Shattering Transitions in Collision-Induced Fragmentation

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.