Fragmentation processes and Stochastic Shattering transition
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Abstract
Shattering or disintegration of mass is a well knownphenomenon in fragmentation processes rst introduced by Kolmogorov and Filippop and extensively studied by many physicists.Though the mass is conserved in each break-up, the total mass decreases in nite time. We investigate this phenomenon in the nparticle system. In this system, shattering can be interpreted suchthat, in uniformly bounded time on n, ordern of mass is locatedin order o(n) of clusters. It turns out that the tagged particle processes associated with the systems are useful tools to analyze thephenomenon. For the newly dened stochastic shattering based onthe above ideas, we derive far sharper conditions of fragmentationkernels which guarantee the occurrence of such a phenomenon thanour previous work [9].
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