| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 31 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2019010 | |
| Published online | 09 April 2020 | |
Controllability of low Reynolds numbers swimmers of ciliate type
1
Université de Lorraine, CNRS, CRAN,
54000
Nancy, France.
2
Université de Lorraine, CNRS, Inria, IECL,
54000
Nancy, France.
* Corresponding author: jerome.loheac@univ-lorraine.fr
Received:
27
July
2017
Accepted:
4
March
2019
We study the locomotion of a ciliated microorganism in a viscous incompressible fluid. We use the Blake ciliated model: the swimmer is a rigid body with tangential displacements at its boundary that allow it to propel in a Stokes fluid. This can be seen as a control problem: using periodical displacements, is it possible to reach a given position and a given orientation? We are interested in the minimal dimension d of the space of controls that allows the microorganism to swim. Our main result states the exact controllability with d = 3 generically with respect to the shape of the swimmer and with respect to the vector fields generating the tangential displacements. The proof is based on analyticity results and on the study of the particular case of a spheroidal swimmer.
Mathematics Subject Classification: 74F10 / 93B27 / 76B75 / 76D07
Key words: Fluid–structure interaction / locomotion / biomechanics / Stokes fluid / geometric control theory
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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