Self-propelled non-linearly diffusing particles. Aggregation and continuum description

TL;DR

This paper models self-propelled particles with density-dependent diffusion, showing that they form clusters and non-homogeneous distributions, supported by simulations and a derived continuum density equation.

Contribution

It introduces a novel model of self-propelled particles with non-linear diffusion based on local density, and derives a continuum equation explaining aggregation phenomena.

Findings

Particles form clusters in certain parameter ranges.

Numerical simulations match the continuum density equation.

Aggregation depends on local density and diffusion parameters.

Abstract

We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of parameters the long-time spatial distribution of particles is non-homogeneous, and clusters can be observed. A number density equation, which explains the emergence of the aggregates and indicates the values of the parameters for which they appear, is derived. Numerical results of this continuum density equation are also shown.