Exact and Asymptotic Scaling Solutions for Fragmentation with Mass Loss

Exact and asymptotic solutions to a linear rate equation for fragmentation with mass loss are presented. Solutions for spatially discrete random bond annihilation illustrate the mutual exclusiveness of the fragmentation and recession terms in the rate equation. Exact solutions for deterministic equal fragment recession show that continuous mass loss between fragmentation events can be approximated by discrete mass loss during fragmentation events when this mass loss is small. Evidence that continuous and discrete mass loss preclude shattering mass loss, the loss of mass to zero-mass particles due to runaway fragmentation, is presented. General asymptotic scaling forms, general solutions reflecting arbitrary initial conditions, and explicit scaling solutions are derived