We study the effect of a rough wall on the controllability of micro-swimmers made of several balls linked by thin jacks: the so-called 3-sphere and 4-sphere swimmers. Our work completes the previous work [F. Alouges and L. Giraldi, Acta Applicandae Mathematicae 128 (2013) 153–179] dedicated to the effect of a flat wall. We show that a controllable swimmer (the 4-sphere swimmer) is not impacted by the roughness. On the contrary, we show that the roughness changes the dynamics of the 3-sphere swimmer, so that it can reach any direction almost everywhere.
Keywords: Low-Reynolds number swimming, self-propulsion, three-sphere swimmer, rough wall effect, Lie brackets, control theory, asymptotic expansion
Gérard-Varet, David 1 ; Giraldi, Laetitia 2
@article{COCV_2015__21_3_757_0,
author = {G\'erard-Varet, David and Giraldi, Laetitia},
title = {Rough wall effect on micro-swimmers},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {757--788},
year = {2015},
publisher = {EDP Sciences},
volume = {21},
number = {3},
doi = {10.1051/cocv/2014046},
zbl = {1315.93015},
mrnumber = {3358629},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2014046/}
}
TY - JOUR AU - Gérard-Varet, David AU - Giraldi, Laetitia TI - Rough wall effect on micro-swimmers JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 757 EP - 788 VL - 21 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2014046/ DO - 10.1051/cocv/2014046 LA - en ID - COCV_2015__21_3_757_0 ER -
%0 Journal Article %A Gérard-Varet, David %A Giraldi, Laetitia %T Rough wall effect on micro-swimmers %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 757-788 %V 21 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2014046/ %R 10.1051/cocv/2014046 %G en %F COCV_2015__21_3_757_0
Gérard-Varet, David; Giraldi, Laetitia. Rough wall effect on micro-swimmers. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 757-788. doi: 10.1051/cocv/2014046
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