airy and the Pearcey cases}, journal = {Physica D: Nonlinear Phenomena}, volume = {241}, number = {23-24}, year = {2012}, note = {Integrable Systems in Pure and Applied Mathematics}, pages = {2237 - 2245}, keywords = {Integrable kernels}, issn = {0167-2789}, doi = {10.1016/j.physd.2012.01.003}, url = {http://www.sciencedirect.com/science/article/pii/S0167278912000115}, author = {Marco Bertola and Mattia Cafasso} } @article {2012, title = {On robust Lie-algebraic stability conditions for switched linear systems}, journal = {Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353}, year = {2012}, abstract = {This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters.}, doi = {10.1016/j.sysconle.2011.11.016}, url = {http://hdl.handle.net/1963/6455}, author = {Andrei A. Agrachev and Yurij Baryshnikov and Daniel Liberzon} } @article {2012, title = {SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension}, journal = {Communications in Mathematical Physics 313 (2012) 1-33}, number = {SISSA;71/2010/M}, year = {2012}, publisher = {Springer}, doi = {10.1007/s00220-012-1480-5}, url = {http://hdl.handle.net/1963/4091}, author = {Stefano Bianchini and Laura Caravenna} } @article {2011, title = {SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)}, journal = {Siam Journal on Mathematical Analysis}, volume = {44}, number = {SISSA;13/2011/M}, year = {2012}, pages = {2179-2203}, publisher = {SISSA}, doi = {10.1137/110827272}, url = {http://hdl.handle.net/20.500.11767/14066}, author = {Stefano Bianchini and Daniela Tonon} } @article {2012, title = {SBV regularity of genuinely nonlinear hyperbolic systems of conservation laws in one space dimension}, journal = {Acta Mathematica Scientia, Volume 32, Issue 1, January 2012, Pages 380-388}, year = {2012}, publisher = {Elsevier}, abstract = {The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered. An overview of the techniques involved in the proof is given, and a collection of related problems concludes the paper. Key words hyperbolic systems; conservation laws; SBV; regularity}, keywords = {Hyperbolic systems}, doi = {10.1016/S0252-9602(12)60024-1}, url = {http://hdl.handle.net/1963/6535}, author = {Stefano Bianchini} } @article {bianchini2012sbv, title = {SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension}, journal = {Rend. Istit. Mat. Univ. Trieste}, volume = {44}, year = {2012}, pages = {439{\textendash}472}, author = {Stefano Bianchini and Lei Yu} } @article {2012, title = {SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian}, journal = {Journal of Mathematical Analysis and Applications}, volume = {391}, number = {SISSA;45/2011/M}, year = {2012}, pages = {190-208}, publisher = {SISSA}, doi = {10.1016/j.jmaa.2012.02.017}, url = {http://hdl.handle.net/20.500.11767/13909}, author = {Stefano Bianchini and Daniela Tonon} } @article {Berti20122579, title = {Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential}, journal = {Nonlinearity}, volume = {25}, number = {9}, year = {2012}, note = {cited By (since 1996)3}, pages = {2579-2613}, abstract = {We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d >= 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the {\textquoteright}separation properties{\textquoteright} of the small divisors assuming weaker non-resonance conditions than in [11]. {\textcopyright} 2012 IOP Publishing Ltd.}, issn = {09517715}, doi = {10.1088/0951-7715/25/9/2579}, author = {Massimiliano Berti and Philippe Bolle} } @article {MR2880030, title = {Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes}, journal = {J. Stat. Phys.}, volume = {146}, number = {3}, year = {2012}, pages = {475{\textendash}518}, issn = {0022-4715}, doi = {10.1007/s10955-011-0409-2}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2}, author = {Marco Bertola and Buckingham, R. and Lee, S. Y. and Pierce, V.} } @article {2012, title = {Sub-Riemannian structures on 3D Lie groups}, journal = {Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44}, number = {arXiv:1007.4970;}, year = {2012}, publisher = {SISSA}, abstract = {

We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups $SL(2)$ and $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

}, doi = {10.1007/s10883-012-9133-8}, url = {http://hdl.handle.net/1963/6453}, author = {Andrei A. Agrachev and Davide Barilari} } @article {2012, title = {Vertices, vortices \& interacting surface operators}, journal = {JHEP 06(2012)178}, number = {SISSA;03/2011/FM-EP}, year = {2012}, note = {22 pages, 4 figures}, publisher = {SISSA}, abstract = {We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.}, doi = {10.1007/JHEP06(2012)178}, url = {http://hdl.handle.net/1963/4134}, author = {Giulio Bonelli and Alessandro Tanzini and Zhao Jian} } @article {2012, title = {Wild quiver gauge theories}, journal = {JHEP 02(2012)031}, number = {arXiv:1112.1691v1;}, year = {2012}, note = {34 pages}, publisher = {SISSA}, abstract = {

We study $N=2$ supersymmetric $SU(2)$ gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional $A_1 (2,0)$ theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

}, doi = {10.1007/JHEP02(2012)031}, url = {http://hdl.handle.net/1963/5184}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {Bertola:Boutroux, title = {Boutroux curves with external field: equilibrium measures without a variational problem}, journal = {Anal. Math. Phys.}, volume = {1}, number = {2-3}, year = {2011}, pages = {167{\textendash}211}, issn = {1664-2368}, doi = {10.1007/s13324-011-0012-3}, url = {http://dx.doi.org/10.1007/s13324-011-0012-3}, author = {Marco Bertola} } @article {Berti2011741, title = {Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs}, journal = {Communications in Mathematical Physics}, volume = {305}, number = {3}, year = {2011}, note = {cited By (since 1996)8}, pages = {741-796}, abstract = {We consider infinite dimensional Hamiltonian systems. We prove the existence of "Cantor manifolds" of elliptic tori-of any finite higher dimension-accumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence of Cantor manifolds of elliptic tori which are "branching" points of other Cantor manifolds of higher dimensional tori. We also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear wave equation. {\textcopyright} 2011 Springer-Verlag.}, issn = {00103616}, doi = {10.1007/s00220-011-1264-3}, author = {Massimiliano Berti and Luca Biasco} } @article {2011, title = {Crepant resolutions of weighted projective spaces and quantum deformations}, journal = {This article will be published in 2011 in the \"Nagoya Mathematical Journal\" Volume 201, March 2011, Pages 1-22, under the title \"Computing certain Gromov-Witten invariants of the crepant resolution of P{double-strock}(1, 3, 4, 4)}, number = {arXiv:math/0610617;}, year = {2011}, note = {Exposition improved, new title, typos corrected. The section\r\n concerning the model for the orbifold Chow ring has been removed (appears now\r\n in our new preprint 0709.4559)}, publisher = {SISSA}, abstract = {We compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity.}, url = {http://hdl.handle.net/1963/6514}, author = {Samuel Boissiere and Etienne Mann and Fabio Perroni} } @article {2011, title = {D-branes, surface operators, and ADHM quiver representations}, number = {SISSA;01/2011/FM}, year = {2011}, note = {45 pages, v2: minor corrections}, institution = {SISSA}, abstract = {A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries.}, url = {http://hdl.handle.net/1963/4133}, author = {Ugo Bruzzo and Duiliu-Emanuel Diaconescu and M. Yardim and G. Pan and Yi Zhang and Chuang Wu-yen} } @article {2011, title = {A Decomposition Theorem for BV functions}, journal = {Communications on Pure and Applied Analysis}, volume = {10}, number = {SISSA;20/2009/M}, year = {2011}, pages = {1549-1566}, publisher = {American Institute of Mathematical Sciences}, doi = {10.3934/cpaa.2011.10.1549}, url = {http://hdl.handle.net/20.500.11767/14599}, author = {Stefano Bianchini and Daniela Tonon} } @article {Bambusi20113379, title = {Degenerate KAM theory for partial differential equations}, journal = {Journal of Differential Equations}, volume = {250}, number = {8}, year = {2011}, note = {cited By (since 1996)3}, pages = {3379-3397}, abstract = {This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of R{\"u}ssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. {\textcopyright} 2010 Elsevier Inc.}, issn = {00220396}, doi = {10.1016/j.jde.2010.11.002}, author = {Dario Bambusi and Massimiliano Berti and Elena Magistrelli} } @article {bonheure2011embedding, title = {Embedding theorems and existence results for nonlinear Schr{\"o}dinger{\textendash}Poisson systems with unbounded and vanishing potentials}, journal = {Journal of Differential Equations}, volume = {251}, number = {4-5}, year = {2011}, pages = {1056{\textendash}1085}, publisher = {Elsevier}, abstract = {

Motivated by existence results for positive solutions of non-autonomous nonlinear Schr{\"o}dinger{\textendash}Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

}, doi = {10.1016/j.jde.2011.04.010}, url = {https://doi.org/10.1016/j.jde.2011.04.010}, author = {Bonheure, Denis and Mercuri, Carlo} } @article {2011, title = {An Estimate on the Flow Generated by Monotone Operators}, journal = {Communications in Partial Differential Equations 36 (2011) 777-796}, number = {SISSA;29/2009/M}, year = {2011}, publisher = {Taylor \& Francis}, doi = {10.1080/03605302.2010.534224}, url = {http://hdl.handle.net/1963/3646}, author = {Stefano Bianchini and Matteo Gloyer} } @article {2011, title = {Generalized matrix models and AGT correspondence at all genera}, journal = {JHEP, Volume 2011, Issue 7, 2011, Article number055}, number = {arXiv:1011.5417;}, year = {2011}, note = {This version is published in : Journal of High Energy Physics, Volume 2011, Issue 7, 2011, Article number055}, publisher = {SISSA}, abstract = {We study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera.}, doi = {10.1007/JHEP07(2011)055}, url = {http://hdl.handle.net/1963/6568}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagib} } @article {2011, title = {Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle}, journal = {Differential Geometry and its Applications 29 (2011) 147-153}, number = {SISSA;05/2010/FM}, year = {2011}, publisher = {Elsevier}, doi = {10.1016/j.difgeo.2011.02.001}, url = {http://hdl.handle.net/1963/3830}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2011, title = {Instantons on ALE spaces and Super Liouville Conformal Field Theories}, number = {arXiv:1106.2505v1;}, year = {2011}, note = {10 pages}, institution = {SISSA}, abstract = {We provide evidence that the conformal blocks of N=1 super Liouville\\r\\nconformal field theory are described in terms of the SU(2) Nekrasov partition\\r\\nfunction on the ALE space O_{P^1}(-2).}, url = {http://hdl.handle.net/1963/4262}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {2011, title = {Invariant manifolds for a singular ordinary differential equation}, journal = {Journal of Differential Equations 250 (2011) 1788-1827}, number = {SISSA;04/2008/M}, year = {2011}, publisher = {Elsevier}, doi = {10.1016/j.jde.2010.11.010}, url = {http://hdl.handle.net/1963/2554}, author = {Stefano Bianchini and Laura Spinolo} } @mastersthesis {2011, title = {Invariants, volumes and heat kernels in sub-Riemannian geometry}, year = {2011}, school = {SISSA}, abstract = {Sub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]).}, keywords = {Sub-Riemannian geometry}, url = {http://hdl.handle.net/1963/6124}, author = {Davide Barilari} } @article {2011, title = {The Liouville side of the vortex}, journal = {JHEP 09(2011)096}, number = {arXiv:1107.2787v1;}, year = {2011}, note = {25pages,11figures}, publisher = {SISSA}, abstract = {We analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.}, doi = {10.1007/JHEP09(2011)096}, url = {http://hdl.handle.net/1963/4304}, author = {Giulio Bonelli and Alessandro Tanzini and Jian Zhao} } @article {2011, title = {Moduli of framed sheaves on projective surfaces}, journal = {Doc. Math. 16 (2011) 399-410}, number = {arXiv:0906.1436;}, year = {2011}, publisher = {Documenta Mathematica}, abstract = {We show that there exists a fine moduli space for torsion-free sheaves on a\\r\\nprojective surface, which have a \\\"good framing\\\" on a big and nef divisor. This\\r\\nmoduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of\\r\\nHuybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space, and discuss some examples on rational surfaces.}, url = {http://hdl.handle.net/1963/5126}, author = {Ugo Bruzzo and Dimitri Markushevich} } @conference {10.1007/978-1-4419-9554-4_10, title = {The Monge Problem in Geodesic Spaces}, booktitle = {Nonlinear Conservation Laws and Applications}, year = {2011}, pages = {217{\textendash}233}, publisher = {Springer US}, organization = {Springer US}, address = {Boston, MA}, abstract = {

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

}, isbn = {978-1-4419-9554-4}, author = {Stefano Bianchini and Fabio Cavalletti}, editor = {Alberto Bressan and Chen, Gui-Qiang G. and Marta Lewicka and Wang, Dehua} } @article {2011, title = {Nonlinear wave and Schr{\"o}dinger equations on compact Lie groups and homogeneous spaces}, journal = {Duke Mathematical Journal}, volume = {159}, year = {2011}, month = {2011}, chapter = {479}, abstract = {We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr{\textasciidieresis}odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.}, issn = {0012-7094}, doi = {10.1215/00127094-1433403}, author = {Massimiliano Berti and Michela Procesi} } @article {BOSCAGGIN2011259, title = {A note on a superlinear indefinite Neumann problem with multiple positive solutions}, journal = {Journal of Mathematical Analysis and Applications}, volume = {377}, number = {1}, year = {2011}, pages = {259 - 268}, abstract = {

We prove the existence of three positive solutions for the Neumann problem associated to u"+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta-(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

}, keywords = {Indefinite weight, Nonlinear boundary value problems, positive solutions, Shooting method}, issn = {0022-247X}, doi = {https://doi.org/10.1016/j.jmaa.2010.10.042}, url = {http://www.sciencedirect.com/science/article/pii/S0022247X10008796}, author = {Alberto Boscaggin} } @article {2011, title = {Poincar{\'e} polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces}, journal = {Communications in Mathematical Physics 304 (2011) 395-409}, volume = {304}, number = {SISSA;56/2009/FM}, year = {2011}, month = {06/2011}, pages = {395-409}, publisher = {Springer}, abstract = {

