@article {2024, title = {Breaking the left-right symmetry in fluttering artificial cilia that perform nonreciprocal oscillations}, year = {2024}, month = {2024/04/06}, abstract = {Recent investigations on active materials have introduced a new paradigm for soft robotics by showing that a complex response can be obtained from simple stimuli by harnessing dynamic instabilities. In particular, polyelectrolyte hydrogel filaments actuated by a constant electric field have been shown to exhibit self-sustained oscillations as a consequence of flutter instability. Owing to the nonreciprocal nature of the emerging oscillations, these artificial cilia are able to generate flows along the stimulus. Building upon these findings, in this paper we propose a design strategy to break the left-right symmetry in the generated flows, by endowing the filament with a natural curvature at the fabrication stage. We develop a mathematical model based on morphoelastic rod theory to characterize the stability of the equilibrium configurations of the filament, proving the persistence of flutter instability. We show that the emerging oscillations are nonreciprocal and generate thrust at an angle with the stimulus. The results we find at the level of the single cilium open new perspectives on the possible applications of artificial ciliary arrays in soft robotics and microfluidics.}, isbn = {1572-9648}, url = {https://doi.org/10.1007/s11012-024-01765-7}, author = {Boiardi, Ariel Surya and Marchello, Roberto} } @article {2024, title = {A non local model for cell migration in response to mechanical stimuli}, journal = {Mathematical Biosciences}, volume = {368}, year = {2024}, month = {2024/02//}, pages = {109124}, isbn = {00255564}, url = {https://linkinghub.elsevier.com/retrieve/pii/S0025556423001645}, author = {Marchello, Roberto and Colombi, Annachiara and Preziosi, Luigi and Giverso, Chiara} } @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 {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 = {A general splitting principle on RCD spaces and applications to spaces with positive spectrum}, year = {2023}, abstract = {

In this paper we develop a general {\textquoteleft}analytic{\textquoteright} splitting principle for RCD spaces: we show that if there is a function with suitable Laplacian and Hessian, then the space is (isomorphic to) a warped product. Our result covers most of the splitting-like results currently available in the literature about RCD spaces. We then apply it to extend to the non-smooth category some structural property of Riemannian manifolds obtained by Li and Wang.

}, author = {Nicola Gigli and Fabio Marconi} } @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} } @booklet {2022, title = {Doubly Intermittent Full Branch Maps with Critical Points and Singularities}, year = {2022}, keywords = {37E05, Dynamical Systems (math.DS), FOS: Mathematics}, doi = {10.48550/ARXIV.2209.12725}, url = {https://arxiv.org/abs/2209.12725}, author = {Douglas Coates and Stefano Luzzatto and Muhammad Mubarak} } @booklet {2022, title = {Doubly Intermittent Maps with Critical Points, Unbounded Derivatives and Regularly Varying Tail}, year = {2022}, keywords = {37A05, 37A25, 37A50, Dynamical Systems (math.DS), FOS: Mathematics}, doi = {10.48550/ARXIV.2211.15648}, url = {https://arxiv.org/abs/2211.15648}, author = {Muhammad Mubarak and Tanja I. Schindler} } @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} } @article {2022, title = {Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature}, year = {2022}, abstract = {

We prove a sharp isoperimetric inequality for Finsler manifolds having non-negative Ricci curvature and Euclidean volume growth. We also prove a rigidity result for this inequality, under the additional hypotheses of boundedness of the isoperimetric set and the finite reversibility of the space.
An application to the weighed anisotropic isoperimetric problem in Euclidean cones is presented.

}, author = {Manini, Davide} } @article {2022, title = {Isoperimetric inequality in noncompact MCP spaces}, journal = {Proc. Am. Math. Soc.}, volume = {150}, year = {2022}, month = {AUG}, pages = {3537-3548}, type = {Article}, abstract = {

We prove a sharp isoperimetric inequality for the class of metric measure spaces verifying the synthetic Ricci curvature lower bounds Measure Contraction property (MCP(0, N)) and having Euclidean volume growth at infinity. We avoid the classical use of the Brunn-Minkowski inequality, not available for MCP(0, N), and of the PDE approach, not available in the singular setting. Our approach will be carried over by using a scaling limit of localization.

}, issn = {0002-9939}, doi = {10.1090/proc/15945}, author = {Cavalletti, Fabio and Manini, Davide} } @article {2022, title = {Long-time stability of the quantum hydrodynamic system on irrational tori}, journal = {Mathematics in Engineering}, volume = {4}, year = {2022}, pages = {1-24}, keywords = {Euler-Korteweg, irrational tori, long time stability, QHD system, Small divisors}, issn = {2640-3501}, doi = {10.3934/mine.2022023}, url = {https://www.aimspress.com/article/doi/10.3934/mine.2022023}, author = {Roberto Feola and Felice Iandoli and Federico Murgante} } @article {2022, title = {The $N$-Link Swimmer in Three Dimensions: Controllability and Optimality Results}, volume = {178}, year = {2022}, month = {2022/03/08}, pages = {6}, abstract = {The controllability of a fully three-dimensional $N$-link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2-link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2-link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all eight linearly independent directions in the combined configuration and shape space, leading to controllability; the swimmer can move from any starting configuration and shape to any target configuration and shape by operating on the two shape variables. The result is subsequently extended to the $N$-link swimmer. Finally, the minimal time optimal control problem and the minimization of the power expended are addressed and a qualitative description of the optimal strategies is provided.}, isbn = {1572-9036}, url = {https://doi.org/10.1007/s10440-022-00480-3}, author = {Marchello, Roberto and Morandotti, Marco and Shum, Henry and Zoppello, Marta} } @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} } @conference {2022, title = {A Proper Orthogonal Decomposition Approach for Parameters Reduction of Single Shot Detector Networks}, booktitle = {2022 IEEE International Conference on Image Processing (ICIP)}, year = {2022}, doi = {10.1109/ICIP46576.2022.9897513}, author = {Laura Meneghetti and Nicola Demo and Gianluigi Rozza} } @article {2022, title = {Rigidities of Isoperimetric inequality under nonnegative Ricci curvature}, year = {2022}, abstract = {

The sharp isoperimetric inequality for non-compact Riemannian manifolds with non-negative Ricci curvature and Euclidean volume growth has been obtained in increasing generality with different approaches in a number of contributions [arXiv:1812.05022,\ arXiv:2012.09490,\ arXiv:2009.13717,\ arXiv:2103.08496] culminated by Balogh and Kristaly [arXiv:2012.11862] covering also m.m.s.{\textquoteright}s verifying the non-negative Ricci curvature condition in the synthetic sense of Lott, Sturm and Villani. In sharp contrast with the compact case of positive Ricci curvature, for a large class of spaces including weighted Riemannian manifolds, no complete characterisation of the equality cases is present in the literature.
The scope of this note is to settle this problem by proving, in the same generality of [arXiv:2012.11862], that the equality in the isoperimetric inequality can be attained only by metric balls. Whenever this happens the space is forced, in a measure theoretic sense, to be a cone.
Our result applies to different frameworks yielding as corollaries new rigidity results: it extend to weighted Riemannian manifold the rigidity results of [arXiv:2009.13717], it extend to general\ RCD\ spaces the rigidity results of [arXiv:2201.04916] and finally applies also to the Euclidean setting by proving that that optimisers in the anisotropic and weighted isoperimetric inequality for Euclidean cones are necessarily the Wulff shapes.

}, author = {Cavalletti, Fabio and Manini, Davide} } @article {ArndtBangerthFeder-2022-a, title = {The \textttdeal.II Library, Version 9.4}, journal = {Journal of Numerical Mathematics}, year = {2022}, author = {Daniel Arndt and Wolfgang Bangerth Marco Feder and Marc Fehling and Rene Gassm{\"o}ller and Timo Heister and Luca Heltai and Martin Kronbichler and Matthias Maier and Peter Munch and Jean-Paul Pelteret and Simon Sticko and Bruno Turcksin and David Wells} } @article {LiuMcBrideSaxena-2022-a, title = {Vibration Analysis of Piezoelectric Kirchhoff-Love shells based on Catmull-Clark Subdivision Surfaces}, journal = {International Journal for Numerical Methods in Engineering}, year = {2022}, author = {Zhaowei Liu and Andrew McBride and Prashant Saxena and Luca Heltai and Yilin Qu and Paul Steinmann} } @article {2021, title = {On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis}, journal = {Computers \& Fluids}, volume = {216}, year = {2021}, pages = {104819}, abstract = {

In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

}, keywords = {Dynamic mode decomposition, Ffowcs Williams and Hawkings, Hydroacoustics, Large eddy simulation, Model reduction, Proper orthogonal decomposition}, issn = {0045-7930}, doi = {https://doi.org/10.1016/j.compfluid.2020.104819}, url = {https://www.sciencedirect.com/science/article/pii/S0045793020303893}, author = {Mahmoud Gadalla and Marta Cianferra and Marco Tezzele and Giovanni Stabile and Andrea Mola 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} } @booklet {2021, title = {A Dimensionality Reduction Approach for Convolutional Neural Networks}, year = {2021}, author = {Laura Meneghetti and Nicola Demo and Gianluigi Rozza} } @article {2021, title = {Equilibrium measure for a nonlocal dislocation energy with physical confinement}, year = {2021}, month = {2021}, url = {https://doi.org/10.1515/acv-2020-0076}, author = {Mora, Maria Giovanna and Alessandro Scagliotti} } @article {2021, title = {Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing}, journal = {Journal of Marine Science and Engineering}, volume = {9}, year = {2021}, pages = {185}, abstract = {

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

}, issn = {2077-1312}, doi = {10.3390/jmse9020185}, url = {https://www.mdpi.com/2077-1312/9/2/185}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {ZancanaroMrosekStabileOthmerRozza2021, title = {Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters}, journal = {Fluids}, volume = {6}, number = {8}, year = {2021}, pages = {296}, publisher = {MDPI AG}, doi = {10.3390/fluids6080296}, url = {https://doi.org/10.3390/fluids6080296}, author = {Matteo Zancanaro and Markus Mrosek and Giovanni Stabile and Carsten Othmer and Gianluigi Rozza} } @article {2021, title = {Independence of synthetic curvature dimension conditions on transport distance exponent}, journal = {Trans. Amer. Math. Soc.}, volume = {374}, year = {2021}, pages = {5877{\textendash}5923}, issn = {0002-9947}, doi = {10.1090/tran/8413}, url = {https://doi.org/10.1090/tran/8413}, author = {Afiny Akdemir and Andrew Colinet and Robert McCann and Fabio Cavalletti and Flavia Santarcangelo} } @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 {14318, title = {Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering}, journal = {arXiv preprint arXiv:2110.14396}, year = {2021}, author = {Francesco Romor and Marco Tezzele and Markus Mrosek and Carsten Othmer and Gianluigi Rozza} } @article {HeltaiCaiazzoMueller-2021-a, title = {Multiscale coupling of one-dimensional vascular models and elastic tissues}, journal = {Annals of Biomedical Engineering}, year = {2021}, author = {Luca Heltai and Alfonso Caiazzo and Lucas M{\"u}eller} } @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 {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 {tezzele2020pygem, title = {PyGeM: Python Geometrical Morphing}, journal = {Software Impacts}, volume = {7}, year = {2021}, pages = {100047}, abstract = {PyGeM is an open source Python package which allows to easily parametrize and deform 3D object described by CAD files or 3D meshes. It implements several morphing techniques such as free form deformation, radial basis function interpolation, and inverse distance weighting. Due to its versatility in dealing with different file formats it is particularly suited for researchers and practitioners both in academia and in industry interested in computational engineering simulations and optimization studies.}, keywords = {Free form deformation, Geometrical morphing, Inverse distance weighting, Python, Radial basis functions interpolation}, issn = {2665-9638}, doi = {10.1016/j.simpa.2020.100047}, author = {Marco Tezzele and Nicola Demo and Andrea Mola and Gianluigi Rozza} } @article {MulitaGianiHeltai-2021-a, title = {Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Methods}, journal = {SIAM Journal on Scientific Computing}, year = {2021}, author = {Ornela Mulita and Stefano Giani and Luca Heltai} } @article {2021, title = {The sharp quantitative isocapacitary inequality}, journal = {Revista Matematica Iberoamericana}, volume = {37}, year = {2021}, month = {2021}, pages = {2191 - 2228}, abstract = {

We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. Analyse Math.{\textquoteright}91). {\textcopyright} 2021 Real Sociedad Matem{\'a}tica Espa{\~n}ola

}, keywords = {Fraenkel asymmetry, isocapacitary inequality, Stability estimates}, isbn = {02132230 (ISSN)}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573\&doi=10.4171\%2frmi\%2f1259\&partnerID=40\&md5=5f88bc37b87a9eea7a502ea63523ff57}, author = {Guido De Philippis and Michele Marini and Ekaterina Mukoseeva} } @article {2021, title = {The sharp quantitative isocapacitary inequality (the case of p-capacity)}, journal = {Advances in Calculus of Variations}, year = {2021}, month = {2021}, abstract = {

We prove a sharp quantitative form of isocapacitary inequality in the case of a general p. This work is a generalization of the author{\textquoteright}s paper with Guido De Philippis and Michele Marini, where we treated the case of 2-capacity. {\textcopyright} 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

}, keywords = {isocapacitary inequality, Stability estimates}, isbn = {18648258 (ISSN)}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85106363307\&doi=10.1515\%2facv-2020-0106\&partnerID=40\&md5=26dbcad781b68c1d873512e272f0e7f4}, author = {Ekaterina Mukoseeva} } @article {GianiGrubisicHeltai-2021-a, title = {Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems}, journal = {Computational Methods in Applied Mathematics}, volume = {21}, number = {2}, year = {2021}, pages = {385-405}, author = {Stefano Giani and Luka Grubisic and Luca Heltai and Ornela Mulita} } @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} } @conference {2020, title = {Advances in reduced order methods for parametric industrial problems in computational fluid dynamics}, booktitle = {Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018}, year = {2020}, abstract = {

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686\&partnerID=40\&md5=fb0b1a3cfdfd35a104db9921bc9be675}, author = {Gianluigi Rozza and M.H. Malik and Nicola Demo and Marco Tezzele and Michele Girfoglio and Giovanni Stabile and Andrea Mola} } @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 {2020, title = {Data-driven POD-Galerkin reduced order model for turbulent flows}, journal = {Journal of Computational Physics}, volume = {416}, year = {2020}, pages = {109513}, abstract = {

In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

}, doi = {10.1016/j.jcp.2020.109513}, url = {https://arxiv.org/abs/1907.09909}, author = {Saddam Hijazi and Giovanni Stabile and Andrea Mola 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} } @article {2020, title = {Enhancing CFD predictions in shape design problems by model and parameter space reduction}, journal = {Advanced Modeling and Simulation in Engineering Sciences}, volume = {7}, year = {2020}, abstract = {

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

}, doi = {https://doi.org/10.1186/s40323-020-00177-y}, url = {https://arxiv.org/abs/2001.05237}, author = {Marco Tezzele and Nicola Demo and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @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 {mine-02-02-011, title = {MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales}, journal = {Mathematics in Engineering}, volume = {2}, number = {mine-02-02-01}, year = {2020}, pages = {230}, type = {Perspective}, abstract = {

Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

}, keywords = {active matter, adhesive locomotion, cell motility, cell sheet folding, knotted DNA, topological defects, unicellular swimmers, unjamming transition}, issn = {2640-3501}, doi = {10.3934/mine.2020011}, url = {http://dx.doi.org/10.3934/mine.2020011}, author = {Daniele Agostinelli and Roberto Cerbino and Del Alamo, Juan C and Antonio DeSimone and Stephanie H{\"o}hn and Cristian Micheletti and Giovanni Noselli and Eran Sharon and Julia Yeomans} } @booklet {2020, title = {Minimality of the ball for a model of charged liquid droplets}, year = {2020}, author = {Ekaterina Mukoseeva and Giulia Vescovo} } @inbook {HijaziStabileMolaRozza2020a, title = {Non-intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: A Comparison and Perspectives}, booktitle = {Quantification of Uncertainty: Improving Efficiency and Technology: QUIET selected contributions}, year = {2020}, pages = {217{\textendash}240}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

}, isbn = {978-3-030-48721-8}, doi = {10.1007/978-3-030-48721-8_10}, url = {https://doi.org/10.1007/978-3-030-48721-8_10}, author = {Saddam Hijazi and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @article {gadalla19bladex, title = {BladeX: Python Blade Morphing}, journal = {The Journal of Open Source Software}, volume = {4}, number = {34}, year = {2019}, pages = {1203}, doi = {10.21105/joss.01203}, author = {Mahmoud Gadalla and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @conference {2019, title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems}, booktitle = {VIII International Conference on Computational Methods in Marine Engineering}, year = {2019}, abstract = {

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry {\textendash}- assuming the topology is inaltered by the deformation {\textendash}-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

}, url = {https://arxiv.org/abs/1905.05982}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @conference {2019, title = {A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems}, booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019}, year = {2019}, abstract = {

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry {\textemdash} assuming the topology is inaltered by the deformation {\textemdash}, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075342565\&partnerID=40\&md5=d76b8a1290053e7a84fb8801c0e6bb3d}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @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 {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} } @conference {2019, title = {Efficient reduction in shape parameter space dimension for ship propeller blade design}, booktitle = {8th International Conference on Computational Methods in Marine Engineering, MARINE 2019}, year = {2019}, abstract = {

In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395143\&partnerID=40\&md5=b6aa0fcedc2f88e78c295d0f437824d0}, author = {Andrea Mola and Marco Tezzele and Mahmoud Gadalla and Valdenazzi, Federica and Grassi, Davide and Padovan, Roberta and Gianluigi Rozza} } @article {doi:10.1142/S0129055X19500053, title = {Ground state energy of mixture of Bose gases}, journal = {Reviews in Mathematical Physics}, volume = {31}, number = {02}, year = {2019}, pages = {1950005}, abstract = {

We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N-1), we show that the leading order of the ground state energy is captured correctly by the Gross{\textendash}Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross{\textendash}Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov{\textquoteright}s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

}, doi = {10.1142/S0129055X19500053}, url = {https://doi.org/10.1142/S0129055X19500053}, author = {Alessandro Michelangeli and Phan Thanh Nam and Alessandro Olgiati} } @article {CANGIANI20193090, title = {hp-adaptive discontinuous Galerkin methods for non-stationary convection{\textendash}diffusion problems}, journal = {Computers \& Mathematics with Applications}, volume = {78}, number = {9}, year = {2019}, note = {Applications of Partial Differential Equations in Science and Engineering}, pages = {3090-3104}, abstract = {An a posteriori error estimator for the error in the (L2(H1)+L$\infty$(L2))-type norm for an interior penalty discontinuous Galerkin (dG) spatial discretisation and backward Euler temporal discretisation of linear non-stationary convection{\textendash}diffusion initial/boundary value problems is derived, allowing for anisotropic elements. The proposed error estimator is used to drive an hp-space{\textendash}time adaptive algorithm wherein directional mesh refinement is employed to give rise to highly anisotropic elements able to accurately capture layers. The performance of the hp-space{\textendash}time adaptive algorithm is assessed via a number of standard test problems characterised by sharp and/or moving layers.}, keywords = {A posteriori error estimation, Adaptive finite element methods, Anisotropic meshes, Discontinuous Galerkin, Unsteady convection{\textendash}diffusion}, issn = {0898-1221}, doi = {https://doi.org/10.1016/j.camwa.2019.04.002}, url = {https://www.sciencedirect.com/science/article/pii/S0898122119302007}, author = {Andrea Cangiani and E.H. Georgoulis and Stefano Giani and S. Metcalfe} } @article {2019, title = {On Krylov solutions to infinite-dimensional inverse linear problems}, journal = {Calcolo}, volume = {56}, year = {2019}, pages = {1{\textendash}25}, abstract = {

We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse problem, together with a series of model examples and numerical experiments.

