Modeling Collective Escape Processes for Nearly Jammed Systems

Abstract

A simple kinetic model is introduced as an elementary contribution to understanding cooperative relaxation processes in condensed matter. This model involves n hard disks mutually trapped initially just inside an impenetrable circular boundary. Disk invasion of the interior of the system requires one of the disks to discover an exit passageway that only appears when the other disks collectively move out of the way. Cell approximations have been used to estimate the escape rate, in particular to show how that rate depends on n and on the increment of the boundary circle radius above the escape threshold.