Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary

TL;DR

This paper investigates how strongly confined, non-aligning self-propelled particles behave within various boundary shapes, revealing boundary-normal alignment, non-local density distributions, and hysteretic dynamics in non-convex geometries.

Contribution

It derives the steady-state boundary density for arbitrary shapes and uncovers the effects of non-convex boundaries on particle dynamics and density distribution.

Findings

Particles align with local boundary normals under strong confinement.

In non-convex shapes, boundary normal non-uniqueness causes hysteresis.

Density distribution depends on the global geometry of the confining box.

Abstract

We study the dynamics of non-aligning, non-interacting self-propelled particles confined to a box in two dimensions. In the strong confinement limit, when the persistence length of the active particles is much larger than the size of the box, particles stay on the boundary and align with the local boundary normal. It is then possible to derive the steady-state density on the boundary for arbitrary box shapes. In non-convex boxes, the non-uniqueness of the boundary normal results in hysteretic dynamics and the density is non-local, i.e. it depends on the global geometry of the box. These findings establish a general connection between the geometry of a confining box and the behavior of an ideal active gas it confines, thus providing a powerful tool to understand and design such confinements.