}, author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati} } @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 {2019, title = {A neutrally stable shell in a Stokes flow: a rotational Taylor{\textquoteright}s sheet}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering SciencesProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {475}, year = {2019}, month = {2019/07/26}, pages = {20190178}, url = {https://doi.org/10.1098/rspa.2019.0178}, author = {Giovanni Corsi and Antonio DeSimone and C. Maurini and S. Vidoli} } @article {Michelangeli2019, title = {Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range}, journal = {Complex Analysis and Operator Theory}, year = {2019}, month = {May}, abstract = {

We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schr{\"o}dinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schr{\"o}dinger operators formed by a fractional Laplacian and a regular potential.

}, issn = {1661-8262}, doi = {10.1007/s11785-019-00927-w}, url = {https://doi.org/10.1007/s11785-019-00927-w}, author = {Alessandro Michelangeli and Raffaele Scandone} } @article {2019, title = {Reducibility for a fast-driven linear Klein{\textendash}Gordon equation}, volume = {198}, year = {2019}, month = {2019/08/01}, pages = {1407 - 1439}, abstract = {

We prove a reducibility result for a linear Klein{\textendash}Gordon equation with a quasi-periodic driving on a compact interval with Dirichlet boundary conditions. No assumptions are made on the size of the driving; however, we require it to be fast oscillating. In particular, provided that the external frequency is sufficiently large and chosen from a Cantor set of large measure, the original equation is conjugated to a time-independent, diagonal one. We achieve this result in two steps. First, we perform a preliminary transformation, adapted to fast oscillating systems, which moves the original equation in a perturbative setting. Then, we show that this new equation can be put to constant coefficients by applying a KAM reducibility scheme, whose convergence requires a new type of Melnikov conditions.

}, isbn = {1618-1891}, url = {https://doi.org/10.1007/s10231-019-00823-2}, author = {Luca Franzoi and Alberto Maspero} } @article {FEOLA2019932, title = {Reducibility of first order linear operators on tori via Moser{\textquoteright}s theorem}, journal = {Journal of Functional Analysis}, volume = {276}, number = {3}, year = {2019}, pages = {932 - 970}, abstract = {

In this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ.∂xu+a(ωt,x).∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser{\textquoteright}s straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

}, keywords = {Hyperbolic PDEs, KAM theory, Nash{\textendash}Moser, Reducibility}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2018.10.009}, url = {http://www.sciencedirect.com/science/article/pii/S0022123618303793}, author = {Roberto Feola and Filippo Giuliani and Riccardo Montalto and Michela Procesi} } @article {Iraso2019, title = {Two-Dimensional Yang{\textendash}Mills Theory on Surfaces with Corners in Batalin{\textendash}Vilkovisky Formalism}, journal = {Communications in Mathematical Physics}, year = {2019}, month = {Mar}, abstract = {

In this paper we recover the non-perturbative partition function of 2D Yang{\textendash}Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang{\textendash}Mills theory on surfaces with boundaries and corners in the Batalin{\textendash}Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting{\textendash}-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces{\textendash}-building blocks{\textendash}-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang{\textendash}Mills theory.

}, issn = {1432-0916}, doi = {10.1007/s00220-019-03392-w}, url = {https://doi.org/10.1007/s00220-019-03392-w}, author = {Riccardo Iraso and Mnev, P.} } @article {2018, title = {Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models}, journal = {Journal of Scientific Computing}, volume = {74}, year = {2018}, pages = {197-219}, doi = {10.1007/s10915-017-0430-y}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114\&doi=10.1007\%2fs10915-017-0430-y\&partnerID=40\&md5=023ef0bb95713f4442d1fa374c92a964}, author = {Immanuel Martini and Bernard Haasdonk and Gianluigi Rozza} } @article {giantesio2017comparison, title = {A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials}, journal = {J. Elast.}, year = {2018}, publisher = {Springer Nature}, author = {Giulia Giantesio and Alessandro Musesti and Davide Riccobelli} } @inbook {AuricchioContiLefieuxMorgantiRealiRozzaVeneziani2018, title = {Computational methods in cardiovascular mechanics}, booktitle = {Cardiovascular Mechanics}, year = {2018}, pages = {54}, publisher = {CRC Press}, organization = {CRC Press}, chapter = {Computational methods in cardiovascular mechanics}, abstract = {

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

}, url = {https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201\%2Fb21917-5}, author = {Auricchio, Ferdinando and Conti, Michele and Lefieux, Adrian and Morganti, Simone and Alessandro Reali and Gianluigi Rozza and Veneziani, Alessandro}, editor = {Michel F. Labrosse} } @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 {TezzeleSalmoiraghiMolaRozza2018, title = {Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems}, journal = {Advanced Modeling and Simulation in Engineering Sciences}, volume = {5}, number = {1}, year = {2018}, month = {Sep}, pages = {25}, abstract = {

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

}, doi = {10.1186/s40323-018-0118-3}, author = {Marco Tezzele and Filippo Salmoiraghi and Andrea Mola and Gianluigi Rozza} } @article {Michelangeli_2018, title = {Effective non-linear spinor dynamics in a spin-1 Bose{\textendash}Einstein condensate}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {51}, number = {40}, year = {2018}, month = {sep}, pages = {405201}, publisher = {IOP Publishing}, abstract = {

We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose{\textendash}Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin{\textendash}spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schr{\"o}dinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.

}, doi = {10.1088/1751-8121/aadbc2}, url = {https://doi.org/10.1088\%2F1751-8121\%2Faadbc2}, author = {Alessandro Michelangeli and Alessandro Olgiati} } @proceedings {demo2018efficient, title = {An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment}, year = {2018}, publisher = {International Society of Offshore and Polar Engineers}, address = {Sapporo, Japan}, abstract = {In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations.}, keywords = {Active subspaces, Boundary element method, Dynamic mode decomposition, Fluid structure interaction, Free form deformation, Fully nonlinear potential, Numerical towing tank}, issn = {978-1-880653-87-6}, url = {https://www.onepetro.org/conference-paper/ISOPE-I-18-481}, author = {Nicola Demo and Marco Tezzele and Andrea Mola and Gianluigi Rozza} } @article {doi:10.1063/1.5033856, title = {Fractional powers and singular perturbations of quantum differential Hamiltonians}, journal = {Journal of Mathematical Physics}, volume = {59}, number = {7}, year = {2018}, pages = {072106}, abstract = {

We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schr{\"o}dinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

}, doi = {10.1063/1.5033856}, url = {https://doi.org/10.1063/1.5033856}, author = {Alessandro Michelangeli and Andrea Ottolini and Raffaele Scandone} } @article {GEORGIEV20181551, title = {On fractional powers of singular perturbations of the Laplacian}, journal = {Journal of Functional Analysis}, volume = {275}, number = {6}, year = {2018}, pages = {1551 - 1602}, abstract = {

We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

}, keywords = {Point interactions, Regular and singular component of a point-interaction operator, Singular perturbations of the Laplacian}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2018.03.007}, url = {http://www.sciencedirect.com/science/article/pii/S0022123618301046}, author = {Vladimir Georgiev and Alessandro Michelangeli and Raffaele Scandone} } @article {2018, title = {On Geometric Quantum Confinement in Grushin-Like Manifolds}, number = {SISSA;36/2018/MATE}, year = {2018}, note = {16 pages}, abstract = {We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl{\textquoteright}s analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.}, url = {http://preprints.sissa.it/handle/1963/35322}, author = {Matteo Gallone and Alessandro Michelangeli and Eugenio Pozzoli} } @article {Antonelli2018, title = {Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials}, journal = {Zeitschrift f{\"u}r angewandte Mathematik und Physik}, volume = {69}, number = {2}, year = {2018}, month = {Mar}, pages = {46}, abstract = {

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schr{\"o}dinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

}, issn = {1420-9039}, doi = {10.1007/s00033-018-0938-5}, url = {https://doi.org/10.1007/s00033-018-0938-5}, author = {Paolo Antonelli and Alessandro Michelangeli and Raffaele Scandone} } @article {2018, title = {Hydrogenoid Spectra with Central Perturbations}, number = {SISSA;34/2018/MATE}, year = {2018}, note = {Mathematics Subject Classification (2010) 34L10 . 34L15 . 34L16 . 47B15 . 47B25 . 47N20 . 81Q10 . 81Q80}, abstract = {Through the Krein-Vi{\v s}ik-Birman extension scheme, unlike the previous classical analysis based on von Neumann{\textquoteright}s theory, we reproduce the construction and classification of all self-adjoint realisations of two intimately related models: the three-dimensional hydrogenoid-like Hamiltonians with singular perturbation supported at the centre (the nucleus), and the Sch{\"o}rdinger operators on the halfline with Coulomb potentials centred at the origin. These two problems are technically equivalent, albeit sometimes treated by their own in the the literature. Based on such scheme, we then recover the formula to determine the eigenvalues of each self-adjoint extension, which are corrections to the non-relativistic hydrogenoid energy levels.We discuss in which respect the Krein-Vi{\v s}ik-Birman scheme is somehow more natural in yielding the typical boundary condition of self-adjointness at the centre of the perturbation and in identifying the eigenvalues of each extension.}, url = {http://preprints.sissa.it/handle/1963/35321}, author = {Matteo Gallone and Alessandro Michelangeli} } @article {Dell{\textquoteright}Antonio2018, title = {Lp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction}, journal = {Annales Henri Poincar{\'e}}, volume = {19}, number = {1}, year = {2018}, month = {Jan}, pages = {283{\textendash}322}, abstract = {

We prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schr{\"o}dinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1\<p\<3 and unbounded otherwise.

}, issn = {1424-0661}, doi = {10.1007/s00023-017-0628-4}, url = {https://doi.org/10.1007/s00023-017-0628-4}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli and Raffaele Scandone and Kenji Yajima} } @conference {tezzele2018model, title = {Model Order Reduction by means of Active Subspaces and Dynamic Mode Decomposition for Parametric Hull Shape Design Hydrodynamics}, booktitle = {Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship \& Maritime Research}, year = {2018}, publisher = {IOS Press}, organization = {IOS Press}, address = {Trieste, Italy}, abstract = {We present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations. The main idea of this work is to employ the AS to identify possible lower dimensional structures in the parameter space. The complete pipeline involves the use of free form deformation to parametrize and deform the hull shape, the full order solver based on unsteady potential flow theory with fully nonlinear free surface treatment directly interfaced with CAD, the use of dynamic mode decomposition to reconstruct the final steady state given only few snapshots of the simulation, and the reduction of the parameter space by AS, and shared subspace. Response surface method is used to minimize the total drag.}, doi = {10.3233/978-1-61499-870-9-569}, url = {http://ebooks.iospress.nl/publication/49270}, author = {Marco Tezzele and Nicola Demo and Mahmoud Gadalla and Andrea Mola and Gianluigi Rozza} } @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 {2018, title = {Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis}, number = {SISSA;35/2018/MATE}, year = {2018}, abstract = {We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.}, url = {http://preprints.sissa.it/handle/1963/35323}, author = {Alessandro Michelangeli and Giuseppe Pitton} } @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 = {On real resonances for the three-dimensional, multi-centre point interaction}, number = {SISSA;40/2018/MATE}, year = {2018}, author = {Alessandro Michelangeli and Raffaele Scandone} } @article {doi:10.1142/S0219891618500200, title = {Regularity estimates for scalar conservation laws in one space dimension}, journal = {Journal of Hyperbolic Differential Equations}, volume = {15}, number = {04}, year = {2018}, pages = {623-691}, abstract = {

We deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function f has on the entropy solution. More precisely, if the set w : f"(w)/=0 is dense, the regularity of the solution can be expressed in terms of BVΦ spaces, where Φ depends on the nonlinearity of f. If moreover the set w : f"(w) = 0 is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that f'o u(t) ∈BV loc(ℝ) for every t \> 0 and that this can be improved to SBVloc(ℝ) regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.

}, doi = {10.1142/S0219891618500200}, url = {https://doi.org/10.1142/S0219891618500200}, author = {Elio Marconi} } @article {doi:10.1098/rspa.2017.0608, title = {Revealing new dynamical patterns in a reaction\&\#x2013;diffusion model with cyclic competition via a novel computational framework}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {474}, number = {2213}, year = {2018}, pages = {20170608}, abstract = {Understanding how patterns and travelling waves form in chemical and biological reaction{\textendash}diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a clear understanding about all possible types of dynamical regimes in classical reaction{\textendash}diffusion models, such as Lotka{\textendash}Volterra competition models with spatial dependence. In this study, we demonstrate some new types of wave propagation and pattern formation in a classical three species cyclic competition model with spatial diffusion, which have been so far missed in the literature. These new patterns are characterized by a high regularity in space, but are different from patterns previously known to exist in reaction{\textendash}diffusion models, and may have important applications in improving our understanding of biological pattern formation and invasion theory. Finding these new patterns is made technically possible by using an automatic adaptive finite element method driven by a novel a posteriori error estimate which is proved to provide a reliable bound for the error of the numerical method. We demonstrate how this numerical framework allows us to easily explore the dynamical patterns in both two and three spatial dimensions.}, doi = {10.1098/rspa.2017.0608}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0608}, author = {Andrea Cangiani and E.H. Georgoulis and Morozov, A. Yu. and Sutton, O. J.} } @article {doi:10.1080/14029251.2018.1503423, title = {Singular Hartree equation in fractional perturbed Sobolev spaces}, journal = {Journal of Nonlinear Mathematical Physics}, volume = {25}, number = {4}, year = {2018}, pages = {558-588}, publisher = {Taylor \& Francis}, abstract = {

We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schr{\"o}dinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.

}, doi = {10.1080/14029251.2018.1503423}, url = {https://doi.org/10.1080/14029251.2018.1503423}, author = {Alessandro Michelangeli and Alessandro Olgiati and Raffaele Scandone} } @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 = {Truncation and convergence issues for bounded linear inverse problems in Hilbert space}, number = {SISSA;50/2018/MATE}, year = {2018}, institution = {SISSA}, abstract = {We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests.}, url = {http://preprints.sissa.it/handle/1963/35326}, author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati} } @inbook {MR3790882, title = {Virtual element methods for elliptic problems on polygonal meshes}, booktitle = {Generalized barycentric coordinates in computer graphics and computational mechanics}, year = {2018}, pages = {263{\textendash}279}, publisher = {CRC Press, Boca Raton, FL}, organization = {CRC Press, Boca Raton, FL}, author = {Andrea Cangiani and Sutton, Oliver J. and Gyrya, Vitaliy and Manzini, Gianmarco} } @article {giulianiEtAl2018, title = {π-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods}, journal = {Advances in Engineering Software}, volume = {121}, year = {2018}, pages = {39{\textendash}58}, author = {Nicola Giuliani and Andrea Mola and Luca Heltai} } @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 {MR3671497, title = {Conforming and nonconforming virtual element methods for elliptic problems}, journal = {IMA J. Numer. Anal.}, volume = {37}, number = {3}, year = {2017}, pages = {1317{\textendash}1354}, issn = {0272-4979}, doi = {10.1093/imanum/drw036}, url = {https://doi.org/10.1093/imanum/drw036}, author = {Andrea Cangiani and Manzini, Gianmarco and Sutton, Oliver J.} } @article {2017, title = {On contact interactions realised as Friedrichs systems}, number = {SISSA;48/2017/MATE}, year = {2017}, abstract = {We realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems.}, url = {http://preprints.sissa.it/handle/1963/35298}, author = {Marko Erceg and Alessandro Michelangeli} } @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 {Dassi2017, title = {Curvature-adapted remeshing of {CAD} surfaces}, journal = {Engineering with Computers}, volume = {34}, number = {3}, year = {2017}, month = {dec}, pages = {565{\textendash}576}, publisher = {Springer Nature}, doi = {10.1007/s00366-017-0558-2}, url = {https://doi.org/10.1007/s00366-017-0558-2}, author = {Franco Dassi and Andrea Mola and Hang Si} } @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 {2017, title = {Discrete spectra for critical Dirac-Coulomb Hamiltonians}, number = {SISSA;44/2017/MATE}, year = {2017}, abstract = {The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished physically most natural one. For the latter, Sommerfeld{\textquoteright}s celebrated fine structure formula provides the well-known expression for the eigenvalues in the gap of the continuum spectrum. Exploiting our recent general classification of all other self-adjoint realisations, we generalise Sommerfeld{\textquoteright}s formula so as to determine the discrete spectrum of all other self-adjoint versions of the Dirac-Coulomb Hamiltonian. Such discrete spectra display naturally a fibred structure, whose bundle covers the whole gap of the continuum spectrum.}, url = {http://preprints.sissa.it/handle/1963/35300}, author = {Matteo Gallone and Alessandro Michelangeli} } @inbook {Iandoli2017, title = {Dispersive Estimates for Schr{\"o}dinger Operators with Point Interactions in ℝ3}, booktitle = {Advances in Quantum Mechanics: Contemporary Trends and Open Problems}, year = {2017}, pages = {187{\textendash}199}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

The study of dispersive properties of Schr{\"o}dinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schr{\"o}dinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$-$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.

}, isbn = {978-3-319-58904-6}, doi = {10.1007/978-3-319-58904-6_11}, url = {https://doi.org/10.1007/978-3-319-58904-6_11}, author = {Felice Iandoli and Raffaele Scandone}, editor = {Alessandro Michelangeli and Gianfausto Dell{\textquoteright}Antonio} } @inbook {Olgiati2017, title = {Effective Non-linear Dynamics of Binary Condensates and Open Problems}, booktitle = {Advances in Quantum Mechanics: Contemporary Trends and Open Problems}, year = {2017}, pages = {239{\textendash}256}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Sch{\"o}dinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

}, isbn = {978-3-319-58904-6}, doi = {10.1007/978-3-319-58904-6_14}, url = {https://doi.org/10.1007/978-3-319-58904-6_14}, author = {Alessandro Olgiati}, editor = {Alessandro Michelangeli and Gianfausto Dell{\textquoteright}Antonio} } @article {2017, title = {Friedrichs systems in a Hilbert space framework: solvability and multiplicity}, number = {SISSA;16/2017/MATE}, year = {2017}, abstract = {The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antoni{\'c} and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.}, url = {http://preprints.sissa.it/handle/1963/35280}, author = {Nenad Antoni{\'c} and Marko Erceg and Alessandro Michelangeli} } @article {doi:10.1080/14029251.2017.1346348, title = {Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates}, journal = {Journal of Nonlinear Mathematical Physics}, volume = {24}, number = {3}, year = {2017}, pages = {426-464}, publisher = {Taylor \& Francis}, abstract = {

We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schr{\"o}dinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schr{\"o}dinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl{\textquoteright}s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.

}, doi = {10.1080/14029251.2017.1346348}, url = {https://doi.org/10.1080/14029251.2017.1346348}, author = {Alessandro Michelangeli and Alessandro Olgiati} } @article {2017, title = {Krein-Visik-Birman self-adjoint extension theory revisited}, number = {SISSA;25/2017/MATE}, year = {2017}, abstract = {The core results of the so-called KreIn-Visik-Birman theory of self-adjoint extensions of semi-bounded symmetric operators are reproduced, both in their original and in a more modern formulation, within a comprehensive discussion that includes missing details, elucidative steps, and intermediate results of independent interest.}, url = {http://preprints.sissa.it/handle/1963/35286}, author = {Matteo Gallone and Alessandro Michelangeli and Andrea Ottolini} } @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 {Michelangeli2017, title = {Mean-field quantum dynamics for a mixture of Bose{\textendash}Einstein condensates}, journal = {Analysis and Mathematical Physics}, volume = {7}, number = {4}, year = {2017}, month = {Dec}, pages = {377{\textendash}416}, abstract = {

We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove that condensation persists at later times and we show quantitatively that the many-body Schr{\"o}dinger dynamics is effectively described by a system of coupled cubic non-linear Schr{\"o}dinger equations, one for each component.