We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

}, doi = {10.1007/s00220-011-1231-z}, url = {http://hdl.handle.net/1963/3738}, author = {Ugo Bruzzo and Rubik Poghossian and Alessandro Tanzini} } @article {2011, title = {Q-factorial Laurent rings}, number = {arXiv:1108.4116v1;}, year = {2011}, note = {5 pages}, institution = {SISSA}, abstract = {Dolgachev proved that, for any field k, the ring naturally associated to a\\r\\ngeneric Laurent polynomial in d variables, $d \\\\geq 4$, is factorial. We prove a\\r\\nsufficient condition for the ring associated to a very general complex Laurent\\r\\npolynomial in d=3 variables to be Q-factorial.}, url = {http://hdl.handle.net/1963/4183}, author = {Ugo Bruzzo and Antonella Grassi} } @article {2011, title = {Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators}, journal = {Commun. Math. Phys. 308 (2011) 567-589}, number = {arXiv:1005.2130;}, year = {2011}, publisher = {Springer}, abstract = {We develop the first steps towards an analysis of geometry on the quantum\\r\\nspacetime proposed in Doplicher et al. (Commun Math Phys 172:187{\textendash}220, 1995). The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra. In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes. The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity. The Euclidean distance operator is shown to have spectrum bounded below by a constant of the order of the Planck length. The corresponding statement is proved also for both the space-space and space-time area operators, as well as for the Euclidean length of the vector representing the 3-volume operators. However, the space 3-volume operator (the time component of that vector) is shown to have spectrum equal to the whole complex plane. All these operators are normal, while the distance operators are also selfadjoint. The Lorentz invariant spacetime volume operator, representing the 4- volume spanned by five\\r\\nindependent events, is shown to be normal. Its spectrum is pure point with a\\r\\nfinite distance (of the order of the fourth power of the Planck length) away\\r\\nfrom the origin. The mathematical formalism apt to these problems is developed and its relation to a general formulation of Gauge Theories on Quantum Spaces is outlined. As a byproduct, a Hodge Duality between the absolute differential and the Hochschild boundary is pointed out.}, doi = {10.1007/s00220-011-1358-y}, url = {http://hdl.handle.net/1963/5203}, author = {Dorothea Bahns and Sergio Doplicher and Klaus Fredenhagen and Gherardo Piacitelli} } @article {2011, title = {Quantum Hitchin Systems via beta-deformed Matrix Models}, number = {arXiv:1104.4016v2;}, year = {2011}, note = {29 pages; v2. refs. added and typos corrected}, institution = {SISSA}, abstract = {

We study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four ndimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

}, url = {http://hdl.handle.net/1963/4181}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini} } @article {2011, title = {Quantum Isometries of the finite noncommutative geometry of the Standard Model}, journal = {Commun. Math. Phys. 307:101-131, 2011}, number = {arXiv:1009.2850;}, year = {2011}, publisher = {Springer}, abstract = {We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.}, doi = {10.1007/s00220-011-1301-2}, url = {http://hdl.handle.net/1963/4906}, author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Ludwik Dabrowski} } @article {BOSCAGGIN20114166, title = {Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincar{\'e}{\textendash}Birkhoff theorem}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {74}, number = {12}, year = {2011}, pages = {4166 - 4185}, abstract = {

In the general setting of a planar first order system (0.1)u'=G(t,u),u∈R2, with G:[0,T]{\texttimes}R2{\textrightarrow}R2, we study the relationships between some classical nonresonance conditions (including the Landesman{\textendash}Lazer one) {\textemdash} at infinity and, in the unforced case, i.e. G(t,0)=0, at zero {\textemdash} and the rotation numbers of {\textquotedblleft}large{\textquotedblright} and {\textquotedblleft}small{\textquotedblright} solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincar{\'e}{\textendash}Birkhoff fixed point theorem, new multiplicity results for T-periodic solutions of unforced planar Hamiltonian systems Ju'=∇uH(t,u) and unforced undamped scalar second order equations x"+g(t,x)=0. In particular, by means of the Landesman{\textendash}Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.

}, keywords = {Multiple periodic solutions, Poincar{\'e}{\textendash}Birkhoff theorem, Resonance, Rotation number}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2011.03.051}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X11001817}, author = {Alberto Boscaggin and Maurizio Garrione} } @article {2011, title = {SBV regularity for Hamilton-Jacobi equations in R^n}, journal = {Arch. Rational Mech. Anal. 200 (2011) 1003-1021}, number = {arXiv:1002.4087;}, year = {2011}, publisher = {Springer}, abstract = {

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in}\quad \Omega\subset \mathbb{R}\times \mathbb{R}^{n} . $$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb{R}^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.

}, doi = {10.1007/s00205-010-0381-z}, url = {http://hdl.handle.net/1963/4911}, author = {Stefano Bianchini and Camillo De Lellis and Roger Robyr} } @article {2011, title = {Semistable and numerically effective principal (Higgs) bundles}, journal = {Advances in Mathematics 226 (2011) 3655-3676}, number = {SISSA;27/2009/FM}, year = {2011}, publisher = {Elsevier}, abstract = {We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian{\textendash}Yang{\textendash}Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles.}, doi = {10.1016/j.aim.2010.10.026}, url = {http://hdl.handle.net/1963/3638}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2011, title = {The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry}, journal = {Journal of Dynamical and Control Systems }, volume = {17 }, number = {arXiv:1009.2612;}, year = {2011}, pages = {141-161}, publisher = {Springer}, abstract = {

We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

}, doi = {10.1007/s10883-011-9113-4}, url = {http://hdl.handle.net/1963/4914}, author = {Bernard Bonnard and Gr{\'e}goire Charlot and Roberta Ghezzi and Gabriel Janin} } @article {2011, title = {Structure of level sets and Sard-type properties of Lipschitz maps}, number = {SISSA;51/2011/M}, year = {2011}, institution = {SISSA}, url = {http://hdl.handle.net/1963/4657}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {boscaggin2011subharmonic, title = {Subharmonic solutions of planar Hamiltonian systems: a rotation number approach}, journal = {Advanced Nonlinear Studies}, volume = {11}, number = {1}, year = {2011}, pages = {77{\textendash}103}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2011-0104}, author = {Alberto Boscaggin} } @article {boscaggin2011subharmonic, title = {Subharmonic solutions of planar Hamiltonian systems via the Poincar{\'e}́-Birkhoff theorem}, journal = {Le Matematiche}, volume = {66}, number = {1}, year = {2011}, pages = {115{\textendash}122}, abstract = {

We revisit some recent results obtained in [1] about the existence of subharmonic solutions for a class of (nonautonomous) planar Hamiltonian systems, and we compare them with the existing literature. New applications to undamped second order equations are discussed, as well.

}, author = {Alberto Boscaggin} } @article {2011, title = {Supercritical conformal metrics on surfaces with conical singularities}, journal = {Int Math Res Notices (2011) 2011 (24): 5625-5643}, number = {SISSA;56/2010/M}, year = {2011}, publisher = {Oxford University Press}, abstract = {

We study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

}, doi = {10.1093/imrn/rnq285}, url = {http://hdl.handle.net/1963/4095}, author = {Mauro Bardelloni and Francesca De Marchis and Andrea Malchiodi} } @article {BertolaCafasso1, title = {The Transition between the Gap Probabilities from the Pearcey to the Airy Process{\textendash}a Riemann-Hilbert Approach}, journal = {International Mathematics Research Notices}, volume = {doi: 10.1093/imrn/rnr066}, year = {2011}, pages = {1-50}, author = {Marco Bertola and Mattia Cafasso} } @article {2011, title = {A uniqueness result for the continuity equation in two dimensions}, number = {SISSA;52/2011/M}, year = {2011}, institution = {SISSA}, url = {http://hdl.handle.net/1963/4663}, author = {Giovanni Alberti and Stefano Bianchini and Gianluca Crippa} } @article {Berti2010377, title = {An abstract Nash-Moser theorem with parameters and applications to PDEs}, journal = {Annales de l{\textquoteright}Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis}, volume = {27}, number = {1}, year = {2010}, note = {cited By (since 1996)9}, pages = {377-399}, abstract = {We prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. {\textcopyright} 2009 Elsevier Masson SAS. All rights reserved.}, keywords = {Abstracting, Aircraft engines, Finite dimensional, Hamiltonian PDEs, Implicit function theorem, Invariant tori, Iterative schemes, Linearized operators, Mathematical operators, Moser theorem, Non-Linearity, Nonlinear equations, Nonlinear wave equation, Periodic solution, Point of interest, Resonance phenomena, Small divisors, Sobolev, Wave equations}, issn = {02941449}, doi = {10.1016/j.anihpc.2009.11.010}, author = {Massimiliano Berti and Philippe Bolle and Michela Procesi} } @article {Bertola:CBOPs, title = {Cauchy biorthogonal polynomials}, journal = {J. Approx. Theory}, volume = {162}, number = {4}, year = {2010}, pages = {832{\textendash}867}, issn = {0021-9045}, doi = {10.1016/j.jat.2009.09.008}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {2010, title = {Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality}, journal = {J. Geom. Phys. 60 (2010) 417-429}, number = {SISSA;56/2008/FM}, year = {2010}, abstract = {We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.}, doi = {10.1016/j.geomphys.2009.11.006}, url = {http://hdl.handle.net/1963/2938}, author = {Andrea Brini and Luca Griguolo and Domenico Seminara and Alessandro Tanzini} } @article {2010, title = {Cohomology of Skew-holomorphic lie algebroids}, number = {SISSA;15/2010/FM}, year = {2010}, abstract = {We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.}, url = {http://hdl.handle.net/1963/3853}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {BertolaIsoTau, title = {The dependence on the monodromy data of the isomonodromic tau function}, journal = {Comm. Math. Phys.}, volume = {294}, number = {2}, year = {2010}, pages = {539{\textendash}579}, issn = {0010-3616}, doi = {10.1007/s00220-009-0961-7}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7}, author = {Marco Bertola} } @article {2010, title = {Estimates on path functionals over Wasserstein Spaces}, journal = {SIAM J. Math. Anal. 42 (2010) 1179-1217}, number = {SISSA;11/2009/M}, year = {2010}, abstract = {In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions.}, doi = {10.1137/100782693}, url = {http://hdl.handle.net/1963/3583}, author = {Stefano Bianchini and Alessio Brancolini} } @article {2010, title = {On the Euler-Lagrange equation for a variational problem : the general case II}, journal = {Math. Z. 265 (2010) 889-923}, number = {SISSA;75/2007/M}, year = {2010}, doi = {10.1007/s00209-009-0547-2}, url = {http://hdl.handle.net/1963/2551}, author = {Stefano Bianchini and Matteo Gloyer} } @article {2010, title = {Existence of planar curves minimizing length and curvature}, journal = {Proc. Steklov Inst. Math. 270 (2010) 43-56}, number = {arXiv.org;0906.5290v2}, year = {2010}, publisher = {Springer}, abstract = {In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles.}, doi = {10.1134/S0081543810030041}, url = {http://hdl.handle.net/1963/4107}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Francesco Rossi} } @article {Bertola:wj, title = {First colonization of a hard-edge in random matrix theory}, journal = {Constr. Approx.}, volume = {31}, number = {2}, year = {2010}, pages = {231{\textendash}257}, issn = {0176-4276}, doi = {10.1007/s00365-009-9052-4}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4}, author = {Marco Bertola and Lee, S. Y.} } @article {2010, title = {Gauge theory: from physics to geometry}, journal = {Rend. Istit. Mat. Univ. Trieste 42 (2010) 103-128}, number = {SISSA;80/2010/FM}, year = {2010}, publisher = {Istituto di matematica. Universita\\\' di Trieste}, abstract = {Maxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.}, url = {http://hdl.handle.net/1963/4105}, author = {Ugo Bruzzo} } @article {2010, title = {On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system}, journal = {Int. Math. Res. Not. (2010) 2010:279-296}, number = {arXiv.org;0902.0953v2}, year = {2010}, publisher = {Oxford University Press}, abstract = {We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.}, doi = {10.1093/imrn/rnp130}, url = {http://hdl.handle.net/1963/3800}, author = {Claudio Bartocci and Gregorio Falqui and Igor Mencattini and Giovanni Ortenzi and Marco Pedroni} } @article {2010, title = {Hitchin systems, N=2 gauge theories and W-gravity}, journal = {Phys. Lett. B 691 (2010) 111-115}, number = {SISSA;60/2009/EP-FM}, year = {2010}, abstract = {We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE\\\'s obtaining that Nekrasov\\\'s partition function satisfies W-geometry constraints.}, doi = {10.1016/j.physletb.2010.06.027}, url = {http://hdl.handle.net/1963/3831}, author = {Giulio Bonelli and Alessandro Tanzini} } @article {boscain2010normal, title = {A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point}, journal = {arXiv preprint arXiv:1008.5036}, year = {2010}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi} } @article {2010, title = {On optimality of c-cyclically monotone transference plans}, journal = {Comptes Rendus Mathematique 348 (2010) 613-618}, year = {2010}, publisher = {Elsevier}, abstract = {Abstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.}, doi = {10.1016/j.crma.2010.03.022}, url = {http://hdl.handle.net/1963/4023}, author = {Stefano Bianchini and Laura Caravenna} } @article {2010, title = {Picard group of hypersurfaces in toric varieties}, number = {SISSA;78/2010/FM}, year = {2010}, abstract = {We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.}, url = {http://hdl.handle.net/1963/4103}, author = {Ugo Bruzzo and Antonella Grassi} } @article {2010, title = {Projective Reeds-Shepp car on $S^2$ with quadratic cost}, journal = {ESAIM COCV 16 (2010) 275-297}, number = {SISSA;34/2008/M}, year = {2010}, abstract = {Fix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.}, doi = {10.1051/cocv:2008075}, url = {http://hdl.handle.net/1963/2668}, author = {Ugo Boscain and Francesco Rossi} } @article {2010, title = {On semistable principal bundles over complex projective manifolds, II}, journal = {Geom. Dedicata 146 (2010) 27-41}, number = {SISSA;85/2008/FM}, year = {2010}, abstract = {Let (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.}, doi = {10.1007/s10711-009-9424-8}, url = {http://hdl.handle.net/1963/3404}, author = {Indranil Biswas and Ugo Bruzzo} } @article {Berti2009609, title = {Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions}, journal = {Archive for Rational Mechanics and Analysis}, volume = {195}, number = {2}, year = {2010}, note = {cited By (since 1996)6}, pages = {609-642}, abstract = {We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". {\textcopyright} Springer-Verlag (2009).}, issn = {00039527}, doi = {10.1007/s00205-008-0211-8}, author = {Massimiliano Berti and Philippe Bolle} } @article {Ballerini_2010, title = {Stable determination of an immersed body in a stationary Stokes fluid}, journal = {Inverse Problems}, volume = {26}, number = {12}, year = {2010}, month = {nov}, pages = {125015}, publisher = {IOP Publishing}, abstract = {

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain an estimate of the stability of log{\textendash}log type.

