Exact solutions for chemical concentration waves of self-propelling camphor particles racing on a ring: A novel potential dynamics perspective

TL;DR

This paper develops a potential dynamics framework to derive exact solutions for wave patterns of self-propelling camphor particles on a ring, elucidating the transition from immobility to self-propulsion.

Contribution

It introduces a novel potential dynamics approach to analytically solve for wave patterns and bifurcations in camphor particle systems on ring-shaped water channels.

Findings

Exact solutions for standing and traveling waves are obtained.

The bifurcation from immobility to self-propulsion is characterized as a pitchfork bifurcation.

The bifurcation diagram is derived semi-analytically, confirming earlier theoretical predictions.

Abstract

A potential dynamics approach is developed to determine the periodic standing and traveling wave patterns associated with self-propelling camphor objects floating on ring-shaped water channels. Exact solutions of the wave patterns are derived. The bifurcation diagram describing the transition between the immobile and self-propelling modes of camphor objects is derived semi-analytically. The bifurcation is of a pitchfork type which is consistent with earlier theoretical work in which natural boundary conditions have been considered.