}, issn = {1664-235X}, doi = {10.1007/s13324-016-0147-3}, url = {https://doi.org/10.1007/s13324-016-0147-3}, author = {Alessandro Michelangeli and Alessandro Olgiati} } @article {2017, title = {Moduli of semistable sheaves as quiver moduli}, number = {arXiv:1709.05555}, year = {2017}, abstract = {

In the 1980s Dr{\'e}zet and Le Potier realized moduli spaces of Gieseker-semistable sheaves on\ P2\ as what are now called quiver moduli spaces. We discuss how this construction can be understood using t-structures and exceptional collections on derived categories, and how it can be extended to a similar result\ on\ P1{\texttimes}P1.

}, url = {https://arxiv.org/abs/1709.05555}, author = {Andrea Maiorana} } @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 {2017, title = {POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder}, journal = {Communications in Applied and Industrial Mathematics}, volume = {8}, year = {2017}, pages = {210-236}, abstract = {

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

}, doi = {10.1515/caim-2017-0011}, author = {Giovanni Stabile and Saddam Hijazi and Andrea Mola and Stefano Lorenzi and Gianluigi Rozza} } @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 = {Regularity estimates for scalar conservation laws in one space dimension}, number = {SISSA;37/2017/MATE}, year = {2017}, abstract = {In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function {\textflorin} has on the entropy solution. More precisely, if the set ⟨w : {\textflorin} " (w) /= 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of {\textflorin}. If moreover the set ⟨w : {\textflorin} " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that {\textflorin}{\textquoteright} 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.}, url = {http://preprints.sissa.it/handle/1963/35291}, author = {Elio Marconi} } @inbook {Olgiati2017, title = {Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian}, booktitle = {Advances in Quantum Mechanics: Contemporary Trends and Open Problems}, year = {2017}, pages = {257{\textendash}266}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, address = {Cham}, abstract = {

The effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation. We elucidate the steps needed to adapt to the magnetic case the proof of the derivation of the Gross-Pitaevskii equation within the {\textquoteleft}{\textquoteleft}projection counting{\textquoteright}{\textquoteright} scheme.

}, isbn = {978-3-319-58904-6}, doi = {10.1007/978-3-319-58904-6_15}, url = {https://doi.org/10.1007/978-3-319-58904-6_15}, author = {Alessandro Olgiati}, editor = {Alessandro Michelangeli and Gianfausto Dell{\textquoteright}Antonio} } @article {2017, title = {Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei}, number = {SISSA;26/2017/MATE}, year = {2017}, abstract = {We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the KreIn-Vi{\v s}ik- Birman extension scheme, or also on Grubb{\textquoteright}s universal classification theory, as opposite to previous works within the standard von Neu- mann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the exten- sion, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.}, url = {http://preprints.sissa.it/handle/1963/35287}, author = {Matteo Gallone and Alessandro Michelangeli} } @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 {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 {MolaHeltaiDeSimone2017, title = {Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations}, journal = {Journal of Ship Research}, volume = {61}, number = {1}, year = {2017}, pages = {1{\textendash}14}, abstract = {

We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov-Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

}, doi = {https://doi.org/10.5957/JOSR.61.1.160016}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {MR3584583, title = {Adaptivity and blow-up detection for nonlinear evolution problems}, journal = {SIAM J. Sci. Comput.}, volume = {38}, number = {6}, year = {2016}, pages = {A3833{\textendash}A3856}, issn = {1064-8275}, doi = {10.1137/16M106073X}, url = {https://doi.org/10.1137/16M106073X}, author = {Andrea Cangiani and E.H. Georgoulis and Kyza, Irene and Metcalfe, Stephen} } @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 {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 {2016, title = {Confinement of dislocations inside a crystal with a prescribed external strain}, year = {2016}, note = {Preprint SISSA 20/2016/MATE}, abstract = {We study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.}, url = {http://urania.sissa.it/xmlui/handle/1963/35247}, author = {Ilaria Lucardesi and Marco Morandotti and Riccardo Scala and Davide Zucco} } @article {Fiorenza2016, title = {Construction of Real-Valued Localized Composite Wannier Functions for Insulators}, journal = {Annales Henri Poincar{\'e}}, volume = {17}, number = {1}, year = {2016}, month = {Jan}, pages = {63{\textendash}97}, abstract = {

We consider a real periodic Schr{\"o}dinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

}, issn = {1424-0661}, doi = {10.1007/s00023-015-0400-6}, url = {https://doi.org/10.1007/s00023-015-0400-6}, author = {Domenico Fiorenza and Domenico Monaco and Gianluca Panati} } @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 {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 {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 {2016, title = {A model for the quasistatic growth of cracks with fractional dimension}, number = {SISSA;10/2016/MATE}, year = {2016}, abstract = {We study a variational model for the quasistatic growth of cracks with fractional dimension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic evolution. Both the antiplane and the planar cases are treated.}, url = {http://urania.sissa.it/xmlui/handle/1963/35175}, author = {Gianni Dal Maso and Marco Morandotti} } @article {2016, title = {Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type}, number = {SISSA;65/2016/MATE}, year = {2016}, abstract = {We reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan- Skornyakov type for a system of two identical fermions coupled with a third particle of different nature through an interaction of zero range. We proceed through an operator-theoretic approach based on the self-adjoint extension theory of Krein, Vi{\v s}iik, and Birman. We identify the explicit {\textquoteleft}Krein-Vi{\v s}ik-Birman extension param- eter{\textquoteright} as an operator on the {\textquoteleft}space of charges{\textquoteright} for this model (the {\textquoteleft}Krein space{\textquoteright}) and we come to formulate a sharp conjecture on the dimensionality of its kernel. Based on our conjecture, for which we also discuss an amount of evidence, we explain the emergence of a multiplicity of extensions in a suitable regime of masses and we re- produce for the first time the previous partial constructions obtained by means of an alternative quadratic form approach.}, url = {http://urania.sissa.it/xmlui/handle/1963/35267}, author = {Alessandro Michelangeli and Andrea Ottolini} } @article {MR3576570, title = {The nonconforming virtual element method for the Stokes equations}, journal = {SIAM J. Numer. Anal.}, volume = {54}, number = {6}, year = {2016}, pages = {3411{\textendash}3435}, issn = {0036-1429}, doi = {10.1137/15M1049531}, url = {https://doi.org/10.1137/15M1049531}, author = {Andrea Cangiani and Gyrya, Vitaliy and Manzini, Gianmarco} } @article {2016, title = {Non-linear Schr{\"o}dinger system for the dynamics of a binary condensate: theory and 2D numerics}, number = {SISSA;63/2016/MATE}, year = {2016}, abstract = {We present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.}, url = {http://urania.sissa.it/xmlui/handle/1963/35266}, author = {Alessandro Michelangeli and Giuseppe Pitton} } @article {2016, title = {On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians}, number = {SISSA;11/2016/MATE}, year = {2016}, abstract = {For quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the {\textquoteleft}{\textquoteleft}Ter-Martirosyan--Skornyakov condition{\textquoteright}{\textquoteright} gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.}, url = {http://urania.sissa.it/xmlui/handle/1963/35195}, author = {Alessandro Michelangeli and Andrea Ottolini} } @article {Modena2016, title = {A quadratic interaction estimate for conservation laws: motivations, techniques and open problems}, journal = {Bulletin of the Brazilian Mathematical Society, New Series}, volume = {47}, number = {2}, year = {2016}, month = {Jun}, pages = {589{\textendash}604}, abstract = {

In a series of joint works with S. Bianchini [3, 4, 5], we proved a quadratic interaction estimate for general systems of conservation laws. Aim of this paper is to present the results obtained in the three cited articles [3, 4, 5], discussing how they are related with the general theory of hyperbolic conservation laws. To this purpose, first we explain why this quadratic estimate is interesting, then we give a brief overview of the techniques we used to prove it and finally we present some related open problems.

}, issn = {1678-7714}, doi = {10.1007/s00574-016-0171-9}, url = {https://doi.org/10.1007/s00574-016-0171-9}, author = {Stefano Modena} } @article {modena2016quadratic, title = {Quadratic interaction estimate for hyperbolic conservation laws, an overview}, journal = {Contemporary Mathematics. Fundamental Directions}, volume = {59}, year = {2016}, pages = {148{\textendash}172}, publisher = {Peoples{\textquoteright} Friendship University of Russia}, author = {Stefano Modena} } @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 {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 {farina2016symmetry, title = {Symmetry properties of some solutions to some semilinear elliptic equations}, journal = {Annali della Scuola Normale Superiore di Pisa. Classe di scienze}, volume = {16}, number = {4}, year = {2016}, pages = {1209{\textendash}1234}, publisher = {Classe di Scienze}, author = {Farina, Alberto and Andrea Malchiodi and Matteo Rizzi} } @article {Fiorenza2016, title = {Z2 Invariants of Topological Insulators as Geometric Obstructions}, journal = {Communications in Mathematical Physics}, volume = {343}, number = {3}, year = {2016}, month = {May}, pages = {1115{\textendash}1157}, abstract = {

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to $-\mathbb{1}$. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a $\mathbb{Z}_2$-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four $\mathbb{Z}_2$ invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.

}, issn = {1432-0916}, doi = {10.1007/s00220-015-2552-0}, url = {https://doi.org/10.1007/s00220-015-2552-0}, author = {Domenico Fiorenza and Domenico Monaco and Gianluca Panati} } @article {2015, title = {A class of Hamiltonians for a three-particle fermionic system at unitarity}, year = {2015}, note = {This SISSA preprint is composed of 29 pages and is recorded in PDF format}, abstract = {We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.}, url = {http://urania.sissa.it/xmlui/handle/1963/34469}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Domenico Finco and Alessandro Michelangeli and Alessandro Teta} } @article {doi:10.1002/mma.3450, title = {A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity}, journal = {Mathematical Methods in the Applied Sciences}, volume = {38}, number = {18}, year = {2015}, pages = {5217-5230}, abstract = {

In this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,$\infty$)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 \< p \< 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,$\infty$)$. Copyright {\textcopyright} 2015\ John Wiley \& Sons, Ltd.

}, keywords = {35J58, 35Q74, compatibility conditions, elasticity, Korn inequality, strain decomposition, subclass74B05}, doi = {10.1002/mma.3450}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450}, author = {Maggiani, Giovanni Battista and Riccardo Scala and Nicolas Van Goethem} } @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 = {Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets}, year = {2015}, institution = {SISSA}, abstract = {We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results {\`a} la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure.}, url = {http://urania.sissa.it/xmlui/handle/1963/35140}, author = {Dario Mazzoleni and Davide Zucco} } @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 {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 {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 {2015, title = {FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows}, journal = {Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22}, year = {2015}, abstract = {

In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov{\textendash}Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

}, doi = {10.1016/j.enganabound.2015.04.006}, url = {http://urania.sissa.it/xmlui/handle/1963/34466}, author = {Nicola Giuliani and Andrea Mola and Luca Heltai and L. Formaggia} } @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} } @mastersthesis {2015, title = {Geometric phases in graphene and topological insulators}, year = {2015}, school = {SISSA}, abstract = {This thesis collects three of the publications that the candidate produced during his Ph.D. studies. They all focus on geometric phases in solid state physics. We first study topological phases of 2-dimensional periodic quantum systems, in absence of a spectral gap, like e.g. (multilayer) graphene. A topological invariant n_v in Z, baptized eigenspace vorticity, is attached to any intersection of the energy bands, and characterizes the local topology of the eigenprojectors around that intersection. With the help of explicit models, each associated to a value of n_v in Z, we are able to extract the decay at infinity of the single-band Wannier function w in mono- and bilayer graphene, obtaining |w(x)| <= const |x|^{-2} as |x| tends to infinity. Next, we investigate gapped periodic quantum systems, in presence of time-reversal symmetry. When the time-reversal operator Theta is of bosonic type, i.e. it satisfies Theta^2 = 1, we provide an explicit algorithm to construct a frame of smooth, periodic and time-reversal symmetric (quasi-)Bloch functions, or equivalently a frame of almost-exponentially localized, real-valued (composite) Wannier functions, in dimension d <= 3. In the case instead of a fermionic time-reversal operator, satisfying Theta^2 = -1, we show that the existence of such a Bloch frame is in general topologically obstructed in dimension d=2 and d=3. This obstruction is encoded in Z_2-valued topological invariants, which agree with the ones proposed in the solid state literature by Fu, Kane and Mele.}, keywords = {Geometric phases, graphene, topological insulators, Wannier functions, Bloch frames}, author = {Domenico Monaco} } @article {2015, title = {Global well-posedness of the magnetic Hartree equation with non-Strichartz external fields}, number = {SISSA;07/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We study the magnetic Hartree equation with external fields to which magnetic Strichartz estimates are not necessarily applicable. We characterise the appropriate notion of energy space and in such a space we prove the global well-posedness of the associated initial value problem by means of energy methods only.}, url = {http://urania.sissa.it/xmlui/handle/1963/34440}, author = {Alessandro Michelangeli} } @article {2015, title = {Homogenization problems in the Calculus of Variations: an overview}, number = {SISSA;13/2015/MATE}, year = {2015}, note = {DEDICATED TO PROF. ORLANDO LOPES}, institution = {SISSA}, abstract = {In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude by mentioning some open problems.}, url = {http://urania.sissa.it/xmlui/handle/1963/34455}, author = {Jose Matias and Marco Morandotti} } @article {https://doi.org/10.1002/nme.4854, title = {Hourglass stabilization and the virtual element method}, journal = {International Journal for Numerical Methods in Engineering}, volume = {102}, number = {3-4}, year = {2015}, pages = {404-436}, abstract = {SummaryIn this paper, we establish the connections between the virtual element method (VEM) and the hourglass control techniques that have been developed since the early 1980s to stabilize underintegrated C0 Lagrange finite element methods. In the VEM, the bilinear form is decomposed into two parts: a consistent term that reproduces a given polynomial space and a correction term that provides stability. The essential ingredients of -continuous VEMs on polygonal and polyhedral meshes are described, which reveals that the variational approach adopted in the VEM affords a generalized and robust means to stabilize underintegrated finite elements. We focus on the heat conduction (Poisson) equation and present a virtual element approach for the isoparametric four-node quadrilateral and eight-node hexahedral elements. In addition, we show quantitative comparisons of the consistency and stabilization matrices in the VEM with those in the hourglass control method of Belytschko and coworkers. Numerical examples in two and three dimensions are presented for different stabilization parameters, which reveals that the method satisfies the patch test and delivers optimal rates of convergence in the L2 norm and the H1 seminorm for Poisson problems on quadrilateral, hexahedral, and arbitrary polygonal meshes. Copyright {\textcopyright} 2015 John Wiley \& Sons, Ltd.}, keywords = {consistency matrix, hourglass control, polygonal and polyhedral finite elements, stabilization matrix, underintegration, virtual element method}, doi = {https://doi.org/10.1002/nme.4854}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4854}, author = {Andrea Cangiani and Manzini, G. and Russo, A. and Sukumar, N.} } @article {MR3340083, title = {Hourglass stabilization and the virtual element method}, journal = {Internat. J. Numer. Methods Engrg.}, volume = {102}, number = {3-4}, year = {2015}, pages = {404{\textendash}436}, issn = {0029-5981}, doi = {10.1002/nme.4854}, url = {https://doi.org/10.1002/nme.4854}, author = {Andrea Cangiani and Manzini, G. and Russo, A. and Sukumar, N.} } @mastersthesis {2015, title = {Interaction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws}, year = {2015}, school = {SISSA}, abstract = {This thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate.}, keywords = {Hyperbolic conservation laws}, url = {http://urania.sissa.it/xmlui/handle/1963/34542}, author = {Stefano Modena} } @mastersthesis {2015, title = {Normal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries}, year = {2015}, school = {SISSA}, abstract = {In this thesis we are going to study normal random matrix models which generalize naturally the polynomially perturbed Ginibre ensamble, focusing in particular on their eigenvalue distribution and on the asymptotics of the associated orthogonal polynomials. \\ The main result we are going to present are the following: \begin{itemize} \item we describe the explicit derivation of the equilibrium measure for a class of potentials with discrete rotational symmetries, namely of the form \[V(z)=|z|^{2n}-t(z^{d}+\bar{z}^{d})\qquad n,d\in\mathbb{N},\ \ d\leq2n\ \ t>0 .\] \item We obtain the strong asymptotics for the orthogonal polynomials associated to the weight \[ e^{-NV(z)},\quad V(z)=|z|^{2s}-t(z^s+\bar{z}^{s}) \qquad z \in \mathbb{C},\;s\in \mathbb{N},\quad t>0,\] and we will show how the density of their zeroes is related to the eigenvalue distribution of the corresponding matrix model; \item We show how the conformal maps used to describe the support of the equilibrium measure for polynomial perturbation of the potential $V(z)=|z|^{2n}$ lead to a natural generalization of the concept of polynomial curves introduced in by Elbau. \end{itemize}}, keywords = {Mathematical Physics}, author = {Dario Merzi} } @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 {2015, title = {Onofri-Type Inequalities for Singular Liouville Equations}, year = {2015}, publisher = {Springer US}, abstract = {

We study the blow-up behavior of minimizing sequences for the singular Moser{\textendash}Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

}, doi = {10.1007/s12220-015-9589-3}, author = {Gabriele Mancini} } @article {2015, title = {The phototransduction machinery in the rod outer segment has a strong efficacy gradient}, number = {Proceedings of the National Academy of Sciences of the United States of America;Volume 112, issue 20; pp. E2715-E2724}, year = {2015}, note = {Open Access article}, publisher = {National Academy of Sciences}, doi = {10.1073/pnas.1423162112}, url = {http://urania.sissa.it/xmlui/handle/1963/35157}, author = {Monica Mazzolini and Giuseppe Facchetti and L. Andolfi and R. Proietti Zaccaria and S. Tuccio and J. Treud and Claudio Altafini and Enzo M. Di Fabrizio and Marco Lazzarino and G. Rapp and Vincent Torre} } @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} } @article {2015, title = {Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system}, journal = {Advances in Computational Mathematics}, volume = {special issue for MoRePaS 2012}, year = {2015}, abstract = {

The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

}, keywords = {Domain decomposition, Error estimation, Non-coercive problem, Porous medium equation, Reduced basis method, Stokes flow}, issn = {1019-7168}, doi = { 10.1007/s10444-014-9396-6}, author = {Immanuel Martini and Gianluigi Rozza and Bernard Haasdonk} } @article {NegriManzoniRozza2015, title = {Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations}, journal = {Computers and Mathematics with Applications}, volume = {69}, number = {4}, year = {2015}, pages = {319{\textendash}336}, abstract = {

This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

}, doi = {10.1016/j.camwa.2014.12.010}, author = {Federico Negri and Andrea Manzoni and Gianluigi Rozza} } @article {2015, title = {Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils}, journal = {Comput Methods Appl Mech Eng. 2015;284:1147{\textendash}1180}, number = {;284}, year = {2015}, abstract = {We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.}, doi = {10.1016/j.cma.2014.11.037}, author = {Andrea Manzoni and Filippo Salmoiraghi and Luca Heltai} } @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 = {Sch{\"o}dinger operators on half-line with shrinking potentials at the origin}, number = {SISSA;06/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We discuss the general model of a Schr{\"o}dinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.}, url = {http://urania.sissa.it/xmlui/handle/1963/34439}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli} } @mastersthesis {2015, title = {Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.}, year = {2015}, school = {SISSA}, abstract = {We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.}, keywords = {Moser-Trudinger}, author = {Gabriele Mancini} } @article {2015, title = {Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results}, year = {2015}, abstract = {

We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34489}, author = {Gabriele Mancini} } @article {2015, title = {Stability of closed gaps for the alternating Kronig-Penney Hamiltonian}, number = {SISSA;16/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {We consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions.}, url = {http://urania.sissa.it/xmlui/handle/1963/34460}, author = {Alessandro Michelangeli and Domenico Monaco} } @article {2015, title = {Stability of the (2+2)-fermionic system with zero-range interaction}, number = {SISSA;29/2015/MATE}, year = {2015}, note = {This SISSA preprint has 17 pages and recorded in PDF format}, abstract = {We introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the the celebrated (and ubiquitous, in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system.}, url = {http://urania.sissa.it/xmlui/handle/1963/34474}, author = {Alessandro Michelangeli and Paul Pfeiffer} } @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 {2015, title = {Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry}, journal = {Acta Applicandae Mathematicae, vol. 137, Issue 1, 2015, pages: 185-203}, year = {2015}, note = {The article is composed of 23 pages and recorded in PDF format}, publisher = {Springer}, abstract = {

We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We shortly review the Bloch-Floquet decomposition of periodic operators, and the related concepts of Bloch frames and composite Wannier functions. We show that the latter are almost-exponentially localized if and only if there exists a smooth periodic Bloch frame, and that the obstruction to the latter condition is the triviality of a Hermitian vector bundle, called the Bloch bundle. The r{\^o}le of additional Z_2-symmetries, as time-reversal and space-reflection symmetry, is discussed, showing how time-reversal symmetry implies the triviality of the Bloch bundle, both in the bosonic and in the fermionic case. Moreover, the same Z_2-symmetry allows to define a finer notion of isomorphism and, consequently, to define new topological invariants, which agree with the indices introduced by Fu, Kane and Mele in the context of topological insulators.