}, doi = {10.1088/0266-5611/26/12/125015}, url = {https://doi.org/10.1088\%2F0266-5611\%2F26\%2F12\%2F125015}, author = {Andrea Ballerini} } @article {2010, title = {Taming open/closed string duality with a Losev trick}, journal = {JHEP 06(2010)063}, number = {SISSA;17/2010/FM-EP}, year = {2010}, abstract = {A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.}, doi = {10.1007/JHEP06(2010)063}, url = {http://hdl.handle.net/1963/3855}, author = {Giulio Bonelli and Andrea Prudenziati and Alessandro Tanzini} } @article {2010, title = {Two-dimensional almost-Riemannian structures with tangency points}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire }, volume = {27}, number = {arXiv.org;0908.2564v1}, year = {2010}, pages = {793-807}, publisher = {Elsevier}, abstract = {

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

}, doi = {10.1016/j.anihpc.2009.11.011}, url = {http://hdl.handle.net/1963/3870}, author = {Andrei A. Agrachev and Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi and Mario Sigalotti} } @article {2010, title = {Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces}, number = {SISSA;59/2010/FM}, year = {2010}, abstract = {We construct a compactification $M^{\\\\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\\\\gamma \\\\colon M^s \\\\to M^{\\\\mu ss}$, where $M^s$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\\\\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.}, url = {http://hdl.handle.net/1963/4049}, author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov} } @article {BertolaTovbis1, title = {Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schr{\"o}dinger equation at the first breaking curve}, journal = {Int. Math. Res. Not. IMRN}, number = {11}, year = {2010}, pages = {2119{\textendash}2167}, issn = {1073-7928}, doi = {10.1093/imrn/rnp196}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196}, author = {Marco Bertola and Alexander Tovbis} } @article {2009, title = {The boundary Riemann solver coming from the real vanishing viscosity approximation}, journal = {Arch. Ration. Mech. Anal. 191 (2009) 1-96}, number = {SISSA;24/2006/M}, year = {2009}, abstract = {We study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.}, doi = {10.1007/s00205-008-0177-6}, url = {http://hdl.handle.net/1963/1831}, author = {Stefano Bianchini and Laura Spinolo} } @article {Bertola:CauchyMM, title = {The Cauchy two{\textendash}matrix model}, journal = {Comm. Math. Phys.}, volume = {287}, number = {3}, year = {2009}, pages = {983{\textendash}1014}, author = {Marco Bertola and M Gekhtman and J Szmigielski} } @article {2009, title = {Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity}, journal = {BMC Research Notes (2009) 2:13}, year = {2009}, publisher = {BioMed Central}, abstract = {BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.}, doi = {10.1186/1756-0500-2-13}, url = {http://hdl.handle.net/1963/3706}, author = {Frederic D. Broccard and Silvia Pegoraro and Maria Elisabetta Ruaro and Claudio Altafini and Vincent Torre} } @article {BertolaAdvances, title = {Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights}, journal = {Adv. Math.}, volume = {220}, number = {1}, year = {2009}, pages = {154{\textendash}218}, issn = {0001-8708}, author = {Marco Bertola and Mo, M. Y.} } @article {2009, title = {A connection between viscous profiles and singular ODEs}, journal = {Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41}, number = {SISSA;05/2008/M}, year = {2009}, url = {http://hdl.handle.net/1963/2555}, author = {Stefano Bianchini and Laura Spinolo} } @article {2009, title = {Controllability of the discrete-spectrum Schrodinger equation driven by an external field}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349}, number = {SISSA;01/2008/M}, year = {2009}, abstract = {We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.}, doi = {10.1016/j.anihpc.2008.05.001}, url = {http://hdl.handle.net/1963/2547}, author = {Thomas Chambrion and Paolo Mason and Mario Sigalotti and Ugo Boscain} } @article {2009, title = {On the convergence of viscous approximations after shock interactions}, journal = {Discrete Contin. Dyn. Syst. 23 (2009) 29-48}, year = {2009}, publisher = {American Institute of Mathematical Sciences}, abstract = {We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.}, doi = {10.3934/dcds.2009.23.29}, url = {http://hdl.handle.net/1963/3412}, author = {Alberto Bressan and Carlotta Donadello} } @article {Bertola:Cubic, title = {Cubic string boundary value problems and Cauchy biorthogonal polynomials}, journal = {J. Phys. A}, volume = {42}, number = {45}, year = {2009}, pages = {454006, 13}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/45/454006}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006}, author = {Marco Bertola and Gekhtman, M. and Szmigielski, J.} } @article {2009, title = {Decoupling A and B model in open string theory: topological adventures in the world of tadpoles}, journal = {JHEP 06 (2009) 046}, number = {SISSA;26/2009/FM-EP}, year = {2009}, abstract = {In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula.}, doi = {10.1088/1126-6708/2009/06/046}, url = {http://hdl.handle.net/1963/3632}, author = {Giulio Bonelli and Andrea Prudenziati and Alessandro Tanzini and Yang Jie} } @article {2009, title = {Equivariant cohomology and localization for Lie algebroids}, journal = {Funct. Anal. Appl. 43 (2009) 18-29}, number = {SISSA;40/2005/FM}, year = {2009}, abstract = {Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.}, isbn = {978-981-270-377-4}, doi = {10.1007/s10688-009-0003-4}, url = {http://hdl.handle.net/1963/1724}, author = {Ugo Bruzzo and Lucio Cirio and Paolo Rossi and Vladimir Rubtsov} } @article {2009, title = {Exact results for topological strings on resolved Yp,q singularities}, journal = {Comm. Math. Phys. 289 (2009) 205-252}, number = {SISSA;22/2008/FM}, year = {2009}, doi = {10.1007/s00220-009-0814-4}, url = {http://hdl.handle.net/1963/2631}, author = {Andrea Brini and Alessandro Tanzini} } @article {2009, title = {On the extremality, uniqueness and optimality of transference plans}, journal = {Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458}, number = {SISSA;46/2009/M}, year = {2009}, abstract = {We consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal.}, url = {http://hdl.handle.net/1963/3692}, author = {Stefano Bianchini and Laura Caravenna} } @article {2009, title = {Families of Monads and Instantons from a Noncommutative ADHM Construction}, number = {SISSA;59/2008/FM}, year = {2009}, abstract = {We give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative {\textquoteleft}families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.}, url = {http://hdl.handle.net/1963/3478}, author = {Simon Brain and Giovanni Landi} } @article {Bertola:Lee, title = {First colonization of a spectral outpost in random matrix theory}, journal = {Constr. Approx.}, volume = {30}, number = {2}, year = {2009}, pages = {225{\textendash}263}, issn = {0176-4276}, doi = {10.1007/s00365-008-9026-y}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y}, author = {Marco Bertola and Lee, S. Y.} } @article {2009, title = {Holomorphic equivariant cohomology of Atiyah algebroids and localization}, number = {SISSA;65/2009/FM}, year = {2009}, url = {http://hdl.handle.net/1963/3774}, author = {Ugo Bruzzo and Vladimir Rubtsov} } @article {2009, title = {Homogenization of fiber reinforced brittle materials: the extremal cases}, journal = {SIAM J. Math. Anal. 41 (2009) 1874-1889}, number = {SISSA;49/2008/M}, year = {2009}, publisher = {SIAM}, abstract = {We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.}, url = {http://hdl.handle.net/1963/2705}, author = {Marco Barchiesi and Gianni Dal Maso} } @article {2009, title = {The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups}, journal = {J. Funct. Anal. 256 (2009) 2621-2655}, number = {SISSA;33/2008/M}, year = {2009}, abstract = {We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation.}, doi = {10.1016/j.jfa.2009.01.006}, url = {http://hdl.handle.net/1963/2669}, author = {Andrei A. Agrachev and Ugo Boscain and Jean-Paul Gauthier and Francesco Rossi} } @article {Mola2009, title = {Low-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners}, journal = {Journal of Structural Engineering}, volume = {135}, number = {7}, year = {2009}, month = {jul}, pages = {828{\textendash}835}, publisher = {American Society of Civil Engineers ({ASCE})}, doi = {10.1061/(asce)st.1943-541x.0000034}, url = {https://doi.org/10.1061/(asce)st.1943-541x.0000034}, author = {Andrea Mola and Giancarlo Bordonaro and Muhammad R. Hajj} } @article {BertolaLeeMo, title = {Mesoscopic colonization in a spectral band}, journal = {J. Phys. A}, volume = {42}, number = {41}, year = {2009}, pages = {415204, 17}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/41/415204}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/415204}, author = {Marco Bertola and Lee, S. Y. and Mo, M. Y.} } @article {2009, title = {A model for the orbifold Chow ring of weighted projective spaces}, journal = {Comm. Algebra 37 (2009) 503-514}, number = {arXiv.org;0709.4559v1}, year = {2009}, publisher = {Taylor and Francis}, abstract = {We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.}, doi = {10.1080/00927870802248902}, url = {http://hdl.handle.net/1963/3589}, author = {Samuel Boissiere and Etienne Mann and Fabio Perroni} } @article {Bertola:MomentTau, title = {Moment determinants as isomonodromic tau functions}, journal = {Nonlinearity}, volume = {22}, number = {1}, year = {2009}, pages = {29{\textendash}50}, author = {Marco Bertola} } @article {Bertola:IZtau, title = {The partition function of the two-matrix model as an isomonodromic τ function}, journal = {J. Math. Phys.}, volume = {50}, number = {1}, year = {2009}, pages = {013529, 17}, issn = {0022-2488}, doi = {10.1063/1.3054865}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1063/1.3054865}, author = {Marco Bertola and Marchal, O.} } @article {BertolaBalogh, title = {Regularity of a vector potential problem and its spectral curve}, journal = {J. Approx. Theory}, volume = {161}, number = {1}, year = {2009}, pages = {353{\textendash}370}, issn = {0021-9045}, doi = {10.1016/j.jat.2008.10.010}, url = {http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.010}, author = {Ferenc Balogh and Marco Bertola} } @article {2009, title = {Stratos: a code for 3D free surface flows with floating constraints}, number = {SISSA;41/2009/M}, year = {2009}, abstract = {This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......}, url = {http://hdl.handle.net/1963/3701}, author = {Antonio DeSimone and B. Bianchi and Luca Heltai} } @article {2009, title = {Topological branes, p-algebras and generalized Nahm equations}, journal = {Phys. Lett. B 672 (2009) 390-395}, number = {SISSA;47/2008/FM}, year = {2009}, abstract = {Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory}, doi = {10.1016/j.physletb.2009.01.051}, url = {http://hdl.handle.net/1963/2702}, author = {Giulio Bonelli and Alessandro Tanzini and Maxim Zabzine} } @article {MR2525872, title = {Topological expansion for the Cauchy two-matrix model}, journal = {J. Phys. A}, volume = {42}, number = {33}, year = {2009}, pages = {335201, 28}, issn = {1751-8113}, doi = {10.1088/1751-8113/42/33/335201}, url = {http://dx.doi.org/10.1088/1751-8113/42/33/335201}, author = {Marco Bertola and Ferrer, A. Prats} } @article {Berti2008151, title = {Cantor families of periodic solutions for completely resonant wave equations}, journal = {Frontiers of Mathematics in China}, volume = {3}, number = {2}, year = {2008}, note = {cited By (since 1996)0}, pages = {151-165}, abstract = {We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. {\textcopyright} 2008 Higher Education Press.}, issn = {16733452}, doi = {10.1007/s11464-008-0011-3}, author = {Massimiliano Berti and Philippe Bolle} } @article {Berti20081671, title = {Cantor families of periodic solutions for wave equations via a variational principle}, journal = {Advances in Mathematics}, volume = {217}, number = {4}, year = {2008}, note = {cited By (since 1996)6}, pages = {1671-1727}, abstract = {We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. {\textcopyright} 2007 Elsevier Inc. All rights reserved.}, issn = {00018708}, doi = {10.1016/j.aim.2007.11.004}, author = {Massimiliano Berti and Philippe Bolle} } @article {Berti2008247, title = {Cantor families of periodic solutions of wave equations with C k nonlinearities}, journal = {Nonlinear Differential Equations and Applications}, volume = {15}, number = {1-2}, year = {2008}, note = {cited By (since 1996)10}, pages = {247-276}, abstract = {We prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. {\textcopyright} 2008 Birkhaueser.}, issn = {10219722}, doi = {10.1007/s00030-007-7025-5}, author = {Massimiliano Berti and Philippe Bolle} } @article {2008, title = {Forced Vibrations of a Nonhomogeneous String}, journal = {SIAM J. Math. Anal. 40 (2008) 382-412}, number = {SISSA;36/2006/M}, year = {2008}, abstract = {We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme.}, doi = {10.1137/060665038}, url = {http://hdl.handle.net/1963/2643}, author = {P Baldi and Massimiliano Berti} } @article {2008, title = {Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices}, journal = {Phys. Rev. B 77 (2008) 245105}, number = {arXiv.org;0712.3364v1}, year = {2008}, abstract = {

Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

}, doi = {10.1103/PhysRevB.77.245105}, url = {http://hdl.handle.net/1963/2694}, author = {Matteo Rizzi and Marco Polini and Miguel A. Cazalilla and M.R. Bakhtiari and Mario P. Tosi and Rosario Fazio} } @article {2008, title = {A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds}, journal = {Discrete Contin. Dyn. Syst. 20 (2008) 801-822}, number = {SISSA;55/2006/M}, year = {2008}, abstract = {We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.}, doi = {10.3934/dcds.2008.20.801}, url = {http://hdl.handle.net/1963/1869}, author = {Andrei A. Agrachev and Ugo Boscain and Mario Sigalotti} } @article {MR2435752, title = {Harish-Chandra integrals as nilpotent integrals}, journal = {Int. Math. Res. Not. IMRN}, number = {16}, year = {2008}, pages = {Art. ID rnn062, 15}, issn = {1073-7928}, author = {Marco Bertola and Ferrer, Aleix Prats} } @article {2008, title = {Instanton counting on Hirzebruch surfaces}, number = {SISSA;55/2008/FM}, year = {2008}, abstract = {We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.}, url = {http://hdl.handle.net/1963/2852}, author = {Ugo Bruzzo and Rubik Poghossian and Alessandro Tanzini} } @article {2008, title = {Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces}, journal = {SIAM J. Control Optim. 47 (2008) 1851-1878}, number = {SISSA;58/2007/M}, year = {2008}, abstract = {In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally).}, doi = {10.1137/070703727}, url = {http://hdl.handle.net/1963/2144}, author = {Ugo Boscain and Francesco Rossi} } @article {2008, title = {Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems}, number = {SISSA;83/2008/M}, year = {2008}, url = {http://hdl.handle.net/1963/3400}, author = {Stefano Bianchini and Laura Spinolo} } @article {2008, title = {Limit Time Optimal Syntheses for a control-affine system on S{\texttwosuperior}}, journal = {SIAM J. Control Optim. 47 (2008) 111-143}, number = {SISSA;48/2006/M}, year = {2008}, abstract = {For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.}, doi = {10.1137/060675988}, url = {http://hdl.handle.net/1963/1862}, author = {Paolo Mason and Rebecca Salmoni and Ugo Boscain and Yacine Chitour} } @article {2008, title = {Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms}, journal = {PLoS ONE 3 (2008) e2981}, year = {2008}, abstract = {Background: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies.}, doi = {10.1371/journal.pone.0002981}, url = {http://hdl.handle.net/1963/2722}, author = {Mattia Zampieri and Nicola Soranzo and Daniele Bianchini and Claudio Altafini} } @article {Berti2008601, title = {On periodic elliptic equations with gradient dependence}, journal = {Communications on Pure and Applied Analysis}, volume = {7}, number = {3}, year = {2008}, note = {cited By (since 1996)1}, pages = {601-615}, abstract = {We construct entire solutions of Δu = f(x, u, ∇u) which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.}, issn = {15340392}, author = {Massimiliano Berti and Matzeu, M and Enrico Valdinoci} } @article {2008, title = {On semistable principal bundles over a complex projective manifold}, journal = {Int. Math. Res. Not. vol. 2008, article ID rnn035}, number = {arXiv.org;0803.4042v1}, year = {2008}, publisher = {Oxford University Press}, abstract = {Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.}, doi = {10.1093/imrn/rnn035}, url = {http://hdl.handle.net/1963/3418}, author = {Indranil Biswas and Ugo Bruzzo} } @article {2008, title = {Stability of planar switched systems: the nondiagonalizable case}, journal = {Commun. Pure Appl. Anal. 7 (2008) 1-21}, number = {SISSA;44/2006/M}, year = {2008}, doi = {10.3934/cpaa.2008.7.1}, url = {http://hdl.handle.net/1963/1857}, author = {Ugo Boscain and Moussa Balde} } @article {2008, title = {Symmetric obstruction theories and Hilbert schemes of points on threefolds}, journal = {Algebra Number Theory 2 (2008) 313-345}, number = {arXiv.org;math/0512556v1}, year = {2008}, abstract = {In an earlier paper by one of us (Behrend), Donaldson-Thomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical\\nZ-valued constructible function on the moduli space. This constructible function associates to\\nany point of the moduli space a certain invariant of the singularity of the space at the point. Here we evaluate this invariant for the case of a singularity that is an isolated point of a C*-action and that admits a symmetric obstruction theory compatible with the C*-action. The answer is (-1)d, where d\\nis the dimension of the Zariski tangent space. We use this result to prove that for any threefold, proper or not, the weighted Euler characteristic of the Hilbert scheme of n points on the threefold is, up to sign, equal to the usual Euler characteristic. For the case of a projective Calabi-Yau threefold, we deduce that the Donaldson-Thomas invariant of the Hilbert scheme of n points is, up to sign, equal to the Euler characteristic. This proves a conjecture of Maulik, Nekrasov, Okounkov and Pandharipande.}, url = {http://hdl.handle.net/1963/2709}, author = {Kai Behrend and Barbara Fantechi} } @article {2008, title = {Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings}, journal = {Adv. Theor. Math. Phys. 12 (2008) 1429-1446}, number = {SISSA;43/2007/EP}, year = {2008}, abstract = {We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.}, url = {http://hdl.handle.net/1963/1992}, author = {Giulio Bonelli and Alessandro Tanzini} } @inbook {2008, title = {Transport Rays and Applications to Hamilton{\textendash}Jacobi Equations}, booktitle = {Nonlinear PDE{\textquoteright}s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, C{\'e}dric Villani. Eds. Luigi Ambrosio, Giuseppe Savar{\'e}. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20}, year = {2008}, note = {This volume collects the notes of the CIME course Nonlinear PDE{\textquoteright}s and\\r\\napplications held in Cetraro (Italy) on June 23{\textendash}28, 2008. The school consisted\\r\\nin 5 series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), Felix Otto (Bonn University), Cedric Villani (Ecole Normale Superieure de Lyon).}, publisher = {Springer}, organization = {Springer}, abstract = {The aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully).}, isbn = {978-3-642-21718-0}, doi = {10.1007/978-3-642-21861-3_1}, url = {http://hdl.handle.net/1963/5463}, author = {Stefano Bianchini and Matteo Gloyer} } @article {Berti2008391, title = {Variational methods for Hamiltonian PDEs}, journal = {NATO Science for Peace and Security Series B: Physics and Biophysics}, year = {2008}, note = {cited By (since 1996)0}, pages = {391-420}, abstract = {We present recent existence results of periodic solutions for completely resonant nonlinear wave equations in which both "small divisor" difficulties and infinite dimensional bifurcation phenomena occur. These results can be seen as generalizations of the classical finite-dimensional resonant center theorems of Weinstein-Moser and Fadell-Rabinowitz. The proofs are based on variational bifurcation theory: after a Lyapunov-Schmidt reduction, the small divisor problem in the range equation is overcome with a Nash-Moser implicit function theorem for a Cantor set of non-resonant parameters. Next, the infinite dimensional bifurcation equation, variational in nature, possesses minimax mountain-pass critical points. The big difficulty is to ensure that they are not in the "Cantor gaps". This is proved under weak non-degeneracy conditions. Finally, we also discuss the existence of forced vibrations with rational frequency. This problem requires variational methods of a completely different nature, such as constrained minimization and a priori estimates derivable from variational inequalities. {\textcopyright} 2008 Springer Science + Business Media B.V.}, isbn = {9781402069628}, issn = {18746500}, doi = {10.1007/978-1-4020-6964-2-16}, author = {Massimiliano Berti} } @article {2007, title = {Asymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy}, journal = {Comm. Pure Appl. Math. 60 (2007) 1559-1622}, number = {SISSA;83/2005/M}, year = {2007}, abstract = {We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition.}, doi = {10.1002/cpa.20195}, url = {http://hdl.handle.net/1963/1780}, author = {Stefano Bianchini and Bernard Hanouzet and Roberto Natalini} } @article {2007, title = {Asymptotic variational wave equations}, journal = {Arch. Ration. Mech. Anal. 183 (2007) 163-185}, number = {arXiv.org;math/0502124v1}, year = {2007}, abstract = {We investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data.}, doi = {10.1007/s00205-006-0014-8}, url = {http://hdl.handle.net/1963/2182}, author = {Alberto Bressan and Zhang Ping and Zheng Yuxi} } @article {Bertola:LOPs, title = {Biorthogonal Laurent polynomials, T{\"o}plitz determinants, minimal Toda orbits and isomonodromic tau functions}, journal = {Constr. Approx.}, volume = {26}, number = {3}, year = {2007}, pages = {383{\textendash}430}, issn = {0176-4276}, author = {Marco Bertola and Gekhtman, M.} } @article {Bertola:semiclassBOPsJAT, title = {Biorthogonal polynomials for two-matrix models with semiclassical potentials}, journal = {J. Approx. Theory}, volume = {144}, number = {2}, year = {2007}, pages = {162{\textendash}212}, issn = {0021-9045}, author = {Marco Bertola} } @article {2007, title = {BV instability for the Lax-Friedrichs scheme}, number = {SISSA;100/2004/M}, year = {2007}, abstract = {It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.}, url = {http://hdl.handle.net/1963/2335}, author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen} } @article {2007, title = {The cohomological crepant resolution conjecture for P(1,3,4,4)}, number = {arXiv:0712.3248;}, year = {2007}, note = {11 pages, 1 figure}, publisher = {SISSA}, abstract = {We prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results.}, url = {http://hdl.handle.net/1963/6513}, author = {Samuel Boissiere and Fabio Perroni and Etienne Mann} } @article {2007, title = {Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data}, journal = {Bioinformatics 23 (2007) 1640-1647}, year = {2007}, abstract = {Motivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/}, doi = {10.1093/bioinformatics/btm163}, url = {http://hdl.handle.net/1963/2028}, author = {Nicola Soranzo and Ginestra Bianconi and Claudio Altafini} } @article {2007, title = {Computing Amplitudes in topological M-theory}, number = {SISSA;74/2006/FM}, year = {2007}, abstract = {We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.}, doi = {10.1088/1126-6708/2007/03/023}, url = {http://hdl.handle.net/1963/1901}, author = {Giulio Bonelli and Alessandro Tanzini and Maxim Zabzine} } @article {Bertola:EffectiveIMRN, title = {Effective inverse spectral problem for rational Lax matrices and applications}, journal = {Int. Math. Res. Not. IMRN}, number = {23}, year = {2007}, pages = {Art. ID rnm103, 39}, issn = {1073-7928}, author = {Marco Bertola and Gekhtman, M.} } @article {2007, title = {On the Euler-Lagrange equation for a variational problem}, journal = {Discrete Contin. Dynam. Systems A 17 (2007) 449-480}, number = {SISSA;95/2005/M}, year = {2007}, url = {http://hdl.handle.net/1963/1792}, author = {Stefano Bianchini} } @article {2007, title = {Gaussian estimates for hypoelliptic operators via optimal control}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 333-342}, number = {SISSA;45/2007/M}, year = {2007}, abstract = {We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.}, doi = {10.4171/RLM/499}, url = {http://hdl.handle.net/1963/1994}, author = {Ugo Boscain and Sergio Polidoro} } @article {2007, title = {High-order angles in almost-Riemannian geometry}, number = {SISSA;59/2007/M}, year = {2007}, abstract = {Let X and Y be two smooth vector fields on a two-dimensional manifold M. If X and Y are everywhere linearly independent, then they define a Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become linearly dependent somewhere on M, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula for domains with piecewise-C2 boundary. The main feature of such formula is the presence of terms that play the role of high-order angles at the intersection points with the set of singularities.}, url = {http://hdl.handle.net/1963/1995}, author = {Ugo Boscain and Mario Sigalotti} } @article {2007, title = {The holomorphic anomaly for open string moduli}, journal = {JHEP 10 (2007) 060}, number = {SISSA;55/2007/EP}, year = {2007}, abstract = {We complete the holomorphic anomaly equations for topological strings with their dependence on open moduli. We obtain the complete system by standard path integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165 (1994) 311) to strings with boundaries. We study both the anti-holomorphic dependence on open moduli and on closed moduli in presence of Wilson lines. By providing the compactification a\\\' la Deligne-Mumford of the moduli space of Riemann surfaces with boundaries, we show that the open holomorphic anomaly equations are structured on the (real codimension one) boundary components of this space.}, doi = {10.1088/1126-6708/2007/10/060}, url = {http://hdl.handle.net/1963/2113}, author = {Giulio Bonelli and Alessandro Tanzini} } @inbook {Bertola:MasslessdeSitter, title = {Massless scalar field in a two-dimensional de Sitter universe}, booktitle = {Rigorous quantum field theory}, series = {Progr. Math.}, volume = {251}, year = {2007}, pages = {27{\textendash}38}, publisher = {Birkh{\"a}user}, organization = {Birkh{\"a}user}, address = {Basel}, author = {Marco Bertola and Corbetta, Francesco and Moschella, Ugo} } @article {2007, title = {Metrics on semistable and numerically effective Higgs bundles}, journal = {J. Reine Angew. Math. 612 (2007) 59-79}, number = {SISSA;17/2006/FM}, year = {2007}, abstract = {We consider fibre metrics on Higgs vector bundles on compact K\\\\\\\"ahler manifolds, providing notions of numerical effectiveness and numerical flatness in terms of such metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, providing semistability criteria for Higgs bundles on projective manifolds of any dimension.}, doi = {10.1515/CRELLE.2007.084}, url = {http://hdl.handle.net/1963/1840}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2007, title = {Nearly time optimal stabilizing patchy feedbacks}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310}, number = {arXiv.org;math/0512531v1}, year = {2007}, abstract = {We consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$.}, doi = {10.1016/j.anihpc.2006.03.010}, url = {http://hdl.handle.net/1963/2185}, author = {Fabio Ancona and Alberto Bressan} } @article {2007, title = {Numerically flat Higgs vector bundles}, number = {SISSA;39/2005/FM}, year = {2007}, abstract = {After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.}, doi = {10.1142/S0219199707002526}, url = {http://hdl.handle.net/1963/1757}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2007, title = {Perturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem}, year = {2007}, institution = {SISSA}, url = {http://preprints.sissa.it/handle/1963/35315}, author = {Stefano Bianchini} } @article {2007, title = {Semistable principal Higgs bundles}, number = {SISSA;89/2007/MP}, year = {2007}, url = {http://hdl.handle.net/1963/2533}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2007, title = {Time optimal swing-up of the planar pendulum}, journal = {46th IEEE Conference on Decision and Control (2007) 5389 - 5394}, number = {SISSA;50/2006/M}, year = {2007}, abstract = {This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.}, doi = {10.1109/CDC.2007.4434688}, url = {http://hdl.handle.net/1963/1867}, author = {Mireille E. Broucke and Paolo Mason and Benedetto Piccoli} } @article {2006, title = {A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs}, journal = {SIAM J. Math. Anal. 37 (2006) 83-102}, number = {arXiv.org;math/0310182v1}, year = {2006}, abstract = {In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.}, doi = {10.1137/S0036141003436107}, url = {http://hdl.handle.net/1963/2159}, author = {Dario Bambusi and Massimiliano Berti} } @article {2006, title = {On Bressan\\\'s conjecture on mixing properties of vector fields}, journal = {Self-Similar Solutions of Nonlinear PDE / Ed. Piotr Biler and Grzegorz Karch. - Banach Center Publ. 74 (2006) 13-31}, number = {SISSA;70/2005/M}, year = {2006}, url = {http://hdl.handle.net/1963/1806}, author = {Stefano Bianchini} } @article {2006, title = {Cantor families of periodic solutions for completely resonant nonlinear wave equations}, journal = {Duke Math. J. 134 (2006) 359-419}, number = {arXiv.org;math/0410618v1}, year = {2006}, abstract = {We prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.}, doi = {10.1215/S0012-7094-06-13424-5}, url = {http://hdl.handle.net/1963/2161}, author = {Massimiliano Berti and Philippe Bolle} } @article {2006, title = {Classification of stable time-optimal controls on 2-manifolds}, journal = {J. Math. Sci. 135 (2006) 3109-3124}, number = {SISSA;20/2004/M}, year = {2006}, doi = {10.1007/s10958-006-0148-0}, url = {http://hdl.handle.net/1963/2196}, author = {Ugo Boscain and Igor Nikolaev and Benedetto Piccoli} } @article {2006, title = {Common Polynomial Lyapunov Functions for Linear Switched Systems}, journal = {SIAM J. Control Optim. 45 (2006) 226-245}, number = {arXiv.org;math/0403209v2}, year = {2006}, abstract = {In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given.}, doi = {10.1137/040613147}, url = {http://hdl.handle.net/1963/2181}, author = {Paolo Mason and Ugo Boscain and Yacine Chitour} } @article {2006, title = {Conservative Solutions to a Nonlinear Variational Wave Equation}, journal = {Comm. Math. Phys. 266 (2006) 471-497}, number = {arXiv.org;math/0502058v1}, year = {2006}, abstract = {We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values.}, doi = {10.1007/s00220-006-0047-8}, url = {http://hdl.handle.net/1963/2184}, author = {Alberto Bressan and Zheng Yuxi} } @article {2006, title = {Forced vibrations of wave equations with non-monotone nonlinearities}, journal = {Ann. Inst. H. Poincar{\'e} Anal. Non Lin{\'e}aire 23 (2006) 439-474}, number = {arXiv.org;math/0410619v1}, year = {2006}, abstract = {We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz.}, doi = {10.1016/j.anihpc.2005.05.004}, url = {http://hdl.handle.net/1963/2160}, author = {Massimiliano Berti and Luca Biasco} } @article {2006, title = {Glimm interaction functional for BGK schemes}, number = {SISSA;69/2005/M}, year = {2006}, url = {http://hdl.handle.net/1963/1770}, author = {Stefano Bianchini} } @article {2006, title = {Infinite Horizon Noncooperative Differential Games}, number = {SISSA;31/2005/M}, year = {2006}, abstract = {For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.}, doi = {10.1016/j.jde.2006.01.005}, url = {http://hdl.handle.net/1963/1720}, author = {Alberto Bressan and Fabio Simone Priuli} } @article {2006, title = {An instability of the Godunov scheme}, journal = {Comm. Pure Appl. Math. 59 (2006) 1604-1638}, number = {arXiv.org;math/0502125v1}, year = {2006}, abstract = {We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes.}, doi = {10.1002/cpa.20141}, url = {http://hdl.handle.net/1963/2183}, author = {Alberto Bressan and Helge Kristian Jenssen and Paolo Baiti} } @article {2006, title = {Normal bundles to Laufer rational curves in local Calabi-Yau threefolds}, number = {SISSA;88/2005/FM}, year = {2006}, abstract = {We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.}, doi = {10.1007/s11005-006-0057-7}, url = {http://hdl.handle.net/1963/1785}, author = {Ugo Bruzzo and Antonio Ricco} } @article {Bertola:PDEBOPs, title = {The PDEs of biorthogonal polynomials arising in the two-matrix model}, journal = {Math. Phys. Anal. Geom.}, volume = {9}, number = {1}, year = {2006}, pages = {23{\textendash}52}, issn = {1385-0172}, author = {Marco Bertola and B. Eynard} } @article {Baldi2006257, title = {Periodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies}, journal = {Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni}, volume = {17}, number = {3}, year = {2006}, note = {cited By (since 1996)5}, pages = {257-277}, abstract = {We prove existence and multiplicity of small amplitude periodic solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for asymptotically full measure sets of frequencies, extending the results of [7] to new types of nonlinearities.