The onset of inelastic collapse in a one-dimensional granular gas

We examine the onset of inelastic collapse for a cluster of 10 ≤ N ≤ 50 grains colliding with a fixed wall. When the restitution coefficient ẽ is less than a threshold, the cluster does not bounce off the wall, but comes to rest after an infinite number of collisions. Near the collapse threshold, a nearly periodic sequence of collisions is established that can be identified by tracking the most energetic collisions. The length of this sequence grows exponentially with N. The dispersal of a colliding cluster can be compared to the decay of a radioactive nucleus: the cluster has a fixed probability per unit time (measured in collisions) of dispersing. The “half-life” of the cluster grows exponentially as the restitution coefficient is decreased. Thus the onset of inelastic collapse is characterized by an exponentially growing time scale.