Phase separation of self-propelled ballistic particles

TL;DR

This paper introduces a new predictive model for phase separation in self-propelled particles that focuses on collision timescales, providing insights into the critical density for phase separation in 2D and 3D.

Contribution

It develops a collision-time based model that accurately predicts phase separation onset in self-propelled particles, especially in low-noise regimes.

Findings

Collision timescales determine phase separation

Critical density varies with dimensionality

Model validated with simulations

Abstract

Self-propelled particles phase separate into coexisting dense and dilute regions above a critical density. The statistical nature of their stochastic motion lends itself to various theories that predict the onset of phase separation. However, these theories are ill equipped to describe such behavior when noise become negligible. To overcome this limitation, we present a predictive model that relies on two density-dependent timescales: $\tau_F$, the mean time particles spend between collisions; and $\tau_C$, the mean lifetime of a collision. We show that only when $\tau_F < \tau_C$ do collisions last long enough to develop a growing cluster and initiate phase separation. Using both analytical calculations and active particle simulations, we measure these timescales and determine the critical density for phase separation in both 2D and 3D.