}, issn = {11206330}, author = {P Baldi and Massimiliano Berti} } @article {2006, title = {Quasi-periodic solutions of completely resonant forced wave equations}, journal = {Comm. Partial Differential Equations 31 (2006) 959 - 985}, number = {SISSA;106/2004/M}, year = {2006}, abstract = {We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.}, doi = {10.1080/03605300500358129}, url = {http://hdl.handle.net/1963/2234}, author = {Massimiliano Berti and Michela Procesi} } @article {Bertola:Semiiso, title = {Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions}, journal = {Comm. Math. Phys.}, volume = {263}, number = {2}, year = {2006}, pages = {401{\textendash}437}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {2006, title = {Semistability vs. nefness for (Higgs) vector bundles}, journal = {Differential Geom. Appl. 24 (2006) 403-416}, number = {arXiv.org;math/0310040v3}, year = {2006}, abstract = {According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.}, doi = {10.1016/j.difgeo.2005.12.007}, url = {http://hdl.handle.net/1963/2237}, author = {Ugo Bruzzo and Daniel Hernandez Ruiperez} } @article {2006, title = {Stability of planar nonlinear switched systems}, number = {SISSA;04/2005/M}, year = {2006}, abstract = {We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 - u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,$\infty$) {\textrightarrow} {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.}, url = {http://hdl.handle.net/1963/1710}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Mario Sigalotti} } @article {2006, title = {Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field}, number = {SISSA;82/2005/M}, year = {2006}, abstract = {In this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| <= M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M {\textrightarrow} $\infty$ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E {\textrightarrow} 0, giving a partial proof of a conjecture formulated in a previous paper.}, doi = {10.1063/1.2203236}, url = {http://hdl.handle.net/1963/1734}, author = {Ugo Boscain and Paolo Mason} } @article {2006, title = {On topological M-theory}, number = {SISSA;64/2005/FM}, year = {2006}, abstract = {We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds.}, url = {http://hdl.handle.net/1963/1765}, author = {Giulio Bonelli and Alessandro Tanzini and Maxim Zabzine} } @article {2006, title = {Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds}, journal = {J. Geom. Phys. 56 (2006) 2379-2401}, number = {arXiv.org;hep-th/0412014v2}, year = {2006}, abstract = {We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT\\\'s (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.}, doi = {10.1016/j.geomphys.2005.12.006}, url = {http://hdl.handle.net/1963/2168}, author = {Laurent Baulieu and Alessandro Tanzini} } @article {Bertola:2MM_extendedWhitham, title = {Two-matrix model with semiclassical potentials and extended Whitham hierarchy}, journal = {J. Phys. A}, volume = {39}, number = {28}, year = {2006}, pages = {8823{\textendash}8855}, issn = {0305-4470}, author = {Marco Bertola} } @article {2005, title = {On the Blow-up for a Discrete Boltzmann Equation in the Plane}, journal = {Discrete Contin. Dyn. Syst. 13 (2005) 1-12}, number = {arXiv.org;math/0403047v2}, year = {2005}, abstract = {We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.}, url = {http://hdl.handle.net/1963/2244}, author = {Alberto Bressan and Massimo Fonte} } @article {2005, title = {Global solutions of the Hunter-Saxton equation}, journal = {SIAM J. Math. Anal. 37 (2005) 996-1026}, number = {SISSA;104/2004/M}, year = {2005}, abstract = {We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.}, doi = {10.1137/050623036}, url = {http://hdl.handle.net/1963/2256}, author = {Alberto Bressan and Adrian Constantin} } @article {Bertola:Isomono_resonant, title = {Isomonodromic deformation of resonant rational connections}, journal = {IMRP Int. Math. Res. Pap.}, number = {11}, year = {2005}, pages = {565{\textendash}635}, issn = {1687-3017}, author = {Marco Bertola and Mo, M. Y.} } @article {2005, title = {Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy}, journal = {Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990}, number = {SISSA;56/2004/M}, year = {2005}, abstract = {We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.}, url = {http://hdl.handle.net/1963/2259}, author = {Ugo Boscain and Thomas Chambrion and Gr{\'e}goire Charlot} } @article {2005, title = {An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation}, number = {SISSA;27/2005/M}, year = {2005}, abstract = {In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) <= κ {\textperiodcentered} J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.}, url = {http://hdl.handle.net/1963/1719}, author = {Alberto Bressan and Massimo Fonte} } @article {2005, title = {Periodic solutions of nonlinear wave equations with non-monotone forcing terms}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 117-124}, year = {2005}, publisher = {Accademia Nazionale dei Lincei}, url = {http://hdl.handle.net/1963/4581}, author = {Massimiliano Berti and Luca Biasco} } @article {2005, title = {Quasi-periodic oscillations for wave equations under periodic forcing}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (2005), no. 2, 109-116}, year = {2005}, publisher = {Accademia Nazionale dei Lincei}, url = {http://hdl.handle.net/1963/4583}, author = {Massimiliano Berti and Michela Procesi} } @inbook {2005, title = {A short introduction to optimal control}, booktitle = {Contr{\^o}le non lin{\'e}aire et applications: Cours donn{\'e}s {\`a} l\\\'{\'e}cole d\\\'{\'e}t{\'e} du Cimpa de l\\\'Universit{\'e} de Tlemcen / Sari Tewfit [ed.]. - Paris: Hermann, 2005}, number = {SISSA;10/2004/M}, year = {2005}, isbn = {2 7056 6511 0}, url = {http://hdl.handle.net/1963/2257}, author = {Ugo Boscain and Benedetto Piccoli} } @article {2005, title = {Time minimal trajectories for two-level quantum systems with drift}, number = {SISSA;5/2005/M}, year = {2005}, abstract = {On a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds.}, url = {http://hdl.handle.net/1963/1688}, author = {Ugo Boscain and Paolo Mason} } @article {2005, title = {Time Optimal Synthesis for Left-Invariant Control Systems on SO(3)}, journal = {SIAM J. Control Optim. 44 (2005) 111-139}, number = {SISSA;21/2004/M}, year = {2005}, abstract = {Consider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations.}, doi = {10.1137/S0363012904441532}, url = {http://hdl.handle.net/1963/2258}, author = {Ugo Boscain and Yacine Chitour} } @article {2005, title = {Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry}, number = {SISSA;24/2005/FM}, year = {2005}, abstract = {The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincar{\'e} supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting \\\"equivariant topological field theory\\\" corresponds to the twist of super Yang-Mills theory on omega backgrounds.}, doi = {10.1088/1126-6708/2005/08/037}, url = {http://hdl.handle.net/1963/1741}, author = {Laurent Baulieu and Guillaume Bossard and Alessandro Tanzini} } @article {2005, title = {Vanishing viscosity solutions of nonlinear hyperbolic systems}, journal = {Ann. of Math. 161 (2005) 223-342}, number = {SISSA;86/2001/M}, year = {2005}, publisher = {Annals of Mathematics}, abstract = {We consider the Cauchy problem for a strictly hyperbolic, $n\\\\times n$ system in one space dimension: $u_t+A(u)u_x=0$, assuming that the initial data has small total variation.\\nWe show that the solutions of the viscous approximations $u_t+A(u)u_x=\\\\ve u_{xx}$ are defined globally in time and satisfy uniform BV estimates, independent of $\\\\ve$. Moreover, they depend continuously on the initial data in the $\\\\L^1$ distance, with a Lipschitz constant independent of $t,\\\\ve$. Letting $\\\\ve\\\\to 0$, these viscous solutions converge to a unique limit, depending Lipschitz continuously on the initial data. In the conservative case where $A=Df$ is the Jacobian of some flux function $f:\\\\R^n\\\\mapsto\\\\R^n$, the vanishing viscosity limits are precisely the unique entropy weak solutions to the system of conservation laws $u_t+f(u)_x=0$.}, url = {http://hdl.handle.net/1963/3074}, author = {Stefano Bianchini and Alberto Bressan} } @article {2004, title = {Bifurcation of free vibrations for completely resonant wave equations}, journal = {Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528}, number = {SISSA;27/2004/M}, year = {2004}, abstract = {We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.}, url = {http://hdl.handle.net/1963/2245}, author = {Massimiliano Berti and Philippe Bolle} } @article {2004, title = {On the convergence rate of vanishing viscosity approximations}, journal = {Comm. Pure Appl. Math. 57 (2004) 1075-1109}, number = {SISSA;60/2003/M}, year = {2004}, publisher = {Wiley}, abstract = {Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.}, doi = {10.1002/cpa.20030}, url = {http://hdl.handle.net/1963/2915}, author = {Alberto Bressan and Tong Yang} } @article {2004, title = {A geometric approach to the separability of the Neumann-Rosochatius system}, journal = {Differential Geom. Appl. 21 (2004) 349-360}, number = {arXiv.org;nlin/0307021}, year = {2004}, abstract = {We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.}, doi = {10.1016/j.difgeo.2004.07.001}, url = {http://hdl.handle.net/1963/2541}, author = {Claudio Bartocci and Gregorio Falqui and Marco Pedroni} } @proceedings {2004, title = {On the minimal degree of a common Lyapunov function for planar switched systems}, year = {2004}, publisher = {IEEE}, abstract = {In this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin.}, doi = {10.1109/CDC.2004.1428884}, url = {http://hdl.handle.net/1963/4834}, author = {Paolo Mason and Ugo Boscain and Yacine Chitour} } @article {2004, title = {Multiplicity of periodic solutions of nonlinear wave equations}, journal = {Nonlinear Anal. 56 (2004) 1011-1046}, year = {2004}, publisher = {Elsevier}, doi = {10.1016/j.na.2003.11.001}, url = {http://hdl.handle.net/1963/2974}, author = {Massimiliano Berti and Philippe Bolle} } @article {2004, title = {Periodic orbits close to elliptic tori and applications to the three-body problem}, journal = {Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004) 87-138}, number = {SISSA;28/2003/M}, year = {2004}, publisher = {Scuola Normale Superiore di Pisa}, abstract = {We prove, under suitable non-resonance and non-degeneracy {\textquoteleft}{\textquoteleft}twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the {\textquoteleft}{\textquoteleft}planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.)}, url = {http://hdl.handle.net/1963/2985}, author = {Massimiliano Berti and Luca Biasco and Enrico Valdinoci} } @article {2004, title = {Resonance of minimizers for n-level quantum systems with an arbitrary cost}, journal = {ESAIM COCV 10 (2004) 593-614}, number = {SISSA;58/2003/M}, year = {2004}, publisher = {EDP Sciences}, abstract = {We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer.}, doi = {10.1051/cocv:2004022}, url = {http://hdl.handle.net/1963/2910}, author = {Ugo Boscain and Gr{\'e}goire Charlot} } @article {2004, title = {Semi-cooperative strategies for differential games}, journal = {Internat. J. Game Theory 32 (2004) 561-593}, number = {SISSA;103/2003/M}, year = {2004}, publisher = {Springer}, abstract = {The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative \\\"semi-cooperative\\\" pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.}, doi = {10.1007/s001820400180}, url = {http://hdl.handle.net/1963/2893}, author = {Alberto Bressan and Wen Shen} } @article {2004, title = {A sharp decay estimate for positive nonlinear waves}, journal = {SIAM J. Math. Anal. 36 (2004) 659-677}, number = {SISSA;59/2003/M}, year = {2004}, publisher = {SIAM}, abstract = {We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers\\\' equation with impulsive sources.}, doi = {10.1137/S0036141003427774}, url = {http://hdl.handle.net/1963/2916}, author = {Alberto Bressan and Tong Yang} } @article {2004, title = {Small BV solutions of hyperbolic noncooperative differential games}, journal = {SIAM J. Control Optim. 43 (2004) 194-215}, number = {SISSA;21/2003/M}, year = {2004}, publisher = {SIAM}, abstract = {The paper is concerned with an n-persons differential game in one space dimension. We state conditions for which the system of Hamilton-Jacobi equations for the value functions is strictly hyperbolic. In the positive case, we show that the weak solution of a corresponding system of conservation laws determines an n-tuple of feedback strategies. These yield a Nash equilibrium solution to the non-cooperative differential game.}, doi = {10.1137/S0363012903425581}, url = {http://hdl.handle.net/1963/2917}, author = {Alberto Bressan and Wen Shen} } @article {2004, title = {Soluzioni periodiche di PDEs Hamiltoniane}, journal = {Bollettino dell\\\'Unione Matematica Italiana Serie 8 7-B (2004), p. 647-661}, year = {2004}, publisher = {Unione Matematica Italiana}, url = {http://hdl.handle.net/1963/4582}, author = {Massimiliano Berti} } @article {2004, title = {Some remarks on multidimensional systems of conservation laws}, journal = {Rend. Mat. Acc. Lincei, s. 9, v. 15 (2004) 3-4, pp. 225 - 233}, year = {2004}, publisher = {Accademia Nazionale dei Lincei}, abstract = {This note is concerned with the Cauchy problem for hyperbolic systems of conservation\\nlaws in several space dimensions. We first discuss an example of ill-posedness, for a special system\\nhaving a radial symmetry property. Some conjectures are formulated, on the compactness of the set of\\nflow maps generated by vector fields with bounded variation.}, url = {http://hdl.handle.net/1963/3642}, author = {Alberto Bressan} } @article {2004, title = {Stability rates for patchy vector fields}, journal = {ESAIM COCV 10 (2004) 168-200}, number = {arXiv.org;math/0111109v1}, year = {2004}, publisher = {EDP Sciences}, abstract = {This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term.}, doi = {10.1051/cocv:2004003}, url = {http://hdl.handle.net/1963/2959}, author = {Fabio Ancona and Alberto Bressan} } @article {2004, title = {Superlocalization formulas and supersymmetric Yang-Mills theories}, journal = {Nucl. Phys. B 678 (2004) 638-655}, number = {arXiv.org;math-ph/0310036v1}, year = {2004}, publisher = {Elsevier}, abstract = {By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.}, doi = {10.1016/j.nuclphysb.2003.11.033}, url = {http://hdl.handle.net/1963/2886}, author = {Ugo Bruzzo and Francesco Fucito} } @article {Bertola:BilinearJAT, title = {Bilinear semiclassical moment functionals and their integral representation}, journal = {J. Approx. Theory}, volume = {121}, number = {1}, year = {2003}, pages = {71{\textendash}99}, issn = {0021-9045}, author = {Marco Bertola} } @article {2003, title = {The calibration method for the Mumford-Shah functional and free-discontinuity problems}, journal = {Calc. Var. Partial Differential Equations 16 (2003) 299-333}, number = {SISSA;35/2001/M}, year = {2003}, publisher = {Springer}, abstract = {We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.}, doi = {10.1007/s005260100152}, url = {http://hdl.handle.net/1963/3051}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} } @article {Bertola:DifferentialCMP, title = {Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem}, journal = {Comm. Math. Phys.}, volume = {243}, number = {2}, year = {2003}, pages = {193{\textendash}240}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {2003, title = {Drift in phase space: a new variational mechanism with optimal diffusion time}, journal = {J. Math. Pures Appl. 82 (2003) 613-664}, number = {arXiv.org;math/0205307v1}, year = {2003}, publisher = {Elsevier}, abstract = {We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of {\textquoteleft}{\textquoteleft}transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory.}, doi = {10.1016/S0021-7824(03)00032-1}, url = {http://hdl.handle.net/1963/3020}, author = {Massimiliano Berti and Luca Biasco and Philippe Bolle} } @article {Bertola:Duality, title = {The duality of spectral curves that arises in two-matrix models}, journal = {Teoret. Mat. Fiz.}, volume = {134}, number = {1}, year = {2003}, pages = {32{\textendash}45}, issn = {0564-6162}, author = {Marco Bertola and B. Eynard and Kharnad, Dzh.} } @article {Bertola:FreeEnergyNPB, title = {Free energy of the two-matrix model/dToda tau-function}, journal = {Nuclear Phys. B}, volume = {669}, number = {3}, year = {2003}, pages = {435{\textendash}461}, issn = {0550-3213}, author = {Marco Bertola} } @article {2003, title = {An ill posed Cauchy problem for a hyperbolic system in two space dimensions}, number = {SISSA;12/2003/M}, year = {2003}, publisher = {Universit{\`a} di Padova}, abstract = {The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed.}, url = {http://hdl.handle.net/1963/2913}, author = {Alberto Bressan} } @article {2003, title = {A lemma and a conjecture on the cost of rearrangements}, journal = {Rend. Sem. Mat. Univ. Padova 110 (2003) 97-102}, number = {SISSA;13/2003/M}, year = {2003}, publisher = {Universit{\`a} di Padova}, abstract = {Consider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement.}, url = {http://hdl.handle.net/1963/2914}, author = {Alberto Bressan} } @article {Bertola:MixedJPA, title = {Mixed correlation functions of the two-matrix model}, journal = {J. Phys. A}, volume = {36}, number = {28}, year = {2003}, pages = {7733{\textendash}7750}, issn = {0305-4470}, author = {Marco Bertola and B. Eynard} } @article {2003, title = {Multi-instanton calculus and equivariant cohomology}, journal = {J.High Energy Phys. 2003,no.5,054,24 pp.}, number = {SISSA;75/2002/FM}, year = {2003}, publisher = {SISSA Library}, doi = {10.1088/1126-6708/2003/05/054}, url = {http://hdl.handle.net/1963/1645}, author = {Ugo Bruzzo and Jose F. Morales and Francesco Fucito and Alessandro Tanzini} } @article {2003, title = {A note on singular limits to hyperbolic systems of conservation laws}, journal = {Commun. Pure Appl. Ana., 2003, 2, 51-64}, number = {SISSA;85/00/M}, year = {2003}, publisher = {SISSA Library}, abstract = {In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation.}, url = {http://hdl.handle.net/1963/1542}, author = {Stefano Bianchini} } @article {Bertola:PartitionJPA, title = {Partition functions for matrix models and isomonodromic tau functions}, journal = {J. Phys. A}, volume = {36}, number = {12}, year = {2003}, note = {Random matrix theory}, pages = {3067{\textendash}3083}, issn = {0305-4470}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {2003, title = {Periodic solutions of nonlinear wave equations with general nonlinearities}, journal = {Comm.Math.Phys. 243 (2003) no.2, 315}, number = {SISSA;78/2002/M}, year = {2003}, publisher = {SISSA Library}, doi = {10.1007/s00220-003-0972-8}, url = {http://hdl.handle.net/1963/1648}, author = {Massimiliano Berti and Philippe Bolle} } @article {Bertola:JPA, title = {Second and third order observables of the two-matrix model}, journal = {J. High Energy Phys.}, number = {11}, year = {2003}, pages = {062, 30 pp. (electronic)}, issn = {1126-6708}, author = {Marco Bertola} } @article {2003, title = {Some results on the boundary control of systems of conservation laws}, journal = {SIAM J.Control Optim. 