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Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall

Or, Yizhar and Zhang, Sebastian and Murray, Richard M. (2011) Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall. SIAM Journal on Applied Dynamical Systems, 10 (3). pp. 1013-1041. ISSN 1536-0040.

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The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer’s trajectories and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying geometric structure of the dynamics, and establish a relation between the reversing symmetry of the system and existence and stability of periodic and steady solutions of motion near the wall. The results are demonstrated by numerical simulations and validated by motion experiments with macroscale robotic swimmer prototypes.

Item Type:Article
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Murray, Richard M.0000-0002-5785-7481
Additional Information:© 2011 Society for Industrial and Applied Mathematics. Received by the editors September 15, 2010; accepted for publication (in revised form) by T. Kaper April 23, 2011; published electronically September 20, 2011. Preliminary versions of these results appeared previously in [55] and [73].
Subject Keywords:dynamics of locomotion, low-Reynolds swimming, dynamic stability
Issue or Number:3
Classification Code:AMS subject classifications. 37J15, 37J25, 76M60
Record Number:CaltechAUTHORS:20111031-100248775
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Official Citation:Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall Yizhar Or, Sebastian Zhang, and Richard M. Murray SIAM J. Appl. Dyn. Syst. 10, pp. 1013-1041 (29 pages)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27516
Deposited By: Ruth Sustaita
Deposited On:31 Oct 2011 18:14
Last Modified:03 Oct 2019 03:24

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