}, doi = {10.1007/s10440-014-9995-8}, url = {http://urania.sissa.it/xmlui/handle/1963/34468}, author = {Domenico Monaco and Gianluca Panati} } @article {2015, title = {Three-sphere low-Reynolds-number swimmer with a passive elastic arm}, number = {European Physical Journal E; Volume 38; Issue 5; Article number 42}, year = {2015}, publisher = {Springer}, abstract = {One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer{\textquoteright}s geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.}, doi = {10.1140/epje/i2015-15042-3}, url = {http://urania.sissa.it/xmlui/handle/1963/34530}, author = {Alessandro Montino and Antonio DeSimone} } @article {jevnikar2015topological, title = {A topological join construction and the Toda system on compact surfaces of arbitrary genus}, journal = {Analysis \& PDE}, volume = {8}, number = {8}, year = {2015}, pages = {1963{\textendash}2027}, publisher = {Mathematical Sciences Publishers}, doi = {10.2140/apde.2015.8.1963}, author = {Aleks Jevnikar and Kallel, Sadok and Andrea Malchiodi} } @article {2015, title = {Translation and adaptation of Birman{\textquoteright}s paper "On the theory of self-adjoint extensions of positive definite operators" (1956)}, number = {SISSA;08/2015/MATE}, year = {2015}, institution = {SISSA}, abstract = {This is an accurate translation from Russian and adaptation to the modern mathematical jargon of a classical paper by M. Sh. Birman published in 1956, which is still today central in the theory of self-adjoint extensions of semi-bounded operators, and for which yet no English version was available so far.}, url = {http://urania.sissa.it/xmlui/handle/1963/34443}, author = {Mikhail Khotyakov and Alessandro Michelangeli} } @article {MR3269437, title = {Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems}, journal = {IMA J. Numer. Anal.}, volume = {34}, number = {4}, year = {2014}, pages = {1578{\textendash}1597}, issn = {0272-4979}, doi = {10.1093/imanum/drt052}, url = {https://doi.org/10.1093/imanum/drt052}, author = {Andrea Cangiani and E.H. Georgoulis and Metcalfe, Stephen} } @article {2014, title = {Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription}, number = {International Mathematics Research Notices;volume 2014; issue 9; pages 2356-2400;}, year = {2014}, publisher = {Oxford University Press}, abstract = {In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant{\textquoteright}s Nodal Domain Theorem. We also show that on any manifold of dimension n>=3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n>=3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.}, doi = {10.1093/imrn/rns295}, url = {http://urania.sissa.it/xmlui/handle/1963/35128}, author = {Rod R. Gover and Yaiza Canzani and Dmitry Jakobson and Rapha{\"e}l Ponge and Andrea Malchiodi} } @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 {2012, title = {Critical points of the Moser-Trudinger functional on a disk}, number = {Journal of the European Mathematical Society}, year = {2014}, note = {16 pages}, publisher = {European Mathematical Society}, abstract = {On the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.}, doi = {10.4171/JEMS/450}, url = {http://hdl.handle.net/1963/6560}, author = {Andrea Malchiodi and Luca Martinazzi} } @article {2014, title = {Curvature-adapted remeshing of CAD surfaces}, journal = {Procedia Engineering}, volume = {82}, number = {Procedia Engineering;volume 82; issue C; pages 253-265;}, year = {2014}, note = {This is an open access article under the CC BY-NC-ND license}, pages = {253{\textendash}265}, publisher = {Elsevier}, abstract = {

A common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of L{\'e}vy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

}, doi = {10.1016/j.proeng.2014.10.388}, url = {https://doi.org/10.1016/j.proeng.2014.10.388}, author = {Franco Dassi and Andrea Mola and Hang Si} } @article {2014, title = {Dynamics on a graph as the limit of the dynamics on a "fat graph"}, number = {SISSA;69/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {We discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (\fat graph") when the transversal section of this region shrinks to zero. We give evidence of the fact that if the limit dynamics exists and is induced by the Laplacian on the graph with certain self-adjoint boundary conditions, such conditions are determined by the possible presence of a zero energy resonance on the fat graph. Pictorially, one may say that in the shrinking limit the resonance acts as a bridge connecting the boundary values at the vertex along the different rays.}, url = {http://urania.sissa.it/xmlui/handle/1963/7485}, author = {Gianfausto Dell{\textquoteright}Antonio and Alessandro Michelangeli} } @article {2014, title = {An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows}, year = {2014}, abstract = {We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy \& Patera, Quarteroni \& Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework.}, keywords = {Reduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability}, author = {Andrea Manzoni} } @article {Kuwert2014, title = {Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds}, journal = {Mathematische Annalen}, volume = {359}, number = {1}, year = {2014}, month = {Jun}, pages = {379{\textendash}425}, abstract = {

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})\>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

}, issn = {1432-1807}, doi = {10.1007/s00208-013-1005-3}, url = {https://doi.org/10.1007/s00208-013-1005-3}, author = {Kuwert, Ernst and Andrea Mondino and Johannes Schygulla} } @article {MONDINO2014707, title = {Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {31}, number = {4}, year = {2014}, pages = {707 - 724}, abstract = {

We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})\>0$ then there exists a smooth embedding $ f:\mathbb{S}^2\ \hookrightarrow\ M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})\>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow\ M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2\ \hookrightarrow\ M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

}, keywords = {Direct methods in the calculus of variations, General Relativity, Geometric measure theory, second fundamental form, Willmore functional}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2013.07.002}, url = {http://www.sciencedirect.com/science/article/pii/S0294144913000851}, author = {Andrea Mondino and Johannes Schygulla} } @article {Mondino2014, title = {Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds}, journal = {Calculus of Variations and Partial Differential Equations}, volume = {49}, number = {1}, year = {2014}, month = {Jan}, pages = {431{\textendash}470}, abstract = {

We prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m\<n$ and $p\>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int\  |H|^p$to\  avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

}, issn = {1432-0835}, doi = {10.1007/s00526-012-0588-y}, url = {https://doi.org/10.1007/s00526-012-0588-y}, author = {Andrea Mondino} } @proceedings {2014, title = {A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures}, year = {2014}, publisher = {SISSA}, abstract = {We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.}, keywords = {ship hydrodynamics}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @mastersthesis {2014, title = {Holomorphically symplectic varieties with Prym Lagrangian fibrations}, year = {2014}, school = {SISSA}, abstract = {The thesis presents a construction of singular holomorphically symplectic varieties as Lagrangian fibrations. They are relative compactified Prym varieties associated to curves on symplectic surfaces with an antisymplectic involution. They are identified with the fixed locus of a symplectic involution on singular moduli spaces of sheaves of dimension 1. An explicit example, giving a singular irreducible symplectic 6-fold without symplectic resolutions, is described for a K3 surface which is the double cover of a cubic surface. In the case of abelian surfaces, a variation of this construction is studied to get irreducible symplectic varieties: relative compactified 0-Prym varieties. A partial classification result is obtained for involutions without fixed points: either the 0-Prym variety is birational to an irreducible symplectic variety of K3[n]-type, or it does not admit symplectic resolutions.}, keywords = {Holomorphically symplectic varieties}, url = {http://urania.sissa.it/xmlui/handle/1963/7434}, author = {Tommaso Matteini} } @article {2014, title = {Homogenization of functional with linear growth in the context of A-quasiconvexity}, number = {SISSA;49/2014/MATE}, year = {2014}, institution = {SISSA}, abstract = {This work deals with the homogenization of functionals with linear growth in the context of A-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the A-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.}, url = {http://urania.sissa.it/xmlui/handle/1963/7436}, author = {Jose Matias and Marco Morandotti and Pedro M. Santos} } @article {2014, title = {Homology computation for a class of contact structures on T3}, number = {Calculus of variations and partial differential equations;volume 50; issue 3; pages 599-614;}, year = {2014}, publisher = {Springer}, abstract = {We consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability.}, doi = {10.1007/s00526-013-0648-y}, url = {http://urania.sissa.it/xmlui/handle/1963/34649}, author = {Ali Maalaoui and Vittorio Martino} } @article {2014, title = {An irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration}, number = {arXiv:1403.5523;}, year = {2014}, abstract = {A new example of an irreducible symplectic variety of dimension 6, with only finite quotient singularities, is described as a relative compactified Prymian of a family of genus 4 curves with involution. It is associated to a K3 surface which is a double cover of a cubic surface. It has a natural Lagrangian fibration in abelian 3-folds with polarization type (1,1,2). It does not admit any symplectic resolution.}, keywords = {Irreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties}, author = {Tommaso Matteini} } @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} } @mastersthesis {2014, title = {KAM for quasi-linear and fully nonlinear perturbations of Airy and KdV equations}, year = {2014}, school = {SISSA}, url = {http://urania.sissa.it/xmlui/handle/1963/7476}, author = {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 = {Legendre duality on hypersurfaces in K{\"a}hler manifolds}, number = {Advances in Geometry;volume 14; issue 2; pages 277-286;}, year = {2014}, publisher = {Walter de Gruyter and Co.}, abstract = {We give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional K{\"a}hler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.}, doi = {10.1515/advgeom-2014-0016}, url = {http://urania.sissa.it/xmlui/handle/1963/34777}, author = {Vittorio Martino} } @article {2014, title = {Lipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups}, number = {Journal of geometric analysis;volume 24; issue 1; pages 169-189;}, year = {2014}, publisher = {Springer}, abstract = {In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.}, doi = {10.1007/s12220-012-9332-2}, url = {http://urania.sissa.it/xmlui/handle/1963/34699}, author = {Vittorio Martino and Annamaria Montanari} } @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 {2014, title = {Model Order Reduction in Fluid Dynamics: Challenges and Perspectives}, number = {Modeling simulation and applications;volume 9; pages 235-273;}, year = {2014}, publisher = {Springer}, abstract = {This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and-in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.}, doi = {10.1007/978-3-319-02090-7_9}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2014, title = {A modular spectral triple for κ-Minkowski space}, number = {Journal of Geometry and Physics;volume 76; pages 136-157;}, year = {2014}, publisher = {Elsevier}, abstract = {We present a spectral triple for κ-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the κ-Poincar{\'e} algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the construction. This forces us to introduce two ingredients which have a modular flavour: the first is a twisted commutator, used to obtain a boundedness condition for the Dirac operator, and the second is a weight replacing the usual operator trace, used to measure the growth of the resolvent of the Dirac operator. We show that, under some assumptions related to the symmetries and the classical limit, there is a unique Dirac operator and automorphism such that the twisted commutator is bounded. Then, using the weight mentioned above, we compute the spectral dimension associated to the spectral triple and find that is equal to the classical dimension. Finally we briefly discuss the introduction of a real structure.}, doi = {10.1016/j.geomphys.2013.10.023}, url = {http://urania.sissa.it/xmlui/handle/1963/34895}, author = {Marco Matassa} } @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} } @mastersthesis {2014, title = {Non-commutative integration for spectral triples associated to quantum groups}, year = {2014}, school = {SISSA}, abstract = {This thesis is dedicated to the study of non-commutative integration, in the sense of spectral triples, for some non-commutative spaces associated to quantum groups.}, keywords = {Non-commutative geometry}, author = {Marco Matassa} } @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 dimension and quantum projective spaces}, number = {Symmetry, Integrability and Geometry: Methods and Applications (SIGMA);volume 10; 13p;}, year = {2014}, publisher = {Institute of Mathematics}, abstract = {We show that the family of spectral triples for quantum projective spaces introduced by D{\textquoteright}Andrea and Dbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2por its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connection with the well known notion of quantum dimension of quantum group theory is pointed out.}, doi = {10.3842/SIGMA.2014.097}, url = {http://urania.sissa.it/xmlui/handle/1963/34764}, author = {Marco Matassa} } @article {2014, title = {Semiclassical limit of focusing NLS for a family of square barrier initial data}, number = {Communications on Pure and Applied Mathematics;volume 67; issue 2; pages 246-320;}, year = {2014}, publisher = {Wiley Periodicals}, abstract = {The small dispersion limit of the focusing nonlinear Schr{\"o}dinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non-self-adjoint scattering problem and ill-posed limiting Whitham equations associated to focusing NLS make rigorous asymptotic results difficult. Previous studies have focused on special classes of analytic initial data for which the limiting elliptic Whitham equations are wellposed. In this paper we consider another exactly solvable family of initial data,the family of square barriers,ψ 0(x) = qχ[-L,L] for real amplitudes q. Using Riemann-Hilbert techniques, we obtain rigorous pointwise asymptotics for the semiclassical limit of focusing NLS globally in space and up to an O(1) maximal time. In particular, we show that the discontinuities in our initial data regularize by the immediate generation of genus-one oscillations emitted into the support of the initial data. To the best of our knowledge, this is the first case in which the genus structure of the semiclassical asymptotics for focusing NLS have been calculated for nonanalytic initial data.}, doi = {10.1002/cpa.21494}, url = {http://urania.sissa.it/xmlui/handle/1963/35066}, author = {Robert Jenkins and Kenneth McLaughlin} } @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 {2014, title = {Topological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene}, journal = {J. Stat. Phys 155 (2014) 1027-1071}, year = {2014}, publisher = {Journal of Statistical Physics}, abstract = {

We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|<=const |x|^{-2} as |x|{\textrightarrow}$\infty$, both in monolayer and bilayer graphene.

}, keywords = {Wannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene}, doi = {10.1007/s10955-014-0918-x}, author = {Domenico Monaco and Gianluca Panati} } @article {2014, title = {The topology of a subspace of the Legendrian curves on a closed contact 3-manifold}, number = {Advanced Nonlinear Studies;volume 14; issue 2; pages 393-426;}, year = {2014}, publisher = {Advanced Nonlinear Studies}, abstract = {In this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry.}, url = {http://urania.sissa.it/xmlui/handle/1963/35016}, author = {Ali Maalaoui and Vittorio Martino} } @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.} } @mastersthesis {2013, title = {Biregular and Birational Geometry of Algebraic Varieties}, year = {2013}, school = {SISSA}, abstract = {Every area of mathematics is characterized by a guiding problem. In algebraic geometry such problem is the classification of algebraic varieties. In its strongest form it means to classify varieties up to biregular morphisms. However, birationally equivalent varieties share many interesting properties. Therefore for any birational equivalence class it is natural to work out a variety, which is the simplest in a suitable sense, and then study these varieties. This is the aim of birational geometry. In the first part of this thesis we deal with the biregular geometry of moduli spaces of curves, and in particular with their biregular automorphisms. However, in doing this we will consider some aspects of their birational geometry. The second part is devoted to the birational geometry of varieties of sums of powers and to some related problems which will lead us to computational geometry and geometric complexity theory.}, keywords = {Moduli spaces of curves, automorphisms, Hassett{\textquoteright}s moduli spaces, varieties of sums of powers}, author = {Alex Massarenti} } @article {2013, title = {A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices}, journal = {Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598}, year = {2013}, publisher = {Elsevier}, abstract = {

We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

}, keywords = {Partial differential equations}, doi = {10.1016/j.crma.2013.07.023}, url = {http://hdl.handle.net/1963/7389}, author = {Denis Devaud and Andrea Manzoni and Gianluigi Rozza} } @article {2013, title = {Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.}, journal = {Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013}, year = {2013}, publisher = {SISSA}, abstract = {

Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

}, doi = {10.1038/srep01251}, author = {Giovanna De Palo and Giuseppe Facchetti and Monica Mazzolini and Anna Menini and Vincent Torre and Claudio Altafini} } @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 {Mondino2013, title = {The Conformal Willmore Functional: A Perturbative Approach}, journal = {Journal of Geometric Analysis}, volume = {23}, number = {2}, year = {2013}, month = {Apr}, pages = {764{\textendash}811}, abstract = {

The conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov{\textendash}Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ {\textendash} where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

}, issn = {1559-002X}, doi = {10.1007/s12220-011-9263-3}, url = {https://doi.org/10.1007/s12220-011-9263-3}, author = {Andrea Mondino} } @article {2013, title = {Connected Sum Construction for σk-Yamabe Metrics}, journal = {Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854}, number = {arXiv:0910.5353;}, year = {2013}, note = {This article has not yet been published.}, publisher = {Springer}, abstract = {In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.}, doi = {10.1007/s12220-011-9265-1}, url = {http://hdl.handle.net/1963/6441}, author = {Giovanni Catino and Lorenzo Mazzieri} } @article {10978, title = {On critical behaviour in systems of Hamiltonian partial differential equations}, year = {2013}, institution = {SISSA}, abstract = {

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

}, author = {Boris Dubrovin and Tamara Grava and Christian Klein and Antonio Moro} } @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 = {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 {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 {2013, title = {Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian}, journal = {Journal of Mathematical Analysis and Applications. Volume 399, Issue 1, 1 March 2013, Pages 333-339}, year = {2013}, note = {The article is composed of 13 pages and is recorded in PDF format}, publisher = {Elsevier}, keywords = {CR-Yamabe}, doi = {10.1016/j.jmaa.2012.10.014}, url = {http://hdl.handle.net/1963/7374}, author = {Ali Maalaoui and Vittorio Martino} } @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 = {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 {2013, title = {One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls}, number = {arXiv:1302.0901;}, year = {2013}, publisher = {SISSA}, abstract = {

In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

}, url = {http://hdl.handle.net/1963/6467}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {DAVOLI2013615, title = {A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {30}, number = {4}, year = {2013}, pages = {615 - 660}, abstract = {

The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic{\textendash}perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl{\textendash}Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff{\textendash}Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

