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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2010

Controllability properties of a class of systems modeling swimming microscopic organisms

Résumé

We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable when the space of controlled velocity fields is at least three-dimensional. We also provide a complete characterization of controllable systems in the case in which the organism has a spherical shape. Finally, we offer a complete picture of controllable and non-controllable systems under the additional hypothesis that the organism and the fluid have densities of the same order of magnitude.
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Dates et versions

hal-00188193 , version 1 (15-11-2007)
hal-00188193 , version 2 (20-05-2008)

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Mario Sigalotti, Jean-Claude Vivalda. Controllability properties of a class of systems modeling swimming microscopic organisms. ESAIM: Control, Optimisation and Calculus of Variations, 2010, 16 (4), pp.1053-1076. ⟨10.1051/cocv/2009034⟩. ⟨hal-00188193v2⟩
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