Intrinsic speed characteristics of a self-propelled camphor disk under repulsive perturbations

TL;DR

This study models and analyzes the speed behavior of a self-propelled camphor disk influenced by a localized perturbation, revealing asymmetrical velocity responses through simulations and analytical solutions.

Contribution

It introduces a one-dimensional model incorporating a distance-dependent potential to describe camphor disk interactions, supported by simulations and analytical results.

Findings

Simulations reproduce experimental velocity behaviors.

Weak perturbations allow for analytical solutions.

Rotor velocity shows asymmetry depending on approach or recession.

Abstract

Camphor is a well-studied material capable of generating self-propelled motion at a water surface, and the resulting dynamics can exhibit a wide range of behaviors. Here, we analyze a one-dimensional model describing a mobile camphor disk perturbed by a second localized camphor source. The interaction between the rotor and the perturbing disk is represented by a distance-dependent potential. The study is motivated by experiments in which a camphor rotor interacts with a fixed camphor disk placed on the water surface. Numerical simulations of the model reproduce the essential features of the experimentally observed position-dependent rotor velocity for all considered forms of the potential. For weak perturbations, we derive analytical solutions valid for arbitrary potential profiles. Both the simulations and the analytical results demonstrate a pronounced asymmetry in the rotor velocity depending on whether the rotor approaches or recedes from the perturbation.