Analytic and numerical analysis of some statistical features of fragmentation processes

In this work, we investigate the following inhomogeneous model of fragmentation with an exponential splitting probability: suppose that an initial particle having a mass x₀>0 (large enough) is broken, with a size-dependent probability , into b>1 pieces. With probability 1−p(x₀), this fragment is left unchanged for ever. The process of fragmentation is repeated recursively for all pieces.Some statistical features are studied, chiefly the fragment size distribution, number of fragments and partition function of the random fragmentation tree. Also, we give details of the numerical analysis of these features.