}, keywords = {-convergence, Perfect plasticity, Prandtl{\textendash}Reuss plasticity, Quasistatic evolution, Rate-independent processes, Thin plates}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2012.11.001}, url = {http://www.sciencedirect.com/science/article/pii/S0294144912001035}, author = {Elisa Davoli and Maria Giovanna Mora} } @article {2013, title = {Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants}, journal = {Numerische Mathematik, 2013}, number = {SISSA Preprint;43/2012/M}, year = {2013}, publisher = {Springer}, abstract = {In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.}, keywords = {parametrized Stokes equations}, url = {http://hdl.handle.net/1963/6339}, author = {Gianluigi Rozza and Phuong Huynh and Andrea Manzoni} } @article {NegriRozzaManzoniQuarteroni2013, title = {Reduced basis method for parametrized elliptic optimal control problems}, journal = {SIAM Journal on Scientific Computing}, volume = {35}, number = {5}, year = {2013}, pages = {A2316{\textendash}A2340}, abstract = {We propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique.}, doi = {10.1137/120894737}, author = {Federico Negri and Gianluigi Rozza and Andrea Manzoni and Alfio Quarteroni} } @article {2013, title = {A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics}, number = {SISSA preprint;15/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows}, number = {SISSA preprint;14/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2013, title = {Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics}, number = {SISSA preprint;13/2013/MATE}, year = {2013}, institution = {SISSA}, author = {Toni Lassila and Andrea Manzoni and Gianluigi Rozza} } @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 {2012, title = {A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions}, journal = {Engineering Analysis with Boundary Elements, 37(1):128 {\textendash} 143, 2013.}, number = {SISSA;06/2012/M}, year = {2013}, publisher = {SISSA}, abstract = {

We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

}, keywords = {Unsteady ship-wave interaction}, url = {http://hdl.handle.net/1963/5669}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @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 {2013, title = {A variational Analysis of the Toda System on Compact Surfaces}, journal = {Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371}, number = {arXiv:1105.3701;}, year = {2013}, note = {pre-peer version, to appear in Comm. Pure Applied Math}, publisher = {Wiley}, abstract = {In this paper we consider the Toda system of equations on a compact surface. We will give existence results by using variational methods in a non coercive case. A key tool in our analysis is a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u_1, u_2.}, doi = {10.1002/cpa.21433}, url = {http://hdl.handle.net/1963/6558}, author = {Andrea Malchiodi and David Ruiz} } @article {2012, title = {On the behaviour of flexible retaining walls under seismic actions}, journal = {Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094}, year = {2012}, publisher = {ICE Publishing}, abstract = {This paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value.}, keywords = {Centrifuge modelling}, doi = {10.1680/geot.11.P.029}, url = {http://hdl.handle.net/1963/6933}, author = {Riccardo Conti and G.S.P. Madabhushi and Giulia M.B. Viggiani} } @article {2012, title = {Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty}, journal = {Mathematical Modelling and Numerical Analysis, in press, 2012-13}, number = {SISSA;42/2012/M}, year = {2012}, publisher = {Cambridge University Press}, abstract = {We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded,\\r\\nfor which the worst-case in terms of recirculation e ffects is inferred to correspond to a strong ori fice flow through near-complete occlusion. A worst-case optimal control approach is applied to the steady\\r\\nNavier-Stokes equations in 2D to identify an anastomosis angle and a cu ed shape that are robust with respect to a possible range of residual \\r\\nflows. We also consider a reduced order modelling framework\\r\\nbased on reduced basis methods in order to make the robust design problem computationally feasible. The results obtained in 2D are compared with simulations in a 3D geometry but without model\\r\\nreduction or the robust framework.}, keywords = {shape optimization}, url = {http://hdl.handle.net/1963/6337}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @article {2012, title = {A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group.}, journal = {Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198}, year = {2012}, publisher = {SISSA}, abstract = {In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1}, doi = {10.1515/CRELLE.2011.159}, url = {http://hdl.handle.net/1963/6556}, author = {Andrea Malchiodi and Paul Yang and Jih-Hsin Cheng and JennFang Hwang} } @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 = {Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density}, number = {arXiv:0901.4041;}, year = {2012}, note = {21 pages}, publisher = {Elsevier}, abstract = {

The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

}, doi = {10.1016/j.jde.2011.09.009}, url = {http://hdl.handle.net/1963/3466}, author = {Maria Giovanna Mora and Lucia Scardia} } @article {2012, title = {Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime}, journal = {Phys. Rev. D 86 (2012) 124035}, number = {arXiv:1206.5315;}, year = {2012}, note = {12 pages, 5 figures}, publisher = {American Physical Society}, abstract = {The interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.}, keywords = {Doubly special relativity}, doi = {10.1103/PhysRevD.86.124035}, author = {Giovanni Amelino-Camelia and Antonino Marciano and Marco Matassa and Giacomo Rosati} } @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 = {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} } @inbook {2012, title = {Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs}, booktitle = {Springer, Indam Series, Vol. 4, 2012}, number = {SISSA Preprint;44/2012/M}, year = {2012}, publisher = {Springer}, organization = {Springer}, abstract = {The set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.}, keywords = {solution manifold}, url = {http://hdl.handle.net/1963/6340}, author = {Toni Lassila and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza} } @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 {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 = {Nonlinear thin-walled beams with a rectangular cross-section-Part I}, journal = {Math. Models Methods Appl. Sci. 22, 1150016 (2012)}, number = {SISSA;79/2010/M}, year = {2012}, publisher = {World Scientific}, abstract = {Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results.}, doi = {10.1142/S0218202511500163}, url = {http://hdl.handle.net/1963/4104}, author = {Lorenzo Freddi and Maria Giovanna Mora and Roberto Paroni} } @article {2012, title = {Non-uniqueness results for critical metrics of regularized determinants in four dimensions}, journal = {Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37}, number = {arXiv:1105.3762;}, year = {2012}, note = {35 pages, title changed, added determinant of half-torsion, references added. Comm. Math. Phys., to appear}, publisher = {Springer}, abstract = {The regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger{\textquoteright}s half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions.}, doi = {10.1007/s00220-012-1535-7}, url = {http://hdl.handle.net/1963/6559}, author = {Matthew Gursky and Andrea Malchiodi} } @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} } @proceedings {2012, title = {Reduction strategies for PDE-constrained oprimization problems in Haemodynamics}, number = {SISSA;41/2012/M}, year = {2012}, abstract = {Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation.}, keywords = {inverse problems}, url = {http://hdl.handle.net/1963/6338}, author = {Gianluigi Rozza and Andrea Manzoni and Federico Negri} } @article {2012, title = {Reverse engineering the euglenoid movement}, journal = {Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879}, year = {2012}, abstract = {Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20\% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340\%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.}, keywords = {microswimmers}, doi = {10.1073/pnas.1213977109}, url = {http://hdl.handle.net/1963/6444}, author = {Marino Arroyo and Luca Heltai and Daniel Mill{\'a}n and Antonio DeSimone} } @article {doi:10.1080/17513758.2011.611260, title = {Self-propelled micro-swimmers in a Brinkman fluid}, journal = {Journal of Biological Dynamics}, volume = {6}, number = {sup1}, year = {2012}, note = {PMID: 22873677}, pages = {88-103}, publisher = {Taylor \& Francis}, abstract = {

We prove an existence, uniqueness, and regularity result for the motion of a self-propelled micro-swimmer in a particulate viscous medium, modelled as a Brinkman fluid. A suitable functional setting is introduced to solve the Brinkman system for the velocity field and the pressure of the fluid by variational techniques. The equations of motion are written by imposing a self-propulsion constraint, thus allowing the viscous forces and torques to be the only ones acting on the swimmer. From an infinite-dimensional control on the shape of the swimmer, a system of six ordinary differential equations for the spatial position and the orientation of the swimmer is obtained. This is dealt with standard techniques for ordinary differential equations, once the coefficients are proved to be measurable and bounded. The main result turns out to extend an analogous result previously obtained for the Stokes system.

}, doi = {10.1080/17513758.2011.611260}, url = {https://doi.org/10.1080/17513758.2011.611260}, author = {Marco Morandotti} } @article {2012, title = {Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions}, journal = {Rev. Math. Phys. 24 (2012), 1250017}, number = {arXiv:1201.5740;}, year = {2012}, publisher = {World Scientific}, abstract = {We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs.}, doi = {10.1142/S0129055X12500171}, url = {http://hdl.handle.net/1963/6069}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Domenico Finco and Alessandro Michelangeli and Alessandro Teta} } @conference {Mola2012, title = {A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves}, booktitle = {17th Int. Conf. Ships Shipp. Res.}, year = {2012}, author = {Andrea Mola and Luca Heltai and Antonio DeSimone} } @article {2012, title = {Thermodynamic phase transitions and shock singularities}, journal = {Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719}, number = {arXiv:1107.0394;}, year = {2012}, publisher = {The Royal Society}, abstract = {We show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed.}, doi = {10.1098/rspa.2011.0459}, url = {http://hdl.handle.net/1963/6090}, author = {Giuseppe De Nittis and Antonio Moro} } @article {2012, title = {Weighted barycentric sets and singular Liouville equations on compact surfaces}, journal = {Journal of Functional Analysis 262 (2012) 409-450}, number = {arXiv:1105.2363;}, year = {2012}, publisher = {Elsevier}, abstract = {Given a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]).}, doi = {10.1016/j.jfa.2011.09.012}, url = {http://hdl.handle.net/1963/5218}, author = {Alessandro Carlotto and Andrea Malchiodi} } @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 {2011, title = {Axial symmetry of some steady state solutions to nonlinear Schr{\"o}dinger equations}, journal = {Proc. Amer. Math. Soc. 139 (2011), 1023-1032}, number = {SISSA;75/2010/M}, year = {2011}, publisher = {American Mathematical Society}, abstract = {In this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space.}, keywords = {Nonlinear Schr{\"o}dinger equation}, doi = {10.1090/S0002-9939-2010-10638-X}, url = {http://hdl.handle.net/1963/4100}, author = {Changfeng Gui and Andrea Malchiodi and Haoyuan Xu and Paul Yang} } @article {2011, title = {A class of existence results for the singular Liouville equation}, journal = {Comptes Rendus Mathematique 349 (2011) 161-166}, year = {2011}, publisher = {Elsevier}, abstract = {We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern{\textendash}Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional.}, doi = {10.1016/j.crma.2010.12.016}, url = {http://hdl.handle.net/1963/5793}, author = {Alessandro Carlotto and Andrea Malchiodi} } @article {MR2796151, title = {Convergence of the mimetic finite difference method for eigenvalue problems in mixed form}, journal = {Comput. Methods Appl. Mech. Engrg.}, volume = {200}, number = {9-12}, year = {2011}, pages = {1150{\textendash}1160}, issn = {0045-7825}, doi = {10.1016/j.cma.2010.06.011}, url = {https://doi.org/10.1016/j.cma.2010.06.011}, author = {Andrea Cangiani and Gardini, Francesca and Manzini, Gianmarco} } @article {2011, title = {Covered by lines and Conic connected varieties}, journal = {Le Matematiche 66 (2011) 137-151}, number = {arXiv:1105.5918;}, year = {2011}, publisher = {Universita\\\' di Catania, Dipartimento di Matematica e Informatica}, abstract = {We study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak.}, doi = {10.4418/2011.66.2.12}, url = {http://hdl.handle.net/1963/5788}, author = {Simone Marchesi and Alex Massarenti and Saeed Tafazolian} } @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 = {Critical points of the Moser-Trudinger functional}, number = {SISSA;46/2011/M}, year = {2011}, institution = {SISSA}, keywords = {Moser-Trudinger inequality}, url = {http://hdl.handle.net/1963/4592}, author = {Francesca De Marchis and Andrea Malchiodi and Luca Martinazzi} } @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 Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers}, journal = {SIAM J. Math. Anal.}, volume = { 43}, number = {SISSA;44/2010/M}, year = {2011}, pages = {1345-1368}, publisher = {Society for Industrial and Applied Mathematics}, abstract = {

We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

}, doi = {10.1137/10080083X}, url = {http://hdl.handle.net/1963/3894}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @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 = {Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems}, journal = {Matematische Annalen 349 (2011) 75-115}, number = {SISSA;12/2009/FM}, year = {2011}, publisher = {Springer}, abstract = {We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.}, doi = {10.1007/s00208-010-0509-3}, url = {http://hdl.handle.net/1963/3584}, author = {Guido Carlet and Boris Dubrovin and Luca Philippe Mertens} } @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 = {Large Time Existence for Thin Vibrating Plates}, journal = {Communication in Partial Differential Equations 36 (2011) 2062-2102}, number = {SISSA;59/2009/M}, year = {2011}, publisher = {Taylor \& Francis}, abstract = {We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.}, doi = {10.1080/03605302.2011.618209}, url = {http://hdl.handle.net/1963/3755}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2011, title = {The matching property of infinitesimal isometries on elliptic surfaces and elasticity on thin shells}, journal = {Archive for Rational Mechanics and Analysis 200 (2011) 1023-1050}, number = {SISSA;75/2008/M}, year = {2011}, publisher = {Springer}, abstract = {Using the notion of Γ-convergence, we discuss the limiting behavior of the three-dimensional nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like h β with 2 < β < 4. We establish that, for the given scaling regime, the limiting theory reduces to linear pure bending. Two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of W 2,2 first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.}, doi = {10.1007/s00205-010-0387-6}, url = {http://hdl.handle.net/1963/3392}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @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} } @article {Mola2011, title = {Multi-physics modelling and sensitivity analysis of olympic rowing boat dynamics}, journal = {Sports Engineering}, volume = {14}, number = {2-4}, year = {2011}, month = {nov}, pages = {85{\textendash}94}, publisher = {Springer Nature}, doi = {10.1007/s12283-011-0075-2}, url = {https://doi.org/10.1007/s12283-011-0075-2}, author = {Andrea Mola and Mehdi Ghommem and Muhammad R. Hajj} } @article {2011, title = {New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces}, journal = {Geometric and Functional Analysis 21 (2011) 1196-1217}, number = {SISSA;74/2010/M}, year = {2011}, publisher = {Springer}, abstract = {We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.}, doi = {10.1007/s00039-011-0134-7}, url = {http://hdl.handle.net/1963/4099}, author = {Andrea Malchiodi and David Ruiz} } @article {2011, title = {Nonlinear thin-walled beams with a rectangular cross-section - Part II}, number = {SISSA;14/2011/M}, year = {2011}, institution = {SISSA}, abstract = {In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..}, keywords = {Thin-walled cross-section beams}, url = {http://hdl.handle.net/1963/4169}, author = {Lorenzo Freddi and Maria Giovanna Mora and Roberto Paroni} } @article {2011, title = {On the number of eigenvalues of a model operator related to a system of three particles on lattices}, journal = {J. Phys. A 44 (2011) 315302}, year = {2011}, publisher = {IOP Publishing}, doi = {10.1088/1751-8113/44/31/315302}, url = {http://hdl.handle.net/1963/5496}, author = {Gianfausto Dell{\textquoteright}Antonio and Zahriddin I. Muminov and Y.M. Shermatova} } @article {2011, title = {Planar loops with prescribed curvature: existence, multiplicity and uniqueness results}, journal = {Proceedings of the American Mathematical Society 139 (2011) 4445-4459}, number = {SISSA;08/2010/M}, year = {2011}, publisher = {American Mathematical Society}, keywords = {Plane curves}, doi = {10.1090/S0002-9939-2011-10915-8}, url = {http://hdl.handle.net/1963/3842}, author = {Roberta Musina} } @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 = {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 {2011, title = {The time-dependent von K{\'a}rm{\'a}n plate equation as a limit of 3d nonlinear elasticity}, journal = {Calculus of Variations and Partial Differential Equations 41 (2011) 241-259}, number = {SISSA;74/2009/M}, year = {2011}, publisher = {Springer}, abstract = {The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.}, doi = {10.1007/s00526-010-0360-0}, url = {http://hdl.handle.net/1963/3835}, author = {Helmut Abels and Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2010, title = {Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results}, journal = {Arch. Ration. Mech. Anal. 196 (2010) 907-950}, number = {SISSA;02/2009/M}, year = {2010}, abstract = {In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.}, doi = {10.1007/s00205-009-0259-0}, url = {http://hdl.handle.net/1963/3406}, author = {Jesus Garcia Azorero and Andrea Malchiodi and Luigi Montoro and Ireneo Peral} } @article {2010, title = {Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56}, number = {SISSA;03/2009/M}, year = {2010}, abstract = {In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in.}, doi = {10.1016/j.anihpc.2009.06.005}, url = {http://hdl.handle.net/1963/3409}, author = {Jesus Garcia Azorero and Andrea Malchiodi and Luigi Montoro and Ireneo Peral} } @article {2010, title = {Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density}, number = {SISSA;67/2010/M}, year = {2010}, abstract = {The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von K{\'a}rm{\'a}n plate theory for rods, and the linear theory.}, url = {http://hdl.handle.net/1963/4086}, author = {Elisa Davoli and Maria Giovanna Mora} } @article {2010, title = {Exact reconstruction of damaged color images using a total variation model}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331}, year = {2010}, publisher = {Elsevier}, abstract = {In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity.}, doi = {10.1016/j.anihpc.2010.06.004}, url = {http://hdl.handle.net/1963/4039}, author = {Irene Fonseca and Giovanni Leoni and Francesco Maggi and Massimiliano Morini} } @article {2010, title = {Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.}, journal = {The European journal of neuroscience. 2010 Oct; 32(8):1364-79}, number = {PMID:20950280;}, year = {2010}, publisher = {Wiley}, abstract = {

We report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

}, doi = {10.1111/j.1460-9568.2010.07403.x}, url = {http://hdl.handle.net/1963/4480}, author = {Dario Motti and Caroline Le Duigou and Nicole Chemaly and Lucia Wittner and Dejan Lazarevic and Helena Krmac and Troels Torben Marstrand and Eivind Valen and Remo Sanges and Elia Stupka and Albin Sandelin and Enrico Cherubini and Stefano Gustincich and Richard Miles} } @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 {mercuri2010global, title = {A global compactness result for the p-Laplacian involving critical nonlinearities}, journal = {Discrete \& Continuous Dynamical Systems-A}, volume = {28}, number = {2}, year = {2010}, pages = {469{\textendash}493}, abstract = {
We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

}, doi = {10.3934/dcds.2010.28.469}, url = {http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097}, author = {Mercuri, Carlo and Willem, Michel} } @article {2010, title = {Homogeneous binary trees as ground states of quantum critical Hamiltonians}, journal = {Phys. Rev. A 81 (2010) 062335}, number = {arXiv.org;0912.0466v2}, year = {2010}, publisher = {American Physical Society}, abstract = {

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

}, doi = {10.1103/PhysRevA.81.062335}, url = {http://hdl.handle.net/1963/3909}, author = {Pietro Silvi and Vittorio Giovannetti and Simone Montangero and Matteo Rizzi and J. Ignacio Cirac and Rosario Fazio} } @article {2010, title = {Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems}, journal = {New J. Phys. 12 (2010) 075018}, year = {2010}, publisher = {IOP Publishing}, abstract = {

In this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems.We discuss in more detail our results for one-dimensional (1D) systems (the Ising and Heisenberg models) and present new data for the 2D Ising model. Together with the results for the critical exponents, we provide a detailed description of the numerical algorithm and a discussion of new optimization\\nstrategies. The relation between the critical properties of the system and the tensor structure of the MERA is expressed using the formalism of quantum channels, which we review and extend.

