Inverse Power-Law Escape Statistics of Open Billiards

Abstract

In a previous study of Dettmann and Georgiou, it was considered such a situation that point-wise particles repeatedly and elastically collided with the wall of a container without any particle-particle collision and eventually escaped through a small window from the container, which can be modeled by an open billiard. In the present study, point-wise particles were replaced with finite-size disks and disk-disk collisions were also considered, and inverse power laws of distributions of dwell time in the container were obtained from numerical simulations.