# Controllability of 3D low Reynolds number swimmers

Jérôme Lohéac; Alexandre Munnier

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 1, page 236-268
- ISSN: 1292-8119

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topLohéac, Jérôme, and Munnier, Alexandre. "Controllability of 3D low Reynolds number swimmers." ESAIM: Control, Optimisation and Calculus of Variations 20.1 (2014): 236-268. <http://eudml.org/doc/272911>.

@article{Lohéac2014,

abstract = {In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots for which the inertia effects can be neglected. Our first main contribution is to prove that any such microswimmer has the ability to track, by performing a sequence of shape changes, any given trajectory in the fluid. We show that, in addition, this can be done by means of arbitrarily small body deformations that can be superimposed to any preassigned sequence of macro shape changes. Our second contribution is to prove that, when no macro deformations are prescribed, tracking is generically possible by means of shape changes obtained as a suitable combination of only four elementary deformations. Eventually, still considering finite dimensional deformations, we state results about the existence of optimal swimming strategies on short time intervals, for a wide class of cost functionals.},

author = {Lohéac, Jérôme, Munnier, Alexandre},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {locomotion; biomechanics; stokes fluid; geometric control theory; Stokes fluid},

language = {eng},

number = {1},

pages = {236-268},

publisher = {EDP-Sciences},

title = {Controllability of 3D low Reynolds number swimmers},

url = {http://eudml.org/doc/272911},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Lohéac, Jérôme

AU - Munnier, Alexandre

TI - Controllability of 3D low Reynolds number swimmers

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 1

SP - 236

EP - 268

AB - In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots for which the inertia effects can be neglected. Our first main contribution is to prove that any such microswimmer has the ability to track, by performing a sequence of shape changes, any given trajectory in the fluid. We show that, in addition, this can be done by means of arbitrarily small body deformations that can be superimposed to any preassigned sequence of macro shape changes. Our second contribution is to prove that, when no macro deformations are prescribed, tracking is generically possible by means of shape changes obtained as a suitable combination of only four elementary deformations. Eventually, still considering finite dimensional deformations, we state results about the existence of optimal swimming strategies on short time intervals, for a wide class of cost functionals.

LA - eng

KW - locomotion; biomechanics; stokes fluid; geometric control theory; Stokes fluid

UR - http://eudml.org/doc/272911

ER -

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