Investigation of the kinetic equation of cascade fragmentation theory at not self-similar subdivision

2008/08/08 by R. E. Brodskii, Brodskii, R. E., Yu P. Virchenko +1
Mathematics · Physics and Astronomy · #74E99 #82-99 #82C31 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:74E99 #msc:82-99 #msc:82C31

paper · pdf · doi:10.48550/arxiv.0808.1214

5 pages

arxiv created 2008/08/10 · arxiv updated 2009/12/01

Abstract

The cascade kinetic fragmentation process of solids is investigated when the condition probability density of splinter formation do not depends on time and has the property P(ρ, r, t) = P(ρ/r). It is obtained the evolution equation for the probability distribution density in terms of its Mellin transformation. In the particular case P(ρ/r) = C (ρ/r)^α, the limit solution of this equation at t → ∞ is found. It differs essentially from the Kolmogorov law.

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