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## Section: New Results

### Numerical aspect of the $N$-link micro-swimmer model

Participants : Hermes Gadhêla [Univ. of York, UK] , Laetitia Giraldi, Clément Moreau, Jean-Baptiste Pomet.

This topic was initiated with a 1 year research invitation of Clément Moreau at University of York and further collaboration. The goal is to compare the ODE given by the “$N$-link swimmer” model with the PDE for an elastic rod.

In [22], we study inertialess fluid-structure interaction of active and passive inextensible filaments. In this work, we compare two different approaches that lead to model the behavior of a microscopic elastic filament immersed into a fluid. The first which derives from a continuous formalism corresponds to solve a PDE, the second method exploits the momentum balance in the asymptotic limit of small rod-like elements which are integrated semi-analytically. The equivalence between the continuous and asymptotic model allows a direct comparison between the two formalisms. The asymptotic model is simple and intuitive to implement, and generalisations for complex interaction of multiple rods. We demonstrate these via four benchmarks: transient dynamics, force-displacement buckling instability, magnetic artificial swimmer and cross-linked filament-bundle dynamics.