Shattering Transitions in Collision-Induced Fragmentation

TL;DR

This paper analyzes the nonlinear collision-induced fragmentation process, revealing how the system undergoes either a discontinuous or continuous shattering transition depending on the collision dynamics, with an analytical description of the fragment mass distribution.

Contribution

It provides an analytical solution for the fragment mass distribution and characterizes the nature of the shattering transition in collision-induced fragmentation.

Findings

Discontinuous transition occurs when the larger fragment splits.

Continuous transition occurs when the smaller fragment splits.

Fragment mass distribution diverges algebraically at the transition.

Abstract

We investigate the kinetics of nonlinear collision-induced fragmentation. We obtain the fragment mass distribution analytically by utilizing its travelling wave behavior. The system undergoes a shattering transition in which a finite fraction of the mass is lost to infinitesimal fragments (dust). The nature of the shattering transition depends on the fragmentation process. When the larger of the two colliding fragments splits, the transition is discontinuous and the entire mass is transformed into dust at the transition point. When the smaller fragment splits, the transition is continuous with the dust gaining mass steadily on the account of the fragments. At the transition point, the fragment mass distribution diverges algebraically for small masses, c(m) ~ m^-a, with a=1.20191.