Enhanced Controllability of Low Reynolds Number Swimmers in the Presence of a Wall |
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Authors: | François Alouges Laetitia Giraldi |
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Affiliation: | 1. Centre de Mathématiques Appliquées de l’Ecole Polytechnique CMAP, Ecole Polytechnique, Plateau de Saclay, 91128, Palaiseau, France
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Abstract: | Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers which is the regime of interest for micro-organisms and micro-robots. We focus on self-propelled stokesian robots composed of assemblies of balls and we prove that the presence of a wall has an effect on their motility. To rest on what has been done in Alouges et al. (Discrete Contin. Dyn. Syst., Ser. B 18(5):1189–1215, 2013) for such systems swimming on R 3, we demonstrate that a controllable swimmer remains controllable in a half space whereas the reachable set of a non fully controllable one is increased by the presence of a wall. |
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