General Criteria for Determining Rotation or Oscillation in a Two-dimensional Axisymmetric System

TL;DR

This paper presents a generic model for self-propelled particles in 2D axisymmetric systems, establishing criteria for when they exhibit rotation or oscillation through symmetry breaking, without requiring asymmetry in the system.

Contribution

It introduces a unified model and analytical criteria for predicting rotational or oscillatory behavior in symmetric 2D systems.

Findings

Criteria for rotation vs. oscillation derived from weakly nonlinear analysis

Model applicable to particles in central force fields or circular confinements

Symmetry breaking explains spontaneous motion types

Abstract

A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion.