Brodskii R. Statistical theory of the solid fragmentation with self-similar subdivision law

The thesis is devoted to investigation of solid media fragmentation processes with self-similar subdivisions on all size scales and with the account of the volume conservation and the energy balance. The general kinetic equation for the distribution density of fragment size g(r, t) number is obtained. It is done on the basis of the probabilistic scheme of the Markov branching process with the independence of different fragment decays. Some solutions of the kinetic equation are found when its subdivision intensity has the property of self-similarity, both in the case of the scale invariance and the in case of its self-similar violation. It is shown that in case of "slow fragmentation" g(r, t) is subjected to the diffusion equation. Some solutions both in the case of the scale invariance and in the case of its self-similar violation when the self-similar power is equal 2 are obtained. Keywords: fragmentation, self-similar subdivisions, scale invariance, size distribution, size distribution density, slow fragmentation.