Phase Separation in Systems of Interacting Active Brownian Particles

TL;DR

This paper models active Brownian particle systems to understand motility-induced phase separation, comparing microscopic and macroscopic models, and identifying conditions under which phase separation occurs without attractive forces.

Contribution

It introduces four microscopic models with different interactions and derives their macroscopic limits, analyzing the conditions for phase separation in active particle systems.

Findings

MIPS occurs in models with short-range interactions

Long-range mean-field model does not exhibit MIPS

Linear stability analysis predicts phase transition boundaries

Abstract

The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive interactions between particles and their associated macroscopic models, which are formally obtained using different coarse-graining methods. The macroscopic limits are integro-differential equations for the density in phase space (positions and orientations) of the particles and may include nonlinearities in both the diffusive and advective components. In contrast to passive particles, systems of active particles can undergo phase separation without any attractive interactions, a mechanism known as motility-induced phase separation (MIPS). We explore the onset of such a transition for each model in the parameter space of occupied volume fraction and P\'eclet number via a linear stability analysis and numerical simulations at both the microscopic and macroscopic levels. We establish that one of the models, namely the mean-field model which assumes long-range repulsive interactions, cannot explain the emergence of MIPS. In contrast, MIPS is observed for the remaining three models that assume short-range interactions that localize the interaction terms in space.