Controllability properties of a class of systems modeling swimming microscopic organisms

Mario Sigalotti; Jean-Claude Vivalda

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 4, page 1053-1076
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Sigalotti, Mario, and Vivalda, Jean-Claude. "Controllability properties of a class of systems modeling swimming microscopic organisms." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 1053-1076. <http://eudml.org/doc/250744>.

@article{Sigalotti2010,
abstract = { 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. },
author = {Sigalotti, Mario, Vivalda, Jean-Claude},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Swimming micro-organisms; ciliata; high viscosity; nonlinear systems; controllability; models of swimming micro-organisms},
language = {eng},
month = {10},
number = {4},
pages = {1053-1076},
publisher = {EDP Sciences},
title = {Controllability properties of a class of systems modeling swimming microscopic organisms},
url = {http://eudml.org/doc/250744},
volume = {16},
year = {2010},
}

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
DA - 2010/10//
PB - EDP Sciences
VL - 16
IS - 4
SP - 1053
EP - 1076
AB - 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.
LA - eng
KW - Swimming micro-organisms; ciliata; high viscosity; nonlinear systems; controllability; models of swimming micro-organisms
UR - http://eudml.org/doc/250744
ER -

References

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