Granular Collapse as a Percolation Transition

TL;DR

This paper investigates a phase transition in a 2D inelastic hard disk system, where a transition from small to large collapsed clusters occurs as the restitution coefficient decreases, resembling a percolation transition.

Contribution

It identifies and characterizes a percolation-like transition in granular collapse, providing scaling laws and critical exponents for the cluster size distribution.

Findings

Transition between small and large collapsed clusters as restitution decreases

Cluster size distribution follows a power law with exponent approximately 2.7

System exhibits a percolation transition behavior

Abstract

Inelastic collapse 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 transition between a state containing small collapsed clusters and a state dominated by a large collapsed 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 $\tau \approx 2.7$.