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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.
Keywords: swimming micro-organisms, ciliata, high viscosity, nonlinear systems, controllability
@article{COCV_2010__16_4_1053_0,
author = {Sigalotti, Mario and Vivalda, Jean-Claude},
title = {Controllability properties of a class of systems modeling swimming microscopic organisms},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1053--1076},
publisher = {EDP-Sciences},
volume = {16},
number = {4},
year = {2010},
doi = {10.1051/cocv/2009034},
mrnumber = {2744162},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009034/}
}
TY - JOUR AU - Sigalotti, Mario AU - Vivalda, Jean-Claude TI - Controllability properties of a class of systems modeling swimming microscopic organisms JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 1053 EP - 1076 VL - 16 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009034/ DO - 10.1051/cocv/2009034 LA - en ID - COCV_2010__16_4_1053_0 ER -
%0 Journal Article %A Sigalotti, Mario %A Vivalda, Jean-Claude %T Controllability properties of a class of systems modeling swimming microscopic organisms %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 1053-1076 %V 16 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009034/ %R 10.1051/cocv/2009034 %G en %F COCV_2010__16_4_1053_0
Sigalotti, Mario; Vivalda, Jean-Claude. Controllability properties of a class of systems modeling swimming microscopic organisms. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1053-1076. doi: 10.1051/cocv/2009034
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