NEW SOLUTIONS TO THE FRAGMENTATION EQUATION

A new general class of exact, explicit scaling solutions to the fragmentation equation is given. This class is described by a breakage rate a(x) = x-lambda and the daughter distribution function ybBAR(x\y) = a-gamma(x/y)gamma-2 + (1-a)delta(x/y)delta-2, and includes as special cases all previously-known scaling solutions to the fragmentation equation. For a subset of this class, with gamma = lambda and a = delta/(delta - lambda), the complete time-dependent solution for a monodisperse initial condition is also given.