Geodesic
Rough wall effect on micro-swimmers
Gérard-Varet, David1  ; Giraldi, Laetitia2 
1 Institut de Mathématiques de Jussieu et Université Paris 7, Bâtiment Sophie Germain, 75205 Paris cedex 13, France
2 Unité de Mathématiques Appliqueés (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA-Paristech), 828 Boulevard des Marchaux, 91762 Palaiseau, France
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 757-788

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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.

DOI : 10.1051/cocv/2014046
Classification : 93B05
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

1 Institut de Mathématiques de Jussieu et Université Paris 7, Bâtiment Sophie Germain, 75205 Paris cedex 13, France
2 Unité de Mathématiques Appliqueés (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA-Paristech), 828 Boulevard des Marchaux, 91762 Palaiseau, France 
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     title = {Rough wall effect on micro-swimmers},
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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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