• Title, Summary, Keyword: stochastic shattering

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STOCHASTIC FRAGMENTATION AND SOME SUFFICIENT CONDITIONS FOR SHATTERING TRANSITION

  • Jeon, In-Tae
    • Journal of the Korean Mathematical Society
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    • v.39 no.4
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    • pp.543-558
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    • 2002
  • We investigate the fragmentation process developed by Kolmogorov and Filippov, which has been studied extensively by many physicists (independently for some time). One of the most interesting phenomena is the shattering (or disintegration of mass) transition which is considered a counterpart of the well known gelation phenomenon in the coagulation process. Though no masses are subtracted from the system during the break-up process, the total mass decreases in finite time. The occurrence of shattering transition is explained as due to the decomposition of the mass into an infinite number of particles of zero mass. It is known only that shattering phenomena occur for some special types of break-up rates. In this paper, by considering the n-particle system of stochastic fragmentation processes, we find general conditions of the rates which guarantee the occurrence of the shattering transition.

FRAGMENTATION PROCESSES AND STOCHASTIC SHATTERING TRANSITION

  • Jeon, In-Tae
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.855-867
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    • 2005
  • Shattering or disintegration of mass is a well known phenomenon in fragmentation processes first 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 finite time. We investigate this phenomenon in the n particle system. In this system, shattering can be interpreted such that, in uniformly bounded time on n, order n of mass is located in order o(n) of clusters. It turns out that the tagged particle processes associated with the systems are useful tools to analyze the phenomenon. For the newly defined stochastic shattering based on the above ideas, we derive far sharper conditions of fragmentation kernels which guarantee the occurrence of such a phenomenon than our previous work [9].