}, doi = {10.1088/1367-2630/12/7/075018}, url = {http://hdl.handle.net/1963/4067}, author = {Matteo Rizzi and Simone Montangero and Pietro Silvi and Vittorio Giovannetti and Rosario Fazio} } @article {2010, title = {Optimally swimming Stokesian Robots}, number = {SISSA;54/2010/M}, year = {2010}, abstract = {We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.}, url = {http://hdl.handle.net/1963/3929}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet} } @article {2010, title = {Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis}, journal = {Nonlinearity. vol. 23, (2010), page 2501-2507}, number = {SISSA;11/2010/FM}, year = {2010}, abstract = {

Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

}, doi = {10.1088/0951-7715/23/10/008}, url = {http://hdl.handle.net/1963/3841}, author = {Davide Masoero} } @article {2010, title = {Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials}, number = {SISSA;31/2010/M}, year = {2010}, abstract = {In this paper we deal with nonnegative distributional supersolutions for a class of linear\\nelliptic equations involving inverse-square potentials and logarithmic weights. We prove sharp nonexistence results.}, url = {http://hdl.handle.net/1963/3869}, author = {Mouhamed Moustapha Fall and Roberta Musina} } @article {2010, title = {Shell theories arising as low energy Gamma-limit of 3d nonlinear elasticity}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010) 253-295}, number = {SISSA;12/2008/M}, year = {2010}, abstract = {We discuss the limiting behavior (using the notion of gamma-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h4, h being the thickness of a shell, we derive a limiting theory which is a generalization of the von Karman theory for plates.}, doi = {10.2422/2036-2145.2010.2.02}, url = {http://hdl.handle.net/1963/2601}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {FormaggiaEtAlRowing2010, title = {A three-dimensional model for the dynamics and hydrodynamics of rowing boats}, journal = {Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology}, volume = {224}, number = {1}, year = {2010}, pages = {51-61}, abstract = {

This paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers{\textendash}-oars{\textendash}-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

}, doi = {10.1243/17543371jset46}, url = {https://doi.org/10.1243/17543371jset46}, author = {L. Formaggia and Andrea Mola and N Parolini and M Pischiutta} } @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 {2009, title = {1D periodic potentials with gaps vanishing at k=0}, journal = {Mem. Differential Equations Math. Phys. 47 (2009) 133-158}, number = {SISSA;12/2006/FM}, year = {2009}, abstract = {Appearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterise themthrough a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occurs of linearly independent solutions of the corresponding Schr{\"o}dinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature.}, url = {http://hdl.handle.net/1963/1818}, author = {Alessandro Michelangeli and Osvaldo Zagordi} } @article {2009, title = {Bubbles with prescribed mean curvature: the variational approach}, number = {SISSA;35/2009/M}, year = {2009}, note = {H-systems, prescribed mean curvature equation, blowup}, url = {http://hdl.handle.net/1963/3659}, author = {Paolo Caldiroli and Roberta Musina} } @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 = {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 {MR2525613, title = {Convergence analysis of the mimetic finite difference method for elliptic problems}, journal = {SIAM J. Numer. Anal.}, volume = {47}, number = {4}, year = {2009}, pages = {2612{\textendash}2637}, issn = {0036-1429}, doi = {10.1137/080717560}, url = {https://doi.org/10.1137/080717560}, author = {Andrea Cangiani and Manzini, Gianmarco and Russo, Alessandro} } @article {2009, title = {Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities}, journal = {Nonlinear Anal. 70 (2009) 3002-3007}, number = {SISSA;53/2008/M}, year = {2009}, abstract = {This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984.}, doi = {10.1016/j.na.2008.12.024}, url = {http://hdl.handle.net/1963/2739}, author = {Roberta Musina} } @article {fall2009foliations, title = {Foliations of small tubes in Riemannian manifolds by capillary minimal discs}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {70}, number = {12}, year = {2009}, pages = {4422{\textendash}4440}, publisher = {Elsevier}, abstract = {

Letting\ Γ\ be an embedded curve in a Riemannian manifold\ M, we prove the existence of minimal disc-type surfaces centered at\ Γinside the surface of revolution of\ M\ around\ Γ, having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

}, doi = {10.1016/j.na.2008.10.024}, url = {https://doi.org/10.1016/j.na.2008.10.024}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} } @article {2009, title = {Hardy-Sobolev-Maz\\\'ja inequalities: symmetry and breaking symmetry of extremal functions}, journal = {Commun. Contemp. Math. 11 (2009) 993-1007}, number = {SISSA;06/2008/M}, year = {2009}, doi = {10.1142/S0219199709003636}, url = {http://hdl.handle.net/1963/2569}, author = {Marita Gazzini and Roberta Musina} } @article {2009, title = {A higher order model for image restoration: the one dimensional case}, journal = {SIAM J. Math. Anal. 40 (2009) 2351-2391}, number = {SISSA;66/2008/M}, year = {2009}, abstract = {The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [6] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed and it is proved analytically that the\\nhigher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.}, doi = {10.1137/070697823}, url = {http://hdl.handle.net/1963/3174}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini} } @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 {fall2009minimal, title = {Minimal disc-type surfaces embedded in a perturbed cylinder}, journal = {Differential and Integral Equations}, volume = {22}, number = {11/12}, year = {2009}, pages = {1115{\textendash}1124}, publisher = {Khayyam Publishing, Inc.}, abstract = {

In the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

}, url = {https://projecteuclid.org/euclid.die/1356019407}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} } @article {Formaggia2009, title = {A model for the dynamics of rowing boats}, journal = {International Journal for Numerical Methods in Fluids}, volume = {61}, number = {2}, year = {2009}, month = {sep}, pages = {119{\textendash}143}, publisher = {Wiley}, doi = {10.1002/fld.1940}, url = {https://doi.org/10.1002/fld.1940}, author = {L. Formaggia and Edie Miglio and Andrea Mola and Antonio Montano} } @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 {2009, title = {A nonlinear theory for shells with slowly varying thickness}, journal = {C. R. Math. 347 (2009) 211-216}, number = {SISSA;23/2008/M}, year = {2009}, abstract = {We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.}, doi = {10.1016/j.crma.2008.12.017}, url = {http://hdl.handle.net/1963/2632}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {2009, title = {A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas}, journal = {J. Funct. Anal. 256 (2009) 2741-2745}, number = {SISSA;45/2008/M}, year = {2009}, doi = {10.1016/j.jfa.2008.08.009}, url = {http://hdl.handle.net/1963/2698}, author = {Roberta Musina} } @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 {2009, title = {On a Sobolev type inequality related to the weighted p-Laplace operator}, journal = {J. Math. Anal. Appl. 352 (2009) 99-111}, number = {SISSA;18/2008/M}, year = {2009}, doi = {10.1016/j.jmaa.2008.06.021}, url = {http://hdl.handle.net/1963/2613}, author = {Marita Gazzini and Roberta Musina} } @article {2009, title = {Some new entire solutions of semilinear elliptic equations on Rn}, journal = {Adv. Math. 221 (2009) 1843-1909}, year = {2009}, publisher = {Elsevier}, doi = {10.1016/j.aim.2009.03.012}, url = {http://hdl.handle.net/1963/3645}, author = {Andrea Malchiodi} } @article {2009, title = {Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II}, number = {SISSA;42/2009/M}, year = {2009}, abstract = {The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.}, url = {http://hdl.handle.net/1963/3700}, author = {Antonio DeSimone and Luca Heltai and Cataldo Manigrasso} } @article {2008, title = {Concentrating solutions of some singularly perturbed elliptic equations}, journal = {Front. Math. China 3 (2008) 239-252}, year = {2008}, abstract = {We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.}, doi = {10.1007/s11464-008-0015-z}, url = {http://hdl.handle.net/1963/2657}, author = {Andrea Malchiodi} } @article {2008, title = {Convergence of equilibria of three-dimensional thin elastic beams}, journal = {Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896}, number = {SISSA;69/2006/M}, year = {2008}, abstract = {A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and M{\"u}ller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.}, doi = {10.1017/S0308210506001120}, url = {http://hdl.handle.net/1963/1896}, author = {Maria Giovanna Mora and Stefan M{\"u}ller} } @article {2008, title = {Entire solutions of autonomous equations on Rn with nontrivial asymptotics}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72}, year = {2008}, abstract = {We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.}, url = {http://hdl.handle.net/1963/2640}, author = {Andrea Malchiodi} } @article {2008, title = {Equivalent definitions of asymptotic 100\% B.E.C.}, journal = {Nuovo Cimento B 123 (2008) 181-192}, number = {SISSA;102/2007/MP}, year = {2008}, abstract = {In the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent.}, doi = {10.1393/ncb/i2008-10521-y}, url = {http://hdl.handle.net/1963/2546}, author = {Alessandro Michelangeli} } @article {2008, title = {Existence of conformal metrics with constant $Q$-curvature}, journal = {Ann. of Math. 168 (2008) 813-858}, number = {SISSA;70/2004/M}, year = {2008}, abstract = {Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.}, url = {http://hdl.handle.net/1963/2308}, author = {Zindine Djadli and Andrea Malchiodi} } @article {Formaggia2008, title = {Fluid{\textendash}structure interaction problems in free surface flows: Application to boat dynamics}, journal = {International Journal for Numerical Methods in Fluids}, volume = {56}, number = {8}, year = {2008}, pages = {965{\textendash}978}, publisher = {Wiley}, doi = {10.1002/fld.1583}, url = {https://doi.org/10.1002/fld.1583}, author = {L. Formaggia and Edie Miglio and Andrea Mola and N Parolini} } @article {MR2376968, title = {Flux reconstruction and solution post-processing in mimetic finite difference methods}, journal = {Comput. Methods Appl. Mech. Engrg.}, volume = {197}, number = {9-12}, year = {2008}, pages = {933{\textendash}945}, issn = {0045-7825}, doi = {10.1016/j.cma.2007.09.019}, url = {https://doi.org/10.1016/j.cma.2007.09.019}, author = {Andrea Cangiani and Manzini, Gianmarco} } @article {2008, title = {Globally stable quasistatic evolution in plasticity with softening}, journal = {Netw. Heterog. Media 3 (2008) 567-614}, number = {SISSA;23/2007/M}, year = {2008}, abstract = {We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.}, url = {http://hdl.handle.net/1963/1965}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @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 = {Morse theory and a scalar field equation on compact surfaces}, journal = {Adv. Differential Equations 13 (2008) 1109-1129}, year = {2008}, publisher = {Khayyam Publishing}, url = {http://hdl.handle.net/1963/3531}, author = {Andrea Malchiodi} } @article {2008, title = {A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces}, number = {SISSA;29/2008/M}, year = {2008}, url = {http://hdl.handle.net/1963/2654}, author = {Massimiliano Morini} } @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 {mercuri2008positive, title = {Positive solutions of nonlinear Schr{\"o}dinger-Poisson systems with radial potentials vanishing at infinity}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl}, volume = {19}, number = {3}, year = {2008}, pages = {211{\textendash}227}, publisher = {Citeseer}, abstract = {

We deal with a weighted nonlinear Schr{\textasciidieresis}odinger-Poisson system, allowing the potentials to vanish at infinity.

}, doi = {10.1.1.510.3635}, url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635\&rep=rep1\&type=pdf}, author = {Mercuri, Carlo} } @article {2008, title = {A second order minimality condition for the Mumford-Shah functional}, journal = {Calc. Var. Partial Differential Equations 33 (2008) 37-74}, number = {SISSA;82/2006/M}, year = {2008}, abstract = {A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.}, doi = {10.1007/s00526-007-0152-3}, url = {http://hdl.handle.net/1963/1955}, author = {Filippo Cagnetti and Maria Giovanna Mora and Massimiliano Morini} } @article {2008, title = {Topological methods for an elliptic equation with exponential nonlinearities}, journal = {Discrete Contin. Dyn. Syst. 21 (2008) 277-294}, year = {2008}, abstract = {We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results.}, doi = {10.3934/dcds.2008.21.277}, url = {http://hdl.handle.net/1963/2594}, author = {Andrea Malchiodi} } @article {2008, title = {Transition layer for the heterogeneous Allen-Cahn equation}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631}, number = {arXiv.org;math/0702878v1}, year = {2008}, abstract = {We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$.}, doi = {10.1016/j.anihpc.2007.03.008}, url = {http://hdl.handle.net/1963/2656}, author = {Fethi Mahmoudi and Andrea Malchiodi and Juncheng Wei} } @article {2008, title = {A vanishing viscosity approach to quasistatic evolution in plasticity with softening}, journal = {Arch. Ration. Mech. Anal. 189 (2008) 469-544}, number = {SISSA;38/2006/M}, year = {2008}, abstract = {We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.}, doi = {10.1007/s00205-008-0117-5}, url = {http://hdl.handle.net/1963/1844}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2007, title = {The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics}, journal = {Ann. Henri Poincar{\textasciiacute}e 8 (2007), 301{\textendash}336}, year = {2007}, publisher = {2007 Birkh{\textasciidieresis}auser Verlag Basel/Switzerland}, abstract = {We study measures generated by systems of linear iterated functions,\r\ntheir Fourier transforms, and those of their orthogonal polynomials. We\r\ncharacterize the asymptotic behaviours of their discrete and continuous averages.\r\nFurther related quantities are analyzed, and relevance of this analysis\r\nto quantum mechanics is briefly discussed}, doi = {10.1007/s00023-006-0309-1}, author = {Davide Guzzetti and Giorgio Mantica} } @article {2007, title = {Bose-Einstein condensation: analysis of problems and rigorous results}, number = {SISSA;70/2007/MP}, year = {2007}, url = {http://hdl.handle.net/1963/2189}, author = {Alessandro Michelangeli} } @article {2007, title = {Boundary interface for the Allen-Cahn equation}, journal = {J. Fixed Point Theory Appl. 1 (2007) 305-336}, year = {2007}, doi = {10.1007/s11784-007-0016-7}, url = {http://hdl.handle.net/1963/2027}, author = {Andrea Malchiodi and Juncheng Wei} } @article {2007, title = {Boundary-clustered interfaces for the Allen{\textendash}Cahn equation}, journal = {Pacific Journal of Mathematics 229 (2007), No. 2, 447{\textendash}468}, year = {2007}, publisher = {Mathematical Sciences Publishers}, url = {http://hdl.handle.net/1963/5089}, author = {Andrea Malchiodi and Wei-Ming Ni and Juncheng Wei} } @article {2007, title = {Canonical structure and symmetries of the Schlesinger equations}, journal = {Comm. Math. Phys. 271 (2007) 289-373}, number = {arXiv.org;math/0311261v4}, year = {2007}, abstract = {The Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m{\texttimes}m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.}, doi = {10.1007/s00220-006-0165-3}, url = {http://hdl.handle.net/1963/1997}, author = {Boris Dubrovin and Marta Mazzocco} } @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 = {Concentration on minimal submanifolds for a singularly perturbed Neumann problem}, journal = {Adv. Math. 209 (2007) 460-525}, number = {arXiv.org;math/0611558}, year = {2007}, abstract = {We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $1

