Fluctuations in fragmentation processes

The authors investigate the role of fluctuations in fragmentation processes using a simple analytic method to verify the stability of the mean-field similarity solution. For the fragmentation process which slows down with decreasing fragment size, the cascade becomes self-averaging in the late stages of branching. For the fragmentation which speeds up with decreasing fragment size, fluctuations dominate. In both cases the deviation from the mean-field solution is neither Gaussian nor symmetric. The steady-state regime in the presence of an external source is investigated and compared with the above results. Some exact solutions are obtained for the case of homogeneous fragmentation and for the discrete Yule-Ferry cascade process of decay into two equal fragments. The connection of the kinetic method with the combinatorial-type analysis of branching is indicated. Applications are made to the process of phonon decay