An explicit solution to a discrete fragmentation model

Abstract

The discrete binary fragmentation equation is solved explicitly for a model where the net rate of breakup of a particle of size k, ak, equals (k-1)/(k+1), and the daughter-size distribution bik/ equals 2/(k-1). This system is closely related to a model of polymer degradation considered by Simha (1941), in which ak=1 and bik/ is as above. In the continuum limit, both of these models go over to a continuous fragmentation model in which all particles break with an equal rate, a(x)=1, and the daughter-size distribution is uniform, b(y mod x)=2/x, which is at the borderline of the shattering transition.