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Séminaire des équipes de recherche
Control and Optimization of Low Reynolds number swimming
Inria Paris - Rocquencourt, amphithéâtre Alan Turing, bâtiment 1.
A 15h, entrée libre.
- Date : 20/09/2011
- Lieu : Amphithéâtre Alan Turing, bâtiment 1 - Inria Paris-Rocquencourt
- Intervenants : Marius Tucsnak, Inria Grand Est
- Organisateurs : Irene Vignon-Clementel
This presentation considers a class of problems arising in the study of self-propelling of solids in a viscous fluid. The main application we have in mind consists in using control theoretical techniques to understand self-propelled motion of a solid (fishes, swimming robots, submarines, micro-organisms) in a viscous fluid. These problems, in which the solid is propelling by changing its shape, raise important theoretical and computational challenges. We focus on the low Reynolds number case, appearing in the study of locomotion of microscopic aquatic organisms (like spermatozoids) or of micro and nano swimming robots. Since the fluid is modeled by the elliptic Stokes system, in which the time appears only as a parameter in the coupling equations with the fluid, the coupled model is, in principle, quite simple: we have a system of nonlinear ODE’s on a finite dimensional manifold. However, an important difficulty has to be solved from the first stage of the problem, which consists in obtaining the wellposedness of the system. Indeed, in order to apply Cauchy-Lipschitz type theorems, it is essential to prove that the solution of the exterior Stokes problem depends smooth enough on the shape of the interface. The next question which is studied is the controllability of the system, which is investigated by combining perturbation results with the classical Chow’s theorem. We end up with time optimal control problems, which are studied from both theoretical and numerical view points.
Mots-clés : Séminaire Paris - Rocquencourt Modélisation et Calcul Scientifique