41 (2003),no.2, 607}, number = {SISSA;44/2002/M}, year = {2003}, publisher = {SISSA Library}, doi = {10.1137/S0363012901392529}, url = {http://hdl.handle.net/1963/1615}, author = {Alberto Bressan and Fabio Ancona and Giuseppe Maria Coclite} } @article {2002, title = {Arnold diffusion: a functional analysis approach}, journal = {Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 43, Part 1, 2, Natsional. Akad. Nauk Ukra{\"\i}ni, Inst. Mat., Kiev, 2002}, year = {2002}, publisher = {Natsional. Akad. Nauk Ukra{\"\i}ni}, abstract = {We present, in the context of nearly integrable Hamiltonian systems, a functional analysis approach to study the {\textquotedblleft}splitting of the whiskers{\textquotedblright} and the {\textquotedblleft}shadowing problem{\textquotedblright} developed in collaboration with P. Bolle in the recent papers [1] and [2] . This method is applied to the problem of Arnold diffusion for nearly integrable partially isochronous systems improving known results.}, author = {Massimiliano Berti} } @article {2002, title = {On the Boundary Control of Systems of Conservation Laws}, journal = {SIAM J. Control Optim. 41 (2002) 607-622}, number = {SISSA;50/2001/M}, year = {2002}, publisher = {SIAM}, abstract = {The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general.}, doi = {10.1137/S0363012901392529}, url = {http://hdl.handle.net/1963/3070}, author = {Alberto Bressan and Giuseppe Maria Coclite} } @article {2002, title = {A center manifold technique for tracing viscous waves}, journal = {Commun. Pure Appl. Anal. 1 (2002) 161-190}, number = {SISSA;85/2001/M}, year = {2002}, publisher = {American Institute of Mathematical Sciences}, abstract = {In this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.}, url = {http://hdl.handle.net/1963/3075}, author = {Stefano Bianchini and Alberto Bressan} } @article {2002, title = {Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems}, journal = {Nonlinear Anal. 48 (2002) 481-504}, number = {SISSA;65/99/M}, year = {2002}, publisher = {Elsevier}, doi = {10.1016/S0362-546X(00)00200-5}, url = {http://hdl.handle.net/1963/1279}, author = {Massimiliano Berti and Carlo Carminati} } @article {Bertola:CoherentJMP, title = {Coherent state realizations of $\rm su(n+1)$ on the $n$-torus}, journal = {J. Math. Phys.}, volume = {43}, number = {7}, year = {2002}, pages = {3425{\textendash}3444}, issn = {0022-2488}, author = {de Guise, Hubert and Marco Bertola} } @article {2002, title = {Curvature theory of boundary phases: the two-dimensional case}, journal = {Interfaces Free Bound. 7 (2002) 345-370}, year = {2002}, publisher = {European Mathematical Society}, abstract = {We describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.}, url = {http://hdl.handle.net/1963/3537}, author = {Andrea Braides and Andrea Malchiodi} } @article {Bertola:DualityCMP, title = {Duality, biorthogonal polynomials and multi-matrix models}, journal = {Comm. Math. Phys.}, volume = {229}, number = {1}, year = {2002}, pages = {73{\textendash}120}, issn = {0010-3616}, author = {Marco Bertola and B. Eynard and Harnad, J.} } @article {2002, title = {Fast Arnold diffusion in systems with three time scales}, journal = {Discrete Contin. Dyn. Syst. 8 (2002) 795-811}, number = {SISSA;21/2001/M}, year = {2002}, publisher = {American Institute of Mathematical Sciences}, abstract = {We consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diffusion takes place with fast (polynomial) speed, even though the \\\"splitting determinant\\\" is exponentially small.}, url = {http://hdl.handle.net/1963/3058}, author = {Massimiliano Berti and Philippe Bolle} } @article {2002, title = {Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization}, journal = {SIAM J. Control Optim. 41 (2002) 1455-1476}, number = {SISSA;71/2001/M}, year = {2002}, publisher = {SIAM}, abstract = {The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances.}, doi = {10.1137/S0363012901391676}, url = {http://hdl.handle.net/1963/3073}, author = {Fabio Ancona and Alberto Bressan} } @article {2002, title = {A functional analysis approach to Arnold diffusion}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 19 (2002) 395-450}, year = {2002}, publisher = {Elsevier}, abstract = {We discuss in the context of nearly integrable Hamiltonian systems a functional analysis approach to the \\\"splitting of separatrices\\\" and to the \\\"shadowing problem\\\". As an application we apply our method to the problem of Arnold Diffusion for nearly integrable partially isochronous systems improving known results.}, doi = {10.1016/S0294-1449(01)00084-1}, url = {http://hdl.handle.net/1963/3151}, author = {Massimiliano Berti and Philippe Bolle} } @inbook {Bertola:JacobiCRM, title = {Jacobi groups, Jacobi forms and their applications}, booktitle = {Isomonodromic deformations and applications in physics (Montr{\'e}al, QC, 2000)}, series = {CRM Proc. Lecture Notes}, volume = {31}, year = {2002}, pages = {99{\textendash}111}, publisher = {Amer. Math. Soc.}, organization = {Amer. Math. Soc.}, address = {Providence, RI}, author = {Marco Bertola} } @article {2002, title = {On the K+P problem for a three-level quantum system: optimality implies resonance}, journal = {J.Dynam. Control Systems 8 (2002),no.4, 547}, number = {SISSA;30/2002/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1023/A:1020767419671}, url = {http://hdl.handle.net/1963/1601}, author = {Ugo Boscain and Thomas Chambrion and Jean-Paul Gauthier} } @article {2002, title = {On a Lyapunov functional relating shortening curves and viscous conservation laws}, journal = {Nonlinear Anal. 51 (2002) 649-662}, number = {SISSA;123/99/M}, year = {2002}, publisher = {Elsevier}, abstract = {We study a nonlinear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the \\\"change of shape\\\" of a BV solution to a scalar conservation law.}, doi = {10.1016/S0362-546X(01)00848-3}, url = {http://hdl.handle.net/1963/1337}, author = {Stefano Bianchini and Alberto Bressan} } @article {2002, title = {An optimal fast-diffusion variational method for non isochronous system}, number = {SISSA;8/2002/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1579}, author = {Luca Biasco and Massimiliano Berti and Philippe Bolle} } @article {2002, title = {Optimal stability and instability results for a class of nearly integrable Hamiltonian systems}, journal = {Atti.Accad.Naz.Lincei Cl.Sci.Fis.Mat.Natur.Rend.Lincei (9) Mat.Appl.13(2002),no.2,77-84}, number = {SISSA;25/2002/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1596}, author = {Massimiliano Berti and Luca Biasco and Philippe Bolle} } @article {2002, title = {The passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case}, journal = {Proc. Steklov Inst. Math. 236 (2002) 395-414}, number = {SISSA;11/2001/M}, year = {2002}, publisher = {MAIK Nauka/Interperiodica}, url = {http://hdl.handle.net/1963/3130}, author = {Andrea Braides and Maria Stella Gelli and Mario Sigalotti} } @article {2002, title = {On the reachability of quantized control systems}, journal = {IEEE Trans. Automat. Contr. 47 (2002) 546-563}, number = {SISSA;43/00/M}, year = {2002}, publisher = {SISSA Library}, abstract = {In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.}, doi = {10.1109/9.995034}, url = {http://hdl.handle.net/1963/1501}, author = {Antonio Bicchi and Alessia Marigo and Benedetto Piccoli} } @article {2002, title = {Relatively stable bundles over elliptic fibrations}, journal = {Math. Nachr. 238 (2002) 23-36}, number = {arXiv.org;math/0109123v2}, year = {2002}, publisher = {Wiley}, abstract = {We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah\\\'s and Tu\\\'s results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.}, url = {http://hdl.handle.net/1963/3132}, author = {Claudio Bartocci and Ugo Bruzzo and Daniel Hernandez Ruiperez and Jose M. Munoz Porras} } @article {2002, title = {Stability of planar switched systems: the linear single input case}, journal = {SIAM J. Control Optim. 41 (2002), no. 1, 89-112}, number = {SISSA;72/00/M}, year = {2002}, publisher = {SIAM}, abstract = {We study the stability of the origin for the dynamical system $\\\\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where A and B are two 2 {\texttimes} 2 real matrices with eigenvalues having strictly negative real part, $x\\\\in {\\\\mbox{{\\\\bf R}}}^2$, and $u(.):[0,\\\\infty[\\\\to[0,1]$ is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). The result is obtained without looking for a common Lyapunov function but studying the locus in which the two vector fields Ax and Bx are collinear. There are only three relevant parameters: the first depends only on the eigenvalues of A, the second depends only on the eigenvalues of B, and the third contains the interrelation among the two systems, and it is the cross ratio of the four eigenvectors of A and B in the projective line CP1. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied.}, doi = {10.1137/S0363012900382837}, url = {http://hdl.handle.net/1963/1529}, author = {Ugo Boscain} } @article {2002, title = {On the Stability of the Standard Riemann Semigroup}, journal = {P. Am. Math. Soc., 2002, 130, 1961}, number = {SISSA;71/00/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1528}, author = {Stefano Bianchini and Rinaldo M. Colombo} } @article {2001, title = {A case study in vanishing viscosity}, journal = {Discrete Cont. Dyn. Syst. 7 (2001) 449-476}, year = {2001}, publisher = {American Institute of Mathematical Sciences}, url = {http://hdl.handle.net/1963/3091}, author = {Stefano Bianchini and Alberto Bressan} } @article {2001, title = {Complex Lagrangian embeddings of moduli spaces of vector bundles}, journal = {Differential Geom. Appl. 14 (2001) 151-156}, number = {arXiv.org;math/0010249v1}, year = {2001}, publisher = {Elsevier}, abstract = {By means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of special Lagrangian submanifolds.}, doi = {10.1016/S0926-2245(00)00040-1}, url = {http://hdl.handle.net/1963/2885}, author = {Ugo Bruzzo and Fabio Pioli} } @article {2001, title = {Extremal synthesis for generic planar systems}, journal = {J. Dynam. Control Systems, 2001, 7, 209}, number = {SISSA;45/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1023/A:1013003204923}, url = {http://hdl.handle.net/1963/1503}, author = {Ugo Boscain and Benedetto Piccoli} } @article {2001, title = {A Fourier transform for sheaves on real tori. I. The equivalence Sky(T)~ Loc (T)}, journal = {J. Geom. Phys. 39 (2001), no. 2, 174--182}, number = {SISSA;68/00/FM}, year = {2001}, publisher = {SISSA Library}, doi = {10.1016/S0393-0440(01)00009-2}, url = {http://hdl.handle.net/1963/1526}, author = {Ugo Bruzzo and Giovanni Marelli and Fabio Pioli} } @article {2001, title = {A Glimm type functional for a special Jin-Xin relaxation model}, journal = {Ann. Inst. H. Poincare\\\' Anal. Non Lineaire 18 (2001), no. 1, 19-42}, number = {SISSA;140/99/M}, year = {2001}, publisher = {Elsevier}, doi = {10.1016/S0294-1449(00)00124-4}, url = {http://hdl.handle.net/1963/1355}, author = {Stefano Bianchini} } @article {Bertola:LietripleRMA, title = {Lie triple systems and warped products}, journal = {Rend. Mat. Appl. (7)}, volume = {21}, number = {1-4}, year = {2001}, pages = {275{\textendash}293}, issn = {1120-7183}, author = {Marco Bertola and Gouthier, D.} } @article {2001, title = {Morse properties for the minimum time function on 2-D manifolds}, journal = {J. Dynam. Control Systems 7 (2001), no. 3, 385--423}, number = {SISSA;84/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1023/A:1013190914234}, url = {http://hdl.handle.net/1963/1541}, author = {Ugo Boscain and Benedetto Piccoli} } @article {2001, title = {On the Multi-Instanton Measure for Super Yang-Mills Theories}, journal = {Nuclear Phys. B 611 (2001), no. 1-3, 205--226.}, number = {SISSA;74/00/FM}, year = {2001}, publisher = {SISSA Library}, doi = {10.1016/S0550-3213(01)00349-2}, url = {http://hdl.handle.net/1963/1531}, author = {Ugo Bruzzo and Francesco Fucito and Alessandro Tanzini and Gabriele Travaglini} } @article {2001, title = {Non-compactness and multiplicity results for the Yamabe problem on Sn}, journal = {J. Funct. Anal. 180 (2001) 210-241}, number = {SISSA;130/99/M}, year = {2001}, publisher = {Elsevier}, doi = {10.1006/jfan.2000.3699}, url = {http://hdl.handle.net/1963/1345}, author = {Massimiliano Berti and Andrea Malchiodi} } @article {2001, title = {Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions}, journal = {Siam J. Math. Anal., 2001, 33, 959}, number = {SISSA;65/00/M}, year = {2001}, publisher = {SISSA Library}, abstract = {We consider a hyperbolic system of conservation laws u_t + f(u)_x = 0 and u(0,\\\\cdot) = u_0, where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates $w$, we prove that there exists a semigroup of solutions $u(t) = \\\\mathcal{S}_t u_0$, defined on initial data $u_0 \\\\in L^\\\\infty$. The semigroup $\\\\mathcal{S}$ is continuous w.r.t. time and the initial data $u_0$ in the $L^1_{\\\\text{loc}}$ topology. Moreover $\\\\mathcal{S}$ is unique and its trajectories are obtained as limits of wave front tracking approximations.}, doi = {10.1137/S0036141000377900}, url = {http://hdl.handle.net/1963/1523}, author = {Stefano Bianchini} } @article {2001, title = {Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems}, journal = {J. Differential Equations 172 (2001) 59-82}, year = {2001}, publisher = {Elsevier}, doi = {10.1006/jdeq.2000.3869}, url = {http://hdl.handle.net/1963/3113}, author = {Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli} } @article {Bertola:Warped, title = {Warped products with special Riemannian curvature}, journal = {Bol. Soc. Brasil. Mat. (N.S.)}, volume = {32}, number = {1}, year = {2001}, pages = {45{\textendash}62}, issn = {0100-3569}, author = {Marco Bertola and Gouthier, Daniele} } @article {2000, title = {Abnormal extremals for minimum time on the plane}, number = {SISSA;50/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1508}, author = {Ugo Boscain and Benedetto Piccoli} } @article {2000, title = {Arnold{\textquoteright}s Diffusion in nearly integrable isochronous Hamiltonian systems}, number = {SISSA;98/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1554}, author = {Massimiliano Berti and Philippe Bolle} } @article {2000, title = {BV estimates for multicomponent chromatography with relaxation}, journal = {Discrete Contin. Dynam. Systems 6 (2000) 21-38}, number = {SISSA;122/99/M}, year = {2000}, publisher = {SISSA Library}, abstract = {We consider the Cauchy problem for a system of $2n$ balance laws which arises from the modelling of multi-component chromatography: $$\\\\left\\\\{ \\\\eqalign{u_t+u_x\&=-{1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr v_t\&={1\\\\over\\\\ve}\\\\big( F(u)-v\\\\big),\\\\cr}\\\\right. \\\\eqno(1)$$ This model describes a liquid flowing with unit speed over a solid bed. Several chemical substances are partly dissolved in the liquid, partly deposited on the solid bed. Their concentrations are represented respectively by the vectors $u=(u_1,\\\\ldots,u_n)$ and $v=(v_1,\\\\ldots,v_n)$. We show that, if the initial data have small total variation, then the solution of (1) remains with small variation for all times $t\\\\geq 0$. Moreover, using the $\\\\L^1$ distance, this solution depends Lipschitz continuously on the initial data, with a Lipschitz constant uniform w.r.t.~$\\\\ve$. Finally we prove that as $\\\\ve\\\\to 0$, the solutions of (1) converge to a limit described by the system $$\\\\big(u+F(u)\\\\big)_t+u_x=0,\\\\qquad\\\\qquad v=F(u).\\\\eqno(2)$$ The proof of the uniform BV estimates relies on the application of probabilistic techniques. It is shown that the components of the gradients $v_x,u_x$ can be interpreted as densities of random particles travelling with speed 0 or 1. The amount of coupling between different components is estimated in terms of the expected number of crossing of these random particles. This provides a first example where BV estimates are proved for general solutions to a class of $2n\\\\times 2n$ systems with relaxation.}, url = {http://hdl.handle.net/1963/1336}, author = {Alberto Bressan and Wen Shen} } @article {2000, title = {BV solutions for a class of viscous hyperbolic systems}, journal = {Indiana Univ. Math. J. 49 (2000) 1673-1714}, year = {2000}, publisher = {Indiana University Mathematics Journal}, doi = {10.1512/iumj.2000.49.1776}, url = {http://hdl.handle.net/1963/3194}, author = {Stefano Bianchini and Alberto Bressan} } @article {2000, title = {On the convergence of Godunov scheme for nonlinear hyperbolic systems}, journal = {Chinese Ann. Math. B, 2000, 21, 269}, number = {SISSA;15/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1473}, author = {Alberto Bressan and Helge Kristian Jenssen} } @article {Bertola:DecomposingNPB, title = {Decomposing quantum fields on branes}, journal = {Nuclear Phys. B}, volume = {581}, number = {1-2}, year = {2000}, pages = {575{\textendash}603}, issn = {0550-3213}, author = {Marco Bertola and Bros, Jacques and Gorini, Vittorio and Moschella, Ugo and Schaeffer, Richard} } @article {2000, title = {Diffusion time and splitting of separatrices for nearly integrable}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235}, number = {SISSA;90/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1547}, author = {Massimiliano Berti and Philippe Bolle} } @article {Bertola:Frobenius1, title = {Frobenius manifold structure on orbit space of Jacobi groups. I}, journal = {Differential Geom. Appl.}, volume = {13}, number = {1}, year = {2000}, pages = {19{\textendash}41}, issn = {0926-2245}, author = {Marco Bertola} } @article {Bertola:Frobenius2, title = {Frobenius manifold structure on orbit space of Jacobi groups. II}, journal = {Differential Geom. Appl.}, volume = {13}, number = {3}, year = {2000}, pages = {213{\textendash}233}, issn = {0926-2245}, author = {Marco Bertola} } @article {Bertola:CFTNPB, title = {A general construction of conformal field theories from scalar anti-de Sitter quantum field theories}, journal = {Nuclear Phys. B}, volume = {587}, number = {1-3}, year = {2000}, pages = {619{\textendash}644}, issn = {0550-3213}, author = {Marco Bertola and Bros, Jacques and Moschella, Ugo and Schaeffer, Richard} } @article {2000, title = {Quantized control systems and discrete nonholonomy}, journal = {Lagrangian and Hamiltonian Methods for Nonlinear Control : a proc. volume from the IFAC Workshop. Princeton, New Jersey, 16-18 March 2000 / ed. by N.E. Leonard, R. Ortega. - Oxford : Pergamon, 2000}, number = {SISSA;44/00/M}, year = {2000}, publisher = {Elsevier}, isbn = {0-08-043658-7}, url = {http://hdl.handle.net/1963/1502}, author = {Alessia Marigo and Benedetto Piccoli and Antonio Bicchi} } @inbook {2000, title = {Reachability Analysis for a Class of Quantized Control Systems}, booktitle = {Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968}, year = {2000}, publisher = {IEEE}, organization = {IEEE}, abstract = {We study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure.}, doi = {10.1109/CDC.2000.912333}, url = {http://hdl.handle.net/1963/3518}, author = {Alessia Marigo and Benedetto Piccoli and Antonio Bicchi} } @article {2000, title = {The semigroup generated by a Temple class system with non-convex flux function}, journal = {Differential Integral Equations 13 (2000) 1529-1550}, number = {SISSA;107/98/M}, year = {2000}, publisher = {Khayyam Publishing}, abstract = {We consider the Cauchy problem for a nonlinear n {\texttimes} n system of conservation laws of Temple class, i.e. with coinciding shock and rarefaction curves and with a coordinate system made of Riemann invariants. Without any assumption on the convexity of the flux function, we prove the existence of a semigroup made of weak solutions of the equations and depending Lipschitz continuously on the initial data with bounded total variation.}, url = {http://hdl.handle.net/1963/3221}, author = {Stefano Bianchini} } @article {2000, title = {On the shift differentiability of the flow generated by a hyperbolic system of conservation laws}, journal = {Discrete Contin. Dynam. Systems 6 (2000), no. 2, 329-350}, number = {SISSA;60/99/M}, year = {2000}, publisher = {American Institute of Mathematical Sciences}, doi = {10.3934/dcds.2000.6.329}, url = {http://hdl.handle.net/1963/1274}, author = {Stefano Bianchini} } @article {2000, title = {Stability of L^infty Solutions of Temple Class Systems}, journal = {Differential Integral Equations 13 (2000) 1503-1528}, number = {SISSA;134/98/M}, year = {2000}, publisher = {Khayyam Publishing}, abstract = {

