@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 = {<p>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.</p>},
	url = {http://hdl.handle.net/1963/6467},
	author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti}
}
@article {2012,
	title = {Ogden-type energies for nematic elastomers},
	journal = {International Journal of Non-Linear mechanics },
	volume = {47},
	year = {2012},
	pages = {402-412},
	publisher = {Elsevier},
	abstract = {<p>Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).</p>},
	keywords = {Nonlinear elasticity},
	doi = {10.1016/j.ijnonlinmec.2011.10.001},
	author = {Virginia Agostiniani and Antonio DeSimone}
}
@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 {2008,
	title = {Optimal Strokes for Low Reynolds Number Swimmers: An Example},
	journal = {J. Nonlinear Sci. 18 (2008) 277-302},
	year = {2008},
	publisher = {Springer},
	abstract = {Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).},
	doi = {10.1007/s00332-007-9013-7},
	url = {http://hdl.handle.net/1963/4006},
	author = {Fran{\c c}ois Alouges and Antonio DeSimone and Aline Lefebvre}
}