In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

}, doi = {10.4171/JEMS/78}, url = {http://hdl.handle.net/1963/2037}, author = {Giovanni Leoni and Massimiliano Morini} } @article {2007, title = {Reduced density matrices and Bose-Einstein condensation}, number = {SISSA;39/2007/MP}, year = {2007}, abstract = {Emergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the level of marginals.\\nThe topic of correlations in the condensed state is addressed in order to show their influence at this level of marginals, both in the true condensed state and in the suitable trial functions one introduces to approximate the many-body structure and energy. Complete condensation is shown to be equivalently defined at any fixed k-body level, both for pure and mixed states. Further, it is proven to be equivalent to some other characterizations in terms of asymptotic factorization of the many-body state, which are currently present in the literature.}, url = {http://hdl.handle.net/1963/1986}, author = {Alessandro Michelangeli} } @article {2007, title = {On the reductions and classical solutions of the Schlesinger equations}, journal = {Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187}, year = {2007}, publisher = {SISSA}, abstract = {The Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m{\texttimes}m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of {\textquotedblleft}more complicated{\textquotedblright}\\r\\nSchlesinger equations S(n,m) to {\textquotedblleft}simpler{\textquotedblright} S(n',m') having n' < n\\r\\nor m' < m.}, url = {http://hdl.handle.net/1963/6472}, author = {Boris Dubrovin and Marta Mazzocco} } @article {2007, title = {On the regularity of weak solutions to H-systems}, journal = {Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219}, number = {SISSA;36/2005/M}, year = {2007}, abstract = {Abstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem....}, url = {http://hdl.handle.net/1963/1753}, author = {Roberta Musina} } @article {2007, title = {Role of scaling limits in the rigorous analysis of Bose-Einstein condensation}, journal = {J. Math. Phys. 48 (2007) 102102}, number = {SISSA;14/2007/MP}, year = {2007}, abstract = {In the context of the rigorous analysis of Bose-Einstein condensation, recent achievements have been obtained in the form of asymptotic results when some appropriate scaling is performed in the Hamiltonian, and the limit of infinite number of particles is taken. In particular, two modified thermodynamic limits of infinite dilution turned out to provide an insight in this analysis, the so-\\ncalled Gross-Pitaevskii limit and the related Tomas-Fermi limit. Here such scalings are discussed with respect to their physical and mathematical motivations, and to the currently known results obtained within this framework.}, doi = {10.1063/1.2783114}, url = {http://hdl.handle.net/1963/1984}, author = {Alessandro Michelangeli} } @article {2007, title = {Smooth toric DM stacks}, number = {SISSA;64/2007/MP}, year = {2007}, abstract = {We give a new definition of smooth toric DM stacks in the same spirit of toric varieties. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.}, url = {http://hdl.handle.net/1963/2120}, author = {Barbara Fantechi and Etienne Mann and Fabio Nironi} } @article {2007, title = {Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part I: study of the limit set and approximate solutions}, number = {SISSA;51/2007/M}, year = {2007}, abstract = {We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase is highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In this first part we provide the characterization of the limit set, with natural stationarity and non-degeneracy conditions. We then construct an approximate solution up to order $\\\\epsilon^2$, showing that these conditions appear naturally in a Taylor expansion of the equation in powers of $\\\\epsilon$. Based on these, an existence result will be proved in the second part.}, url = {http://hdl.handle.net/1963/2112}, author = {Fethi Mahmoudi and Andrea Malchiodi and Marcelo Montenegro} } @article {2007, title = {Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result}, number = {SISSA;52/2007/M}, year = {2007}, abstract = {We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.}, url = {http://hdl.handle.net/1963/2111}, author = {Fethi Mahmoudi and Andrea Malchiodi} } @article {2007, title = {Some existence results for the Toda system on closed surfaces}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 391-412}, number = {SISSA;75/2005/M}, year = {2007}, abstract = {Given a compact closed surface $\\\\Sig$, we consider the {\\\\em generalized Toda} system of equations on $\\\\Sig$: $- \\\\D u_i = \\\\sum_{j=1}^2 \\\\rho_j a_{ij} \\\\left( \\\\frac{h_j e^{u_j}}{\\\\int_\\\\Sig h_j e^{u_j} dV_g} - 1 \\\\right)$ for $i = 1, 2$, where $\\\\rho_1, \\\\rho_2$ are real parameters and $h_1, h_2$ are smooth positive functions. Exploiting the variational structure of the problem and using a new minimax scheme we prove existence of solutions for generic values of $\\\\rho_1$ and for $\\\\rho_2 < 4 \\\\pi$.}, doi = {10.4171/RLM/504}, url = {http://hdl.handle.net/1963/1775}, author = {Andrea Malchiodi and Cheikh Birahim Ndiaye} } @article {2007, title = {Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws}, journal = {NoDEA Nonlinear Differential Equations Appl. 14 (2007) 569-592}, number = {SISSA;68/2005/M}, year = {2007}, doi = {10.1007/s00030-007-5010-7}, url = {http://hdl.handle.net/1963/1769}, author = {Andrea Marson and Carlotta Donadello} } @article {2007, title = {Strengthened convergence of marginals to the cubic nonlinear Schroedinger equation}, number = {SISSA;35/2007/MP}, year = {2007}, abstract = {We rewrite a recent derivation of the cubic non-linear Schroedinger equation by Adami, Golse, and Teta in the more natural formof the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the\\nnon-linear effective dynamics of a large system of interacting bosons is\\nproved in the literature.}, url = {http://hdl.handle.net/1963/1977}, author = {Alessandro Michelangeli} } @article {2007, title = {Surfactants in Foam Stability: A Phase-Field Model}, journal = {Arch. Rational Mech. Anal. 183 (2007) 411-456}, year = {2007}, abstract = {The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.}, doi = {10.1007/s00205-006-0012-x}, url = {http://hdl.handle.net/1963/2035}, author = {Irene Fonseca and Massimiliano Morini and Valeriy Slastikov} } @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 {2007, title = {Time-dependent systems of generalized Young measures}, number = {SISSA;98/2005/M}, year = {2007}, abstract = {In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.}, url = {http://hdl.handle.net/1963/1795}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora and Massimiliano Morini} } @article {2006, title = {Born approximation in the problem of the rigorous derivation of the Gross-Pitaevskii equation}, number = {SISSA;13/2006/FM}, year = {2006}, abstract = {\\\"It has a flavour of Mathematical Physics...\\\"With these words, just few years ago, prof. Di Giacomo\\nused to introduce the topic of the Born approximation within a nonrelativistic potential theory, in his {\textquoteleft}oversize\\\' course of Theoretical Physics in Pisa. Something maybe too fictitious inside the formal theory of the scattering he was teaching us at that point of the course. Now that I\\\'m (studying to become) a Mathematical Physicist indeed, dealing with such an {\textquoteleft}exotic tasting\\\' topic, those words come back to the mind, into a new perspective. Here the very recent problem of the rigorous derivation of\\nthe cubic nonlinear Schr{\"o}dinger equation (the Gross-Pitaevski{\^\i} equation) is reviewed and discussed, with respect to the role of the Born approximation that one ends up with in an appropriate scaling limit}, url = {http://hdl.handle.net/1963/1819}, author = {Alessandro Michelangeli} } @article {2006, title = {Bound states of Nonlinear Schroedinger Equations with Potentials Vanishing at Infinity}, journal = {J. Anal. Math. 98 (2006) 317-348}, number = {SISSA;18/2005/M}, year = {2006}, doi = {10.1007/BF02790279}, url = {http://hdl.handle.net/1963/1756}, author = {Antonio Ambrosetti and Andrea Malchiodi and David Ruiz} } @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 = {Compactness of solutions to some geometric fourth-order equations}, journal = {J. Reine Angew. Math. 594 (2006) 137-174}, number = {arXiv.org;math/0410140v2}, year = {2006}, abstract = {We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.}, doi = {10.1515/CRELLE.2006.038}, url = {http://hdl.handle.net/1963/2126}, author = {Andrea Malchiodi} } @article {2006, title = {Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem}, journal = {Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290}, year = {2006}, abstract = {We consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$.}, url = {http://hdl.handle.net/1963/2170}, author = {Fethi Mahmoudi and Andrea Malchiodi} } @article {2006, title = {The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results}, journal = {Arch. Ration. Mech. Anal. 181 (2006) 1-42}, number = {SISSA;79/2004/M}, year = {2006}, doi = {10.1007/s00205-005-0398-x}, url = {http://hdl.handle.net/1963/2252}, author = {Paolo Caldiroli and Roberta Musina} } @article {2006, title = {Experimental and modeling studies of desensitization of P2X3 receptors.}, journal = {Molecular pharmacology. 2006 Jul; 70(1):373-82}, number = {PMID:16627751;}, year = {2006}, publisher = {the American Society for Pharmacology and Experimental Therapeutics}, abstract = {The function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain.}, doi = {10.1124/mol.106.023564}, url = {http://hdl.handle.net/1963/4974}, author = {Elena Sokolova and Andrei Skorinkin and Igor Moiseev and Andrei A. Agrachev and Andrea Nistri and Rashid Giniatullin} } @article {2006, title = {N=1 superpotentials from multi-instanton calculus}, number = {SISSA;73/2005/FM}, year = {2006}, abstract = {In this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.}, doi = {10.1088/1126-6708/2006/01/031}, url = {http://hdl.handle.net/1963/1773}, author = {Francesco Fucito and Jose F. Morales and Rubik Poghossian and Alessandro Tanzini} } @article {2006, title = {On Palais-Smale sequences for H-systems: some examples}, journal = {Adv. Differential Equations 11 (2006) 931-960}, number = {SISSA;32/2005/M}, year = {2006}, abstract = {We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour.}, url = {http://hdl.handle.net/1963/2157}, author = {Paolo Caldiroli and Roberta Musina} } @article {2006, title = {Q-curvature flow on S^4}, journal = {J. Differential Geom. 73 (2006) 1-44}, year = {2006}, url = {http://hdl.handle.net/1963/2193}, author = {Andrea Malchiodi and Michael Struwe} } @article {2006, title = {Quantisation of bending flows}, journal = {Czechoslovak Journal of Physics 56 (2006), n. 10-11, 1143-1148}, number = {arXiv.org;nlin/0610003}, year = {2006}, abstract = {We briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\\\\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we consider the quantisation problem of the set of Hamiltonians pertaining to the problem, quite naturally called Bending Hamiltonians, and prove that their commutativity is preserved at the quantum level.}, doi = {10.1007/s10582-006-0415-9}, url = {http://hdl.handle.net/1963/2537}, author = {Gregorio Falqui and Fabio Musso} } @article {2006, title = {Quasistatic evolution problems for linearly elastic-perfectly plastic materials}, journal = {Arch. Ration. Mech. Anal. 180 (2006) 237-291}, number = {arXiv.org;math/0412212v1}, year = {2006}, abstract = {The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.}, doi = {10.1007/s00205-005-0407-0}, url = {http://hdl.handle.net/1963/2129}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora} } @inbook {2006, title = {Recent analytical developments in micromagnetics}, booktitle = {The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381.}, number = {SISSA;76/2004/M}, year = {2006}, isbn = {978-0-12-480874-4}, url = {http://hdl.handle.net/1963/2230}, author = {Antonio DeSimone and Robert V. Kohn and Stefan M{\"u}ller and Felix Otto} } @article {2006, title = {On Separation of Variables for Homogeneous SL(r) Gaudin Systems}, number = {SISSA;106/2003/FM}, year = {2006}, abstract = {By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.}, doi = {10.1007/s11040-006-9012-1}, url = {http://hdl.handle.net/1963/2538}, author = {Gregorio Falqui and Fabio Musso} } @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 {2005, title = {Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$}, journal = {Comm. Anal. Geom. 13 (2005) 187-252}, number = {arXiv.org;math/0205106v1}, year = {2005}, publisher = {International Press}, abstract = {Given a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron.}, url = {http://hdl.handle.net/1963/3533}, author = {Sagun Chanillo and Andrea Malchiodi} } @article {2005, title = {Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains}, journal = {Geometric and Functional Analysis 15 (6) 1162-1222 (2005)}, year = {2005}, publisher = {Springer}, abstract = {We prove new concentration phenomena for the equation -ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ {\textrightarrow} 0.}, doi = {10.1007/s00039-005-0542-7}, url = {http://hdl.handle.net/1963/4866}, author = {Andrea Malchiodi} } @article {2005, title = {A fourth order uniformization theorem on some four manifolds with large total Q-curvature}, journal = {C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346.}, year = {2005}, publisher = {Elsevier}, abstract = {Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open.}, doi = {10.1016/j.crma.2005.01.013}, url = {http://hdl.handle.net/1963/4868}, author = {Zindine Djadli and Andrea Malchiodi} } @article {2005, title = {Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity}, journal = {J. Eur. Math. Soc. 7 (2005) 117-144}, number = {SISSA;16/2004/M}, year = {2005}, abstract = {We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$.}, url = {http://hdl.handle.net/1963/2352}, author = {Antonio Ambrosetti and Veronica Felli and Andrea Malchiodi} } @article {2005, title = {Ionization for Three Dimensional Time-dependent Point Interactions}, journal = {Comm. Math. Phys. 257 (2005) 169-192}, number = {SISSA;11/2004/FM}, year = {2005}, abstract = {We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the {\textquoteleft}{\textquoteleft}strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.}, doi = {10.1007/s00220-005-1293-x}, url = {http://hdl.handle.net/1963/2297}, author = {Michele Correggi and Gianfausto Dell{\textquoteright}Antonio and Rodolfo Figari and Andrea Mantile} } @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 = {Minimal surfaces in pseudohermitian geometry}, journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177.}, number = {arXiv:math/0401136;}, year = {2005}, publisher = {Scuola Normale Superiore}, abstract = {We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold.}, doi = {10.2422/2036-2145.2005.1.05}, url = {http://hdl.handle.net/1963/4579}, author = {Jih-Hsin Cheng and JennFang Hwang and Andrea Malchiodi and Paul Yang} } @article {2005, title = {Multiple clustered layer solutions for semilinear Neumann problems on a ball}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163}, year = {2005}, publisher = {Elsevier}, doi = {10.1016/j.anihpc.2004.05.003}, url = {http://hdl.handle.net/1963/3532}, author = {Andrea Malchiodi and Wei-Ming Ni and Juncheng Wei} } @article {2005, title = {Self-similar folding patterns and energy scaling in compressed elastic sheets}, journal = {Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549}, year = {2005}, publisher = {Elsevier}, abstract = {Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves.}, doi = {10.1016/j.cma.2004.07.044}, url = {http://hdl.handle.net/1963/3000}, author = {Sergio Conti and Antonio DeSimone and Stefan M{\"u}ller} } @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 {2004, title = {Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains}, journal = {Ann. Inst. H. Poincar{\'e}. Anal. Non Lin{\'e}aire 21 (2004), (4), p. 445-486.}, number = {SISSA;40/2002/M}, year = {2004}, publisher = {SISSA Library}, abstract = {We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains.}, url = {http://hdl.handle.net/1963/1611}, author = {Gianni Dal Maso and Francois Murat} } @article {marraEtAl2004, title = {Calculation of impulsively started incompressible viscous flows}, journal = {Int. J. Numer. Meth. Fluids}, volume = {46}, year = {2004}, pages = {877{\textendash}902}, author = {Marra, Andrea and Andrea Mola and Quartapelle, Luigi and Riviello, Luca} } @article {2004, title = {Existence of H-bubbles in a perturbative setting}, journal = {Rev. Mat. Iberoamericana 20 (2004) 611-626}, number = {SISSA;35/2002/M}, year = {2004}, publisher = {SISSA Library}, abstract = {Given a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function.}, url = {http://hdl.handle.net/1963/1606}, author = {Paolo Caldiroli and Roberta Musina} } @article {2004, title = {H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method}, journal = {Duke Math. J. 122 (2004), no. 3, 457--484}, number = {SISSA;36/2002/M}, year = {2004}, publisher = {SISSA Library}, abstract = {Given a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a {\textquoteleft}{\textquoteleft}good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$.}, doi = {10.1215/S0012-7094-04-12232-8}, url = {http://hdl.handle.net/1963/1607}, author = {Paolo Caldiroli and Roberta Musina} } @article {2004, title = {Higher order quasiconvexity reduces to quasiconvexity}, journal = {Arch. Ration. Mech. Anal. 171 (2004) 55-81}, number = {SISSA;41/2003/M}, year = {2004}, publisher = {Springer}, abstract = {In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.}, doi = {10.1007/s00205-003-0278-1}, url = {http://hdl.handle.net/1963/2911}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni and Massimiliano Morini} } @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 = {Multidimensional boundary layers for a singularly perturbed Neumann problem}, journal = {Duke Math. J. 124 (2004) 105-143}, year = {2004}, publisher = {Duke University Press}, doi = {10.1215/S0012-7094-04-12414-5}, url = {http://hdl.handle.net/1963/2960}, author = {Andrea Malchiodi and Marcelo Montenegro} } @article {2004, title = {The role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem}, journal = {J. Anal. Math. 94 (2004) 265-291}, number = {SISSA;30/2003/M}, year = {2004}, publisher = {Hebrew University Magnes Press}, doi = {10.1007/BF02789050}, url = {http://hdl.handle.net/1963/2894}, author = {Roberta Musina} } @article {2004, title = {Singularity perturbed elliptic equations with symmetry: existence of solutions concetrating on spheres, Part II}, journal = {Indiana Univ. Math. J. 53 (2004) 297-392}, number = {SISSA;93/2002/M}, year = {2004}, publisher = {Indiana University Mathematics Journal}, doi = {10.1512/iumj.2004.53.2400}, url = {http://hdl.handle.net/1963/1663}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2004, title = {Solutions concentrating at curves for some singularly perturbed elliptic problems}, journal = {C. R. Acad. Sci. Paris, Ser. I 338 (2004) 775-780}, year = {2004}, publisher = {Elsevier}, doi = {10.1016/j.crma.2004.03.023}, url = {http://hdl.handle.net/1963/4869}, author = {Andrea Malchiodi} } @article {2004, title = {Well-posedness for general 2x2 systems of conservation laws}, journal = {Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp.}, number = {SISSA;27/99/M}, year = {2004}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1241}, author = {Fabio Ancona and Andrea Marson} } @article {2003, title = {Gaudin models and bending flows: a geometrical point of view}, journal = {J. Phys. A: Math. Gen. 36 (2003) 11655-11676}, number = {SISSA;45/2003/FM}, year = {2003}, publisher = {IOP Publishing}, abstract = {In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the \\\'standard\\\' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the \\\'bending flows\\\' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.}, doi = {10.1088/0305-4470/36/46/009}, url = {http://hdl.handle.net/1963/2884}, author = {Gregorio Falqui and Fabio Musso} } @article {2003, title = {Hybrid optimal control: case study of a car with gears}, journal = {Int. J. Control 76 (2003) 1272-1284}, year = {2003}, publisher = {Taylor and Francis}, abstract = {The purpose of this paper is to show the use of some analytical tools for hybrid optimal control. We illustrate both the hybrid maximum principle and the hybrid necessary principle at work on a simple example of a car with gears. The model is sufficiently rich to generate non-trivial optimization problems and the obtained results match with intuition. Finally, computer simulations confirm the theoretical analysis.}, doi = {10.1080/0020717031000147520}, url = {http://hdl.handle.net/1963/3022}, author = {Ciro D{\textquoteright}Apice and Mauro Garavello and Rosanna Manzo and Benedetto Piccoli} } @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 = {Prescribing scalar and boundary mean curvature on the three dimensional half sphere}, journal = {J. Geom. Anal. 13 (2003) 255-289}, number = {SISSA;36/2001/M}, year = {2003}, publisher = {Springer}, abstract = {We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results.}, doi = {10.1007/BF02930697}, url = {http://hdl.handle.net/1963/3086}, author = {Zindine Djadli and Andrea Malchiodi and Mohameden Ould Ahmedou} } @article {2003, title = {Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems}, journal = {SIAM J. Math. Anal. 35 (2003) 759-805}, number = {SISSA;60/2001/M}, year = {2003}, publisher = {SIAM}, abstract = {We prove that a wide class of singularly perturbed functionals generates as $\\\\Gamma$-limit a functional related to a free-discontinuity problem. Several applications of the result are shown.}, doi = {10.1137/S0036141001395388}, url = {http://hdl.handle.net/1963/3071}, author = {Massimiliano Morini} } @article {2003, title = {Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I}, journal = {Comm. Math. Phys. 235 (2003) no.3, 427-466}, number = {SISSA;63/2002/M}, year = {2003}, publisher = {Springer}, doi = {10.1007/s00220-003-0811-y}, url = {http://hdl.handle.net/1963/1633}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2002, title = {Admissible Riemann solvers for genuinely nonlinear P-systems of mixed type}, journal = {J. Differ. Equations, 2002, 180, 395}, number = {SISSA;33/00/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1006/jdeq.2001.4066}, url = {http://hdl.handle.net/1963/1491}, author = {Jean-Marc Mercier and Benedetto Piccoli} } @article {2002, title = {The Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps}, journal = {J. Convex Anal. 9 (2002) 1-29}, number = {SISSA;61/2001/M}, year = {2002}, publisher = {Heldermann Verlag}, abstract = {The calibration method is a classical minimality criterion, which has been recently adapted to functionals with free discontinuities by Alberti, Bouchitt{\'e}, Dal Maso. In this paper we present a further generalization of this theory to functionals defined on vector-valued maps.}, url = {http://hdl.handle.net/1963/3049}, author = {Maria Giovanna Mora} } @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 {2002, title = {Existence of minimal H-bubbles}, journal = {Commun. Contemp. Math. 4 (2002) 177-209}, number = {SISSA;67/00/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1142/S021919970200066X}, url = {http://hdl.handle.net/1963/1525}, author = {Paolo Caldiroli and Roberta Musina} } @article {2002, title = {Global calibrations for the non-homogeneous Mumford-Shah functional}, journal = {Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648}, number = {SISSA;41/2001/M}, year = {2002}, publisher = {Scuola Normale Superiore di Pisa}, abstract = {Using a calibration method we prove that, if $\\\\Gamma\\\\subset \\\\Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\\\\Gamma$ and regular outside, then the function $u_{\\\\beta}$ which solves $$ \\\\begin{cases} \\\\Delta u_{\\\\beta}=\\\\beta(u_{\\\\beta}-g)\& \\\\text{in $\\\\Omega\\\\setminus\\\\Gamma$} \\\\partial_{\\\\nu} u_{\\\\beta}=0 \& \\\\text{on $\\\\partial\\\\Omega\\\\cup\\\\Gamma$} \\\\end{cases} $$ is in turn discontinuous along $\\\\Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \\\\int_{\\\\Omega\\\\setminus S_u}|\\\\nabla u|^2 dx +{\\\\cal H}^{n-1}(S_u)+\\\\beta\\\\int_{\\\\Omega\\\\setminus S_u}(u-g)^2 dx, $$ over $SBV(\\\\Omega)$, for $\\\\beta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.}, url = {http://hdl.handle.net/1963/3089}, author = {Massimiliano Morini} } @article {2002, title = {Local calibrations for minimizers of the Mumford-Shah functional with a triple junction}, journal = {Commun. Contemp. Math. 4 (2002) 297-326}, number = {SISSA;39/2001/M}, year = {2002}, publisher = {World Scientific}, abstract = {We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method.}, doi = {10.1142/S0219199702000646}, url = {http://hdl.handle.net/1963/3050}, author = {Maria Giovanna Mora} } @article {2002, title = {Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result}, journal = {Commun. Contemp. Math., 2002, 4, 375}, number = {SISSA;82/00/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1142/S0219199702000695}, url = {http://hdl.handle.net/1963/1539}, author = {Zindine Djadli and Mohameden Ould Ahmedou and Andrea Malchiodi} } @article {2002, title = {Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications}, journal = {Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387}, number = {SISSA;83/00/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1540}, author = {Zindine Djadli and Andrea Malchiodi and Mohameden Ould Ahmedou} } @article {2002, title = {Quantum mechanics and stochastic mechanics for compatible observables at different times}, journal = {Ann.Physics 296 (2002), no.2, 371}, number = {SISSA;6/2002/FM}, year = {2002}, publisher = {SISSA Library}, doi = {10.1006/aphy.2002.6236}, url = {http://hdl.handle.net/1963/1577}, author = {Michele Correggi and Giovanni Morchio} } @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 = {The scalar curvature problem on $S\\\\sp n$: an approach via Morse theory}, journal = {Calc. Var. Partial Differential Equations 14 (2002), no. 4, 429-445}, number = {SISSA;117/99/M}, year = {2002}, publisher = {Springer}, doi = {10.1007/s005260100110}, url = {http://hdl.handle.net/1963/1331}, author = {Andrea Malchiodi} } @article {2002, title = {Singular elliptic problems with critical growth}, journal = {Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876}, number = {SISSA;54/99/M}, year = {2002}, publisher = {Dekker}, doi = {10.1081/PDE-120004887}, url = {http://hdl.handle.net/1963/1268}, author = {Paolo Caldiroli and Andrea Malchiodi} } @article {2002, title = {Solutions concentrating on spheres to symmetric singularly perturbed problems}, journal = {C.R.Math.Acad.Sci. Paris 335 (2002),no.2,145-150}, number = {SISSA;23/2002/M}, year = {2002}, publisher = {SISSA Library}, abstract = {We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere.}, doi = {10.1016/S1631-073X(02)02414-7}, url = {http://hdl.handle.net/1963/1594}, author = {Antonio Ambrosetti and Andrea Malchiodi and Wei-Ming Ni} } @article {2002, title = {On the Yamabe problem and the scalar curvature problems under boundary conditions}, journal = {Math. Ann., 2002, 322, 667}, number = {SISSA;52/00/M}, year = {2002}, publisher = {SISSA Library}, doi = {10.1007/s002080100267}, url = {http://hdl.handle.net/1963/1510}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @article {2001, title = {Adiabatic limits of closed orbits for some Newtonian systems in R-n}, journal = {Asymptotic Anal., 2001, 25, 149-181}, number = {SISSA;53/00/M}, year = {2001}, publisher = {SISSA Library}, abstract = {We deal with a Newtonian system like x\\\'\\\' + V\\\'(x) = 0. We suppose that V: \\\\R^n \\\\to \\\\R possesses an (n-1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M.}, url = {http://hdl.handle.net/1963/1511}, author = {Andrea Malchiodi} } @article {2001, title = {Bihamiltonian geometry and separation of variables for Toda lattices}, journal = {J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127}, number = {SISSA;139/99/FM}, year = {2001}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1354}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni} } @article {2001, title = {Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations}, journal = {Adv. Differential Equations 6 (2001), no. 3, 303-326}, number = {SISSA;105/99/M}, year = {2001}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1319}, author = {Paolo Caldiroli and Roberta Musina} } @article {2001, title = {Finite Difference Approximation of Free Discontinuity Problems}, journal = {Proc. Royal Soc. Edinb. Ser. A 131 (2001), no. 3, 567-595}, number = {SISSA;14/99/M}, year = {2001}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1228}, author = {Massimo Gobbino and Maria Giovanna Mora} } @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} } @mastersthesis {2001, title = {Free-discontinuity problems: calibration and approximation of solutions}, year = {2001}, school = {SISSA}, keywords = {Calibration of solutions}, url = {http://hdl.handle.net/1963/5398}, author = {Massimiliano Morini} } @article {2001, title = {Global continuous Riemann solver for nonlinear elasticity}, journal = {Arch. Ration. Mech. An., 2001, 156, 89}, number = {SISSA;35/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1007/s002050100118}, url = {http://hdl.handle.net/1963/1493}, author = {Jean-Marc Mercier and Benedetto Piccoli} } @article {2001, title = {Instantons on the Quantum 4-Spheres S^4_q}, journal = {Comm. Math. Phys. 221 (2001) 161-168}, number = {arXiv.org;math/0012103v2}, year = {2001}, publisher = {Springer}, abstract = {We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $ch_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $ch_2(e)$ does not vanish as well and the couple $(ch_1(e), ch_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology.}, doi = {10.1007/PL00005572}, url = {http://hdl.handle.net/1963/3135}, author = {Ludwik Dabrowski and Giovanni Landi and Tetsuya Masuda} } @article {2001, title = {Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set}, journal = {Ann. I. H. Poincare - An., 2001, 18, 403}, number = {SISSA;21/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1016/S0294-1449(01)00075-0}, url = {http://hdl.handle.net/1963/1479}, author = {Maria Giovanna Mora and Massimiliano Morini} } @article {2001, title = {Multiple positive solutions of some elliptic equations in \\\\bold R\\\\sp N}, journal = {Nonlinear Anal. 43 (2001) 159-172}, number = {SISSA;133/1998/M}, year = {2001}, publisher = {Elsevier}, doi = {10.1016/S0362-546X(99)00186-8}, url = {http://hdl.handle.net/1963/3094}, author = {Andrea Malchiodi} } @article {2001, title = {Multiplicity results for some nonlinear Schrodinger equations with potentials}, journal = {Arch. Ration. Mech. An., 2001, 159, 253}, number = {SISSA;108/00/AF}, year = {2001}, publisher = {SISSA Library}, doi = {10.1007/s002050100152}, url = {http://hdl.handle.net/1963/1564}, author = {Antonio Ambrosetti and Andrea Malchiodi and Simone Secchi} } @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 = {Picard and Chazy solutions to the Painlev{\'e} VI equation}, journal = {Math. Ann. 321 (2001) 157-195}, number = {SISSA;89/98/FM}, year = {2001}, publisher = {Springer}, abstract = {