Let $u_t+f(u)_x=0$ be a strictly hyperbolic, genuinely nonlinear system of conservation laws of Temple class. In this paper, a continuous semigroup of solutions is constructed on a domain of $L^\infty$ functions, with possibly unbounded variation. Trajectories depend Lipschitz continuously on the initial data, in the $L^1$ distance. Moreover, we show that a weak solution of the Cauchy problem coincides with the corresponding semigroup trajectory if and only if it satisfies an entropy condition of Oleinik type, concerning the decay of positive waves.

}, url = {http://hdl.handle.net/1963/3256}, author = {Alberto Bressan and Paola Goatin} } @article {2000, title = {A Uniqueness Condition for Hyperbolic Systems of Conservation Laws}, journal = {Discrete Contin. Dynam. Systems 6 (2000) 673-682}, number = {SISSA;88/98/M}, year = {2000}, publisher = {American Institute of Mathematical Sciences}, abstract = {Consider the Cauchy problem for a hyperbolic $n\\\\times n$ system of conservation laws in one space dimension: $$u_t+f(u)_x=0, u(0,x)=\\\\bar u(x).\\\\eqno(CP)$$ Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions $u=u(t,x)$ which have bounded variation along a suitable family of space-like curves.}, url = {http://hdl.handle.net/1963/3195}, author = {Alberto Bressan and Marta Lewicka} } @book {2000, title = {Well-posedness of the Cauchy problem for n x n systems of conservation laws}, series = {Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p.}, number = {SISSA;184/96/M}, year = {2000}, note = {Chapter 1 and 2}, publisher = {American Mathematical Society}, organization = {American Mathematical Society}, url = {http://hdl.handle.net/1963/3495}, author = {Alberto Bressan and Graziano Crasta and Benedetto Piccoli} } @article {1999, title = {The calibration method for the Mumford-Shah functional}, journal = {C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254}, number = {SISSA;21/99/M}, year = {1999}, publisher = {Elsevier}, abstract = {In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3).}, doi = {10.1016/S0764-4442(00)88602-4}, url = {http://hdl.handle.net/1963/1235}, author = {Giovanni Alberti and Guy Bouchitte and Gianni Dal Maso} } @article {1999, title = {Categorial mirror symmetry for K3 surfaces}, journal = {Comm. Math. Phys. 206 (1999) 265-272}, number = {SISSA;100/98/FM/GEO}, year = {1999}, publisher = {Springer}, abstract = {We study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$.}, doi = {10.1007/s002200050705}, url = {http://hdl.handle.net/1963/2887}, author = {Claudio Bartocci and Ugo Bruzzo and Guido Sanguinetti} } @article {Bertola:CorrespondencePLB, title = {Correspondence between Minkowski and de Sitter quantum field theory}, journal = {Phys. Lett. B}, volume = {462}, number = {3-4}, year = {1999}, pages = {249{\textendash}253}, issn = {0370-2693}, author = {Marco Bertola and Gorini, Vittorio and Moschella, Ugo and Schaeffer, Richard} } @article {1999, title = {Enhanced gauge symmetries on elliptic K3}, journal = {Phys.Lett. B452 (1999) 244-250}, number = {SISSA;74/98/EP-FM}, year = {1999}, publisher = {Elsevier}, abstract = {We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s.}, doi = {10.1016/S0370-2693(99)00295-6}, url = {http://hdl.handle.net/1963/3366}, author = {Loriano Bonora and Cesare Reina and Alessandro Zampa} } @article {1999, title = {Extremal faces of the range of a vector measure and a theorem of Lyapunov}, journal = {J. Math. Anal. Appl. 231 (1999) 301-318}, number = {SISSA;4/98/M}, year = {1999}, publisher = {Elsevier}, doi = {10.1006/jmaa.1998.6260}, url = {http://hdl.handle.net/1963/3370}, author = {Stefano Bianchini} } @article {1999, title = {Hyperbolic Systems of Conservation Laws}, journal = {Rev. Mat. Complut. 12 (1999) 135-200}, year = {1999}, abstract = {This is a survey paper, written in the occasion of an invited talk given by the author at the Universidad Complutense in Madrid, October 1998. Its purpose is to provide an account of some recent advances in the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After a brief review of basic concepts, we describe in detail the method of wave-front tracking approximation and present some of the latest results on uniqueness and stability of entropy weak solutions.}, url = {http://hdl.handle.net/1963/1855}, author = {Alberto Bressan} } @article {1999, title = {L-1 stability estimates for n x n conservation laws}, journal = {Arch. Ration. Mech. Anal. 149 (1999), no. 1, 1--22}, number = {SISSA;80/98/M}, year = {1999}, publisher = {Springer}, abstract = {Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws, each characteristic field being linearly degenerate or genuinely nonlinear. In this paper we explicitly define a functional $\\\\Phi=\\\\Phi(u,v)$, equivalent to the $L^1$ distance, which is {\textquoteleft}almost decreasing\\\', i.e., $\\\\Phi(u(t),v(t))-\\\\Phi(u(s),v(s))\\\\leq\\\\break O (\\\\epsilon){\textperiodcentered}(t-s)$ for all $t>s\\\\geq 0$, for every pair of $\\\\epsilon$-approximate solutions $u,v$ with small total variation, generated by a wave-front-tracking algorithm. The small parameter $\\\\epsilon$ here controls the errors in the wave speeds, the maximum size of rarefaction fronts and the total strength of all non-physical waves in $u$ and in $v$. From the above estimate, it follows that front-tracking approximations converge to a unique limit solution, depending Lipschitz continuously on the initial data, in the $L^1$ norm. This provides a new proof of the existence of the standard Riemann semigroup generated by an $n\\\\times n$ system of conservation laws.\\\'\\\'}, doi = {10.1007/s002050050165}, url = {http://hdl.handle.net/1963/3373}, author = {Alberto Bressan and Tai-Ping Liu and Tong Yang} } @article {1999, title = {Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws}, journal = {J. Differential Equations 151 (1999) 345-372}, number = {SISSA;139/97/M}, year = {1999}, publisher = {Elsevier}, abstract = {The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.}, doi = {10.1006/jdeq.1998.3513}, url = {http://hdl.handle.net/1963/3312}, author = {Debora Amadori and Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli} } @article {1999, title = {Oleinik type estimates and uniqueness for n x n conservation laws}, journal = {J. Differential Equations 156 (1999), no. 1, 26--49}, number = {SISSA;150/97/M}, year = {1999}, publisher = {Elsevier}, abstract = {Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleinik in the scalar case.}, doi = {10.1006/jdeq.1998.3606}, url = {http://hdl.handle.net/1963/3375}, author = {Alberto Bressan and Paola Goatin} } @article {1999, title = {Projection singularities of extremals for planar systems}, number = {SISSA;90/99/M}, year = {1999}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1304}, author = {Ugo Boscain and Benedetto Piccoli} } @article {1999, title = {Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws}, journal = {Indiana Univ. Math. J. 48 (1999), no. 1, 43--84}, number = {SISSA;96/97/M}, year = {1999}, publisher = {Indiana University}, abstract = {The paper is concerned with the qualitative structure of entropy solutions to a strictly hyperbolic, genuinely nonlinear system of conservation laws. We first give an accurate description of the local and global wave-front structure of a BV solution, generated by a front tracking algorithm.}, doi = {10.1512/iumj.1999.48.1524}, url = {http://hdl.handle.net/1963/3374}, author = {Alberto Bressan and Philippe G. LeFloch} } @article {1999, title = {Vanishing viscosity solutions of hyperbolic systems on manifolds}, number = {SISSA;24/99/M}, year = {1999}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1238}, author = {Stefano Bianchini and Alberto Bressan} } @article {1999, title = {Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case}, journal = {Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58}, number = {SISSA;160/97/M}, year = {1999}, publisher = {Springer}, abstract = {Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included.}, doi = {10.1007/s002050050135}, url = {http://hdl.handle.net/1963/3371}, author = {Andrea Braides and Gianni Dal Maso and Adriana Garroni} } @article {1999, title = {The vector measures whose range is strictly convex}, journal = {J. Math. Anal. Appl. 232 (1999) 1-19}, number = {SISSA;108/96/M}, year = {1999}, publisher = {Elsevier}, doi = {10.1006/jmaa.1998.6215}, url = {http://hdl.handle.net/1963/3546}, author = {Stefano Bianchini and Carlo Mariconda} } @article {1998, title = {Error bounds for a deterministic version of the Glimm scheme}, journal = {Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176}, number = {SISSA;143/95/M}, year = {1998}, publisher = {Springer}, abstract = {Consider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let $u$ be the unique viscosity solution with initial condition $u(0,x)=\\\\bar u(x)$ and let $u^\\\\varepsilon$ be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\\\\Delta x,\\\\Delta t=O(\\\\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$}, doi = {10.1007/s002050050088}, url = {http://hdl.handle.net/1963/1045}, author = {Andrea Marson and Alberto Bressan} } @article {Bertola:GenerationGC, title = {Generation of primordial fluctuations in curved spaces}, journal = {Gravit. Cosmol.}, volume = {4}, number = {2}, year = {1998}, pages = {121{\textendash}127}, issn = {0202-2893}, author = {Schaeffer, Richard and Moschella, Ugo and Marco Bertola and Gorini, Vittorio} } @article {1998, title = {A generic classification of time-optimal planar stabilizing feedbacks}, journal = {SIAM J. Control Optim. 36 (1998) 12-32}, number = {SISSA;96/95/M}, year = {1998}, publisher = {SISSA Library}, abstract = {Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto.}, doi = {10.1137/S0363012995291117}, url = {http://hdl.handle.net/1963/998}, author = {Alberto Bressan and Benedetto Piccoli} } @article {1998, title = {Geometric control approach to synthesis theory}, journal = {Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001)}, number = {SISSA;63/99/M}, year = {1998}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1277}, author = {Ugo Boscain and Benedetto Piccoli} } @article {1998, title = {Mirror Symmetry on K3 Surfaces as a Hyper-K{\"a}hler Rotation}, journal = {Lett. Math. Phys. 45 (1998) 295-301}, number = {arXiv.org;physics/9802044v2}, year = {1998}, publisher = {Springer}, abstract = {We show that under the hypotheses of Strominger, Yau and Zaslow\\\'s paper, a mirror partner of a K3 surface $X$ with a fibration in special Lagrangian tori can be obtained by rotating the complex structure of $X$ within its hyperk\\\\\\\"ahler family of complex structures. The same hypotheses force the B-field to vanish.}, doi = {10.1023/A:1007446916202}, url = {http://hdl.handle.net/1963/2888}, author = {Ugo Bruzzo and Guido Sanguinetti} } @article {1998, title = {Special functions with bounded variation and with weakly differentiable traces on the jump set}, journal = {NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243}, number = {SISSA;123/95/M}, year = {1998}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1025}, author = {Luigi Ambrosio and Andrea Braides and Adriana Garroni} } @article {1998, title = {Uniqueness for discontinuous ODE and conservation laws}, journal = {Nonlinear Analysis 34 (1998) 637-652}, number = {SISSA;26/97/M}, year = {1998}, publisher = {Elsevier}, abstract = {Consider a scalar O.D.E. of the form $\\\\dot x=f(t,x),$ where $f$ is possibly discontinuous w.r.t. both variables $t,x$. Under suitable assumptions, we prove that the corresponding Cauchy problem admits a unique solution, which depends H\\\\\\\"older continuously on the initial data.\\nOur result applies in particular to the case where $f$ can be written in the form $f(t,x)\\\\doteq g\\\\big( u(t,x)\\\\big)$, for some function $g$ and some solution $u$ of a scalar conservation law, say $u_t+F(u)_x=0$. In turn, this yields the uniqueness and continuous dependence of solutions to a class of $2\\\\times 2$ strictly hyperbolic systems, with initial data in $\\\\L^\\\\infty$.}, doi = {10.1016/S0362-546X(97)00590-7}, url = {http://hdl.handle.net/1963/3699}, author = {Alberto Bressan and Wen Shen} } @mastersthesis {1997, title = {On Existence and Continuous Dependence for Systems of Conservation Laws}, year = {1997}, school = {SISSA}, keywords = {Conservation laws}, url = {http://hdl.handle.net/1963/5588}, author = {Paolo Baiti} } @article {1997, title = {The semigroup generated by a temple class system with large data}, journal = {Differential Integral Equations 10 (1997), no. 3, 401-418}, number = {SISSA;121/95/M}, year = {1997}, publisher = {SISSA Library}, abstract = {We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation.}, url = {http://hdl.handle.net/1963/1023}, author = {Paolo Baiti and Alberto Bressan} } @article {1997, title = {Shift-differentiability of the flow generated by a conservation law}, journal = {Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58.}, number = {SISSA;131/95/M}, year = {1997}, publisher = {SISSA Library}, abstract = {The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition.}, url = {http://hdl.handle.net/1963/1033}, author = {Alberto Bressan and Graziano Guerra} } @article {1997, title = {Structural stability for time-optimal planar sytheses}, journal = {Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371}, number = {SISSA;95/95/M}, year = {1997}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/997}, author = {Alberto Bressan and Benedetto Piccoli} } @article {1996, title = {The semigroup approach to systems of conservation laws}, journal = {Mat. Contemp. 10 (1996) 21-74}, number = {SISSA;135/95/M}, year = {1996}, publisher = {Sociedade Brasileira de Matematica}, url = {http://hdl.handle.net/1963/1037}, author = {Alberto Bressan} } @article {1995, title = {Special functions of bounded deformation}, number = {SISSA;76/95/M}, year = {1995}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/978}, author = {Giovanni Bellettini and Alessandra Coscia and Gianni Dal Maso} } @article {1995, title = {Unique solutions of 2x2 conservation laws with large data}, journal = {Indiana Univ. Math. J. 44 (1995), no. 3, 677-725}, number = {SISSA;73/95/M}, year = {1995}, publisher = {Indiana University Mathematics Journal}, abstract = {For a 2x2 hyperbolic system of conservation laws, we first consider a Riemann problem with arbitrarily large data. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. We then establish a uniqueness result for large BV solutions, valid within the same class of functions where a local existence theorem can be proved.}, doi = {10.1512/iumj.1995.44.2004}, url = {http://hdl.handle.net/1963/975}, author = {Alberto Bressan and Rinaldo M. Colombo} } @article {10572, title = {Hilbert schemes of points on some K3 surfaces and Gieseker stable boundles}, journal = {MATH PROC CAMBRIDGE 120: 255-261 Part 2}, number = {SISSA;34/95/GEO-FM}, year = {1994}, publisher = {SISSA Library}, abstract = {

