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A limit modeling for a low Reynold number swimmer with N passive elastic arms.

Jessie Levillain
École polytechnique CMAP
Friday, June 16, 2023 - 14:00

Swimming at the microscopic scale is a subject that has multiple links in several fields of science, ranging from biology to physics. The mathematics underlying to the many questions that arise have also opened up a field of research for a little less than fifteen years.

In particular many artificial swimmers have been proposed and studied in the literature showing swimming capabilities at low Reynolds numbers. As a sake of example, a simple mathematical model of microswimmers was introduced by Najafi and Golestanian, in which the swimmer consists in three spheres linked by rigid extensible arms. This model was then extended to a three-sphere swimmer with a spring by Montino and De Simone.

Following those ideas, we study a simple model of artificial microswimmer, consisting of a rigid extensible arm followed by an N-mass-spring system. We further study the limit as the number of springs tends to infinity and the parameters are scaled conveniently, and provide a rigorous proof of the convergence of the discrete model to the continuous one. Numerical experiments show performances of the displacement in terms of frequency or amplitude of the oscillation of the active arm.

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