Brownian motion of a circle swimmer in a harmonic trap

TL;DR

This paper analyzes the motion of a Brownian circle swimmer in a harmonic trap, exploring optimal strategies and resonance effects through analytical and simulation methods, with implications for microswimmer experiments.

Contribution

It provides a comprehensive analysis of a Brownian circle swimmer's dynamics in a time-dependent harmonic trap, including optimal strategies and resonance phenomena.

Findings

Maximum escape distance at resonance frequencies.

Complex spiral and rosette-like patterns due to noise.

Comparison of noise-free and noisy trajectories.

Abstract

We study the dynamics of a Brownian circle swimmer with a time-dependent self-propulsion velocity in an external temporally varying harmonic potential. For several situations, the noise-free swimming paths, the noise-averaged mean trajectories, and the mean square displacements are calculated analytically or by computer simulation. Based on our results, we discuss optimal swimming strategies in order to explore a maximum spatial range around the trap center. In particular, we find a resonance situation for the maximum escape distance as a function of the various frequencies in the system. Moreover, the influence of the Brownian noise is analyzed by comparing noise-free trajectories at zero temperature with the corresponding noise-averaged trajectories at finite temperature. The latter reveal various complex self-similar spiral or rosette-like patterns. Our predictions can be tested in experiments on artificial and biological microswimmers under dynamical external confinement.