By using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces $X$ the punctual Hilbert schemes $\\\\Hilb^n(X)$ can be identified, for all $n\\\\geq 1$, with moduli spaces of Gieseker stable vector bundles on $X$ of rank $1+2n$. We also introduce a new Fourier-Mukai type transform for such surfaces.

}, url = {http://hdl.handle.net/1963/937}, author = {Ugo Bruzzo and Antony Maciocia} } @article {1991, title = {A class of absolute retracts of dwarf spheroidal galaxies}, journal = {Proc.Amer.Math.Soc. 112 (1991), no.2, 413}, number = {SISSA;79/89/M}, year = {1991}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/837}, author = {Alberto Bressan and Arrigo Cellina and Andrzej Fryszkowski} } @article {1991, title = {Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions}, journal = {Appl.Math.Optim. 23 (1991), no.1, p. 17-49.}, number = {SISSA;124/89/M}, year = {1991}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/880}, author = {Giuseppe Buttazzo and Gianni Dal Maso} } @article {1990, title = {Chern-Simons forms on principal superfiber bundles}, journal = {J.Math.Phys.31:45,1990}, number = {SISSA;109/87/FM}, year = {1990}, publisher = {SISSA Library}, abstract = {A graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a {\textquoteleft}{\textquoteleft}superextension\\\'\\\' of the Dirac monopole is discussed.}, doi = {10.1063/1.528826}, url = {http://hdl.handle.net/1963/590}, author = {Giovanni Landi and Claudio Bartocci and Ugo Bruzzo} } @article {1990, title = {Existence and continuous dependence for discontinuous O.D.E.s}, journal = {Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311}, number = {SISSA;120/88/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/716}, author = {Alberto Bressan and Giovanni Colombo} } @article {1990, title = {Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions}, journal = {Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535.}, number = {SISSA;49/89/M}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/809}, author = {Giuseppe Buttazzo and Gianni Dal Maso} } @article {1989, title = {Upper semicontinuous differential inclusions without convexity}, journal = {Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775}, number = {SISSA;74/88/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/670}, author = {Alberto Bressan and Arrigo Cellina and Giovanni Colombo} } @article {1988, title = {On differential systems with vector-valued impulsive controls.}, journal = {Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656}, number = {SISSA;54/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/535}, author = {Alberto Bressan and Franco Rampazzo} } @article {1988, title = {Generalized Baire category and differential inclusions in Banach spaces.}, journal = {J. Differential Equations 76 (1988), no. 1, 135-158.}, number = {SISSA;56/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/538}, author = {Alberto Bressan and Giovanni Colombo} } @article {1986, title = {Dirichlet problems for demicoercive functionals}, journal = {Nonlinear anal. 10(1986), no.6, 603-613}, number = {SISSA;03/85/M}, year = {1986}, publisher = {SISSA Library}, doi = {10.1016/0362-546X(86)90145-8}, url = {http://hdl.handle.net/1963/390}, author = {Gabriele Anzellotti and Giuseppe Buttazzo and Gianni Dal Maso} }