# A limiting model for a low Reynolds number swimmer with N passive elastic arms

## TL;DR

This paper analyzes a low Reynolds number swimmer with an active arm and multiple passive elastic arms, proving the convergence of a discrete model to a continuous limit and exploring its swimming performance through numerical experiments.

## Contribution

It introduces a generalized model with N passive springs, proves its convergence to a continuous model as N increases, and evaluates its swimming efficiency numerically.

## Key findings

- Convergence of discrete to continuous model established
- Swimmer's displacement depends on oscillation frequency and amplitude
- Numerical results demonstrate performance variations with parameters

## Abstract

We consider a low Reynolds number artificial swimmer that consists of an active arm followed by $N$ passive springs separated by spheres. This setup generalizes an approach proposed in Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015. 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. Several numerical experiments show the performances of the displacement in terms of the frequency or the amplitude of the oscillation of the active arm.