I study the solutions of a particular family of Painlev{\'e} VI equations with the parameters $\beta=\gamma=0, \delta=1/2$ and $2\alpha=(2\mu-1)^2$, for $2\mu\in\mathbb{Z}$. I show that the case of half-integer $\mu$ is integrable and that the solutions are of two types: the so-called Picard solutions and the so-called Chazy solutions. I give explicit formulae for them and completely determine their asymptotic behaviour near the singular points $0,1,\infty$ and their nonlinear monodromy. I study the structure of analytic continuation of the solutions to the PVI$\mu$ equation for any $\mu$ such that $2\mu\in\mathbb{Z}$. As an application, I classify all the algebraic solutions. For $\mu$ half-integer, I show that they are in one to one correspondence with regular polygons or star-polygons in the plane. For $\mu$ integer, I show that all algebraic solutions belong to a one-parameter family of rational solutions.

}, doi = {10.1007/PL00004500}, url = {http://hdl.handle.net/1963/3118}, author = {Marta Mazzocco} } @inbook {2001, title = {S^2 type parametric surfaces with prescribed mean curvature and minimal energy}, booktitle = {Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkh{\"a}user, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77}, number = {SISSA;34/2002/M}, year = {2001}, publisher = {Birkhauser}, organization = {Birkhauser}, url = {http://hdl.handle.net/1963/1605}, author = {Paolo Caldiroli and Roberta Musina} } @article {2001, title = {Stationary states for a two-dimensional singular Schrodinger equation}, journal = {Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633.}, number = {SISSA;35/99/M}, year = {2001}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1249}, author = {Paolo Caldiroli and Roberta Musina} } @article {2001, title = {On the symmetric scalar curvature problem on S\\\\sp n}, journal = {J. Differential Equations 170 (2001) 228-245}, year = {2001}, publisher = {Elsevier}, abstract = {We discuss some existence results dealing with the scalar curvature problem on S\\\\sp n in the presence of various symmetries.}, doi = {10.1006/jdeq.2000.3816}, url = {http://hdl.handle.net/1963/3095}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {2000, title = {A bi-Hamiltonian theory for stationary KDV flows and their separability}, journal = {Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52}, number = {SISSA;137/99/FM}, year = {2000}, publisher = {SISSA Library}, doi = {10.1070/rd2000v005n01ABEH000122}, url = {http://hdl.handle.net/1963/1352}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni and Jorge P. Zubelli} } @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 = {An elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy}, journal = {Theor. Math. Phys. 122 (2000) 17-28}, number = {SISSA;117/98/FM}, year = {2000}, publisher = {Springer}, abstract = {We give an elementary construction of the solutions of the KP hierarchy associated with polynomial τ-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a consequence, we establish a Wronskian formula for the polynomial τ-functions of the KP hierarchy. This formula, known in the literature, is obtained very directly.}, doi = {10.1007/BF02551166}, url = {http://hdl.handle.net/1963/3223}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni and Jorge P. Zubelli} } @mastersthesis {2000, title = {Existence and multiplicity results for some problems in Riemannian geometry}, year = {2000}, school = {SISSA}, keywords = {Yamabe problem}, url = {http://hdl.handle.net/1963/5948}, author = {Andrea Malchiodi} } @article {2000, title = {Functionals depending on curvatures with constraints}, journal = {Rend. Sem. Mat. Univ. Padova 104 (2000), 173--199}, number = {SISSA;85/99/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1299}, author = {Maria Giovanna Mora and Massimiliano Morini} } @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 = {Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets}, journal = {J. Math. Pures Appl. 79, 2 (2000) 141-162}, number = {SISSA;47/99/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0021-7824(99)00140-3}, url = {http://hdl.handle.net/1963/1261}, author = {Gianni Dal Maso and Maria Giovanna Mora and Massimiliano Morini} } @article {2000, title = {Monodromy of certain Painlev{\'e}-VI transcendents and reflection groups}, journal = {Invent. Math. 141 (2000) 55-147}, number = {arXiv.org;math/9806056v1}, year = {2000}, publisher = {Springer}, abstract = {We study the global analytic properties of the solutions of a particular family of Painleve\\\' VI equations with the parameters $\\\\beta=\\\\gamma=0$, $\\\\delta={1\\\\over2}$ and $\\\\alpha$ arbitrary. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. This result is used to classify all the algebraic solutions of our Painleve\\\' VI equation.}, doi = {10.1007/PL00005790}, url = {http://hdl.handle.net/1963/2882}, author = {Boris Dubrovin and Marta Mazzocco} } @article {2000, title = {A note on the scalar curvature problem in the presence of symmetries}, journal = {Ricerche Mat. 49 (2000), suppl., 169-176}, number = {SISSA;150/99/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1365}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @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 = {Reduction of bi-Hamiltonian systems and separation of variables: an example from the Boussinesq hierarchy}, journal = {Theor. Math. Phys. 122 (2000) 176-192}, number = {SISSA;123/98/FM}, year = {2000}, publisher = {Springer}, abstract = {We discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel\\\'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.}, doi = {10.1007/BF02551195}, url = {http://hdl.handle.net/1963/3219}, author = {Gregorio Falqui and Franco Magri and G. Tondo} } @article {2000, title = {Scalar curvature under boundary conditions}, journal = {Cr. Acad. Sci. I-Math, 2000, 330, 1013}, number = {SISSA;48/00/M}, year = {2000}, publisher = {SISSA Library}, doi = {10.1016/S0764-4442(00)00312-8}, url = {http://hdl.handle.net/1963/1506}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @article {2000, title = {On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature}, number = {SISSA;102/00/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1558}, author = {Roberta Musina and Paolo Caldiroli} } @mastersthesis {1999, title = {Approximation, Stability and control for Conservation Laws}, year = {1999}, school = {SISSA}, url = {http://hdl.handle.net/1963/5500}, author = {Andrea Marson} } @inbook {1999, title = {A bihamiltonian approach to separation of variables in mechanics}, booktitle = {Proceedings of the workshop on nonlinearity, integrability and all that : twenty years after NEEDS \\\'79, Lecce, Italy, July 1 - 10, 1999 / ed. by M. Boiti. - Singapore : World Scientific, 2000. - p. 258-266}, year = {1999}, publisher = {World Scientific}, organization = {World Scientific}, abstract = {This paper is a report on a recent approach to the theory of separability of the Hamilton-Jacobi equations from the viewpoint of bihamiltonian geometry.}, url = {http://hdl.handle.net/1963/3222}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni} } @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} } @inbook {1999, title = {The method of Poisson pairs in the theory of nonlinear PDEs}, booktitle = {Direct and inverse methods in nonlinear evolution equations : Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999 / Robert Conte ... ; Antonio M. Greco ed. - Berlin : Springer, 2003. - (Lecture Notes in Physics ; 632)}, number = {SISSA;135/99/FM}, year = {1999}, publisher = {Springer}, organization = {Springer}, abstract = {The aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear partial differential equations. The prototype of these equations is the well-known Korteweg-de Vries (KdV) equation.\\nIn these lectures we touch the following subjects:\\ni) the birth and the role of the method of Poisson pairs inside the theory of the KdV equation;\\nii) the theoretical basis of the method of Poisson pairs;\\niii) the Gel\\\'fand-Zakharevich theory of integrable systems on bi-Hamiltonian manifolds;\\niv) the Hamiltonian interpretation of the Sato picture of the KdV flows and of its linearization on an infinite-dimensional Grassmannian manifold.\\nv) the reduction technique(s) and its use to construct classes of solutions;\\nvi) the role of the technique of separation of variables in the study of the reduced systems;\\nvii) some relations intertwining the method of Poisson pairs with the method of Lax pairs.}, doi = {10.1007/b13714}, url = {http://hdl.handle.net/1963/1350}, author = {Gregorio Falqui and Franco Magri and Marco Pedroni} } @article {1999, title = {A multiplicity result for the Yamabe problem on $S\\\\sp n$}, journal = {J. Funct. Anal. 168 (1999), no. 2, 529-561}, number = {SISSA;50/99/M}, year = {1999}, publisher = {Elsevier}, abstract = {We prove a multiplicity result for the Yamabe problem on the manifold (S, g), where g is a perturbation of the standard metric g0 of Sn. Solutions are found by variational methods via an abstract perturbation result.}, doi = {10.1006/jfan.1999.3458}, url = {http://hdl.handle.net/1963/1264}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @article {10445, title = {Recurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory}, number = {arXiv:solv-int/990400;}, year = {1999}, institution = {SISSA}, abstract = {

We present here the iteration procedure for the determination of free energy ǫ2-expansion using the theory of KdV - type equations. In our approach we use the conservation laws for KdV - type equations depending explicitly on times t1, t2, . . . to find the ǫ2-expansion of u(x, t1, t2, . . .) after the infinite number of shifts of u(x, 0, 0, . . .) = x along t1, t2, . . . in recurrent form. The formulas for the free energy expansion are just obtained then as a result of quite simple integration procedure applied to un(x).

}, url = {http://hdl.handle.net/1963/6489}, author = {Boris Dubrovin and Andrei Ya A Maltsev} } @article {1999, title = {Renormalized solutions of elliptic equations with general measure data}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808}, number = {SISSA;22/99/M}, year = {1999}, publisher = {Scuola Normale Superiore di Pisa}, url = {http://hdl.handle.net/1963/1236}, author = {Gianni Dal Maso and Francois Murat and Luigi Orsina and Alain Prignet} } @article {1999, title = {On the scalar curvature problem under symmetry}, number = {SISSA;73/99/M}, year = {1999}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1287}, author = {Antonio Ambrosetti and Andrea Malchiodi} } @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} } @mastersthesis {1998, title = {Algebraic Solutions to the Painlev{\'e}-VI Equation and Reflection Groups}, year = {1998}, school = {SISSA}, keywords = {Painlev{\'e} VI equation}, url = {http://hdl.handle.net/1963/5574}, author = {Marta Mazzocco} } @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 {1997, title = {Kam theorem for generic analytic perturbations of the Guler system}, journal = {Z. Angew. Math. Phys. 48 (1997), no. 2, 193-219}, number = {SISSA;136/95/FM}, year = {1997}, publisher = {Springer}, abstract = {We apply here KAM theory to the fast rotations of a rigid body with a fixed point, subject to a purely positional potential. The problem is equivalent to a small perturbation of the Euler system. The difficulty is that the unperturbed system is properly degenerate, namely the unperturbed Hamiltonian depends only on two actions. Following the scheme used by Arnol\\\'d for the N-body problem, we use part of the perturbation to remove the degeneracy: precisely, we construct Birkhoff normal form up to a suitable finite order, thus eliminating the two fast angles; the resulting system is nearly integrable and (generically) no more degenerate, so KAM theorem applies. The resulting description of the motion is that, if the initial kinetic energy is sufficiently large, then for most initial data the angular momentum has nearly constant module, and moves slowly in the space, practically following the level curves of the initial potential averaged on the two fast angles; on the same time the body precesses around the instantaneous direction of the angular momentum, essentially as in the Euler-Poinsot motion. We also provide two simple physical examples, where the procedure does apply.}, doi = {10.1007/PL00001474}, url = {http://hdl.handle.net/1963/1038}, author = {Marta Mazzocco} } @article {1997, title = {Some properties of reachable solutions of nonlinear elliptic equations with measure data}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. S{\'e}r. 4, 25 no. 1-2 (1997), p. 375-396}, year = {1997}, publisher = {SISSA}, url = {http://hdl.handle.net/1963/6434}, author = {Gianni Dal Maso and Annalisa Malusa} } @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 {1992, title = {A variational method in image segmentation: existence and approximation result}, journal = {Acta Math. 168 (1992), no.1-2, p. 89-151}, number = {SISSA;48/89/M}, year = {1992}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/808}, author = {Gianni Dal Maso and Jean-Michel Morel and Sergio Solimini} } @article {1990, title = {Algebraic differential calculus for gauge theories}, journal = {Nuclear Phys. B. Proc. Suppl. 18A (1990), 171}, number = {SISSA;135/89/FM}, year = {1990}, publisher = {SISSA Library}, doi = {10.1016/0920-5632(90)90649-F}, url = {http://hdl.handle.net/1963/891}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1989, title = {An approach to the thin obstacle problem for variational functionals depending on vector}, journal = {Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743.}, number = {SISSA;41/89/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/802}, author = {Gianni Dal Maso and Roberta Musina} } @article {1989, title = {A pointwise regularity theory for the two-obstacle problem}, journal = {Acta Math. 163 (1989), no. 1-2, 57-107}, number = {SISSA;47/88/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/643}, author = {Gianni Dal Maso and Umberto Mosco and Maria Agostina Vivaldi} } @article {1989, title = {Surfaces of minimal area enclosing a given body in R\\\\sp 3.}, journal = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990).}, number = {SISSA;23/88/M}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/619}, author = {Giovanni Mancini and Roberta Musina} } @article {1988, title = {Algebraic reduction of the \\\'t Hooft-Polyakov monopole to the Dirac monopole.}, journal = {Phys. Lett. B 201 (1988), no. 1, 101-104.}, number = {SISSA;97/87/FM}, year = {1988}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(88)90088-3}, url = {http://hdl.handle.net/1963/578}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1988, title = {Einstein algebras and the algebraic Kaluza-Klein monopole.}, journal = {Phys. Lett. B 210 (1988), no. 1-2, 68--72.}, number = {SISSA;7/88/FM}, year = {1988}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(88)90351-6}, url = {http://hdl.handle.net/1963/603}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1988, title = {Holes and obstacles}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988), no. 4, 323-345}, number = {SISSA;20/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/501}, author = {Roberta Musina and Giovanni Mancini} } @article {1988, title = {H-surfaces with obstacles. (Italian)}, journal = {Ann. Univ. Ferrara Sez. VII (N.S.) 34 (1988), 1-14}, number = {SISSA;9/87/M}, year = {1988}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/491}, author = {Roberta Musina} } @mastersthesis {1988, title = {Variational Problems with Obstructions}, year = {1988}, school = {SISSA}, url = {http://hdl.handle.net/1963/5832}, author = {Roberta Musina} } @article {1987, title = {Extensions of Lie superalgebras and supersymmetric Abelian gauge fields.}, journal = {Phys. Lett. B 193 (1987), no. 1, 61-66.}, number = {SISSA;26/87/FM}, year = {1987}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(87)90456-4}, url = {http://hdl.handle.net/1963/507}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1987, title = {Graded Chern-Simons terms}, journal = {Phys. Lett. B 192 (1987), no. 1-2, 81-88.}, number = {SISSA;27/87/FM}, year = {1987}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(87)91146-4}, url = {http://hdl.handle.net/1963/508}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1987, title = {Lie algebra extensions and abelian monopoles.}, journal = {Phys. Lett. B 195 (1987), no. 3, 429-434}, number = {SISSA;25/87/FM}, year = {1987}, publisher = {SISSA Library}, doi = {10.1016/0370-2693(87)90043-8}, url = {http://hdl.handle.net/1963/506}, author = {Giovanni Landi and Giuseppe Marmo} } @article {1985, title = {Weak convergence of measures on spaces of semicontinuous functions.}, journal = {Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106}, number = {SISSA;76/85/MP}, year = {1985}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/463}, author = {Gianni Dal Maso and Ennio De Giorgi and Luciano Modica} }