Optimal strokes at low Reynolds number: a geometric and numeric study using the Copepod and Purcell swimmers

Abstract : In this article, we make a comparative geometric and numeric analysis of the optimal strokes at low Reynolds number using two specific rigid links swimmers: the Copepod swimmer, a symmetric swimmer introduced recently 30 and the historical three-link Pur-cell swimmer 27 where the cost to minimize is the mechanical power dissipated by the fluid viscous drag forces. This leads to a sub-Riemannian problem which can be analyzed in this rich framework. In particular nilpotent approximation can be used to compute strokes with small amplitudes and they can be continued numerically to compute more general strokes. The concept of geometric efficiency corresponding to the ratio between the displacement and the length of the stroke is introduced to analyze the global opti-mality. The role of both abnormal and normal strokes is described, in particular in the symmetric case, in relation with observed motions of the microorganisms. Moreover C 1-optimality is studied using the concept of conjugate and focal points, depending upon their respective shapes. In parallel direct and indirect numerical schemes implemented in the Bocop (www.bocop.org 6) and HamPath (www.hampath.org 14) software allow to perform numerical simulations, crucial to complete the theoretical study and to evaluate the optimal solutions.
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Pré-publication, Document de travail
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Contributeur : Jérémy Rouot <>
Soumis le : mardi 2 août 2016 - 20:15:46
Dernière modification le : mardi 31 janvier 2017 - 01:03:54


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  • HAL Id : hal-01326790, version 2




Piernicola Bettiol, Bernard Bonnard, Jérémy Rouot. Optimal strokes at low Reynolds number: a geometric and numeric study using the Copepod and Purcell swimmers. 2016. <hal-01326790v2>



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