A SIMPLE SOLUBLE MODEL OF DISCRETE SEQUENTIAL FRAGMENTATION

A simple model of discrete sequential fragmentation consists in first breaking a unit segment into q(greater than or equal to 2) pieces of e qual length. A fragment is then selected at random among all fragments and broken in turn into q pieces of equal length and so on ad infinit um. Fragments of size L = q(-s)(s = 0,..., f) are thus produced after f fragmentation events. The distribution of the ensemble averaged numb er of fragments of 'size' s is calculated exactly in terms of signless Stirling numbers of the first kind and shown to tend asymptotically t o a Poisson distribution with parameter (q/(q - 1))log(f). An asymptot ic lognormal distribution is thus found for the distribution of L.