The escape problem for active particles confined to a disc

TL;DR

This paper investigates the escape dynamics of interacting self-propelled particles confined to a disc, revealing a transition from exponential to sub-exponential escape probabilities due to interactions, modeled through a novel phenomenological approach.

Contribution

It introduces a new phenomenological model incorporating the Allee effect to explain escape statistics in interacting active particles.

Findings

Interacting particles show a crossover from exponential to sub-exponential escape behavior.

The proposed model successfully captures the escape dynamics across different noise levels.

Abstract

We study the escape problem for interacting, self-propelled particles confined to a disc, where particles can exit through one open slot on the circumference. Within a minimal 2D Vicsek model, we numerically study the statistics of escape events when the self-propelled particles can be in a flocking state. We show that while an exponential survival probability is characteristic for non-interaction self-propelled particles at all times, the interacting particles have an initial exponential phase crossing over to a sub-exponential late-time behavior. We propose a new phenomenological model based on non-stationary Poisson processes which includes the Allee effect to explain this sub-exponential trend and perform numerical simulations for various noise intensities.