01596nas a2200133   4500008004100000245010900041210006900150260001000219520113200229100002101361700002201382700002201404856003601426       2013                        en  d00aOne-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls0 aOnedimensional swimmers in viscous fluids dynamics controllabili  bSISSA3 a<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>1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco  uhttp://hdl.handle.net/1963/646701684nas a2200157   4500008004100000245004700041210004600088260001300134300001200147490000700159520120600166653002501372100002601397700002201423856008101445       2012                        en  d00aOgden-type energies for nematic elastomers0 aOgdentype energies for nematic elastomers  bElsevier  a402-4120 v473 a<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>10aNonlinear elasticity1 aAgostiniani, Virginia1 aDeSimone, Antonio  uhttps://www.math.sissa.it/publication/ogden-type-energies-nematic-elastomers01187nas a2200145   4500008004300000245004000043210004000083520078100123100002300904700002200927700001700949700002000966700001900986856003601005       2010                        en_Ud  00aOptimally swimming Stokesian Robots0 aOptimally swimming Stokesian Robots3 aWe 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.1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca1 aLefebvre, Aline1 aMerlet, Benoit  uhttp://hdl.handle.net/1963/392901131nas a2200133   4500008004300000245006500043210006400108260001300172520071100185100002300896700002200919700002000941856003600961       2008                        en_Ud  00aOptimal Strokes for Low Reynolds Number Swimmers: An Example0 aOptimal Strokes for Low Reynolds Number Swimmers An Example  bSpringer3 aSwimming, 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).1 aAlouges, François1 aDeSimone, Antonio1 aLefebvre, Aline  uhttp://hdl.handle.net/1963/4006