Escape problem for active particles confined to a disk

We study the escape problem for interacting, self-propelled particles confined to a disk, where particles can exit through one open slot on the circumference. Within a minimal two-dimensional 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 noninteracting self-propelled particles at all times, the interacting particles have an initial exponential phase crossing over to a subexponential late-time behavior. We use a phenomenological model based on nonstationary Poisson processes which includes the Allee effect to explain this subexponential trend and perform numerical simulations for various noise intensities.