AN EXPLICIT SOLUTION TO A DISCRETE FRAGMENTATION MODEL

The discrete binary fragmentation equation is solved explicitly for a model where the net rate of breakup of a particle of size k, a(k), equals (k - 1)/(k + 1), and the daughter-size distribution b(i/k) equals 2/(k - 1). This system is closely related to a model of polymer degradation considered by Simha, in which a(k) = 1 and b(i/k) 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/x) = 2/x, which is at the borderline of the shattering transition.