Granular Collapse as a Percolation Transition

Clustering is found in a two-dimensional system of inelastic hard disks confined between two walls which act as an energy source. As the coefficient of restitution is lowered, there is a sharp collapse transition between configurations of small clusters of slow moving particles and configurations dominated by a large cluster. The transition is analogous to that of a percolation transition. At the transition the number of clusters $n_s$ of size $s$ scales as $n_s \sim s^{-\tau}$ with $\tau \approx 2.7$.