Optimal Strokes for Low Reynolds Number Swimmers: An Example
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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. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901–062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).
KeywordsBiological and artificial micro-swimmers Optimal control Optimal gait Propulsion efficiency Movement and locomotion Low-Reynolds-number (creeping) flow
AMS Subject Classifications76Z10 49J20 92C10 93B05
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