Abstract
A stochastic particle model for fragmentation process is considered. Evolution of the system of particles is described by a stochastic process on a space of discrete measures on a Polish space. A phenomenon of shattering into dust is studied and some criteria for mass conservation and loss of mass in our model are proven.
Highlights
The fragmentation phenomenon can be observed commonly in many physical, industrial and biological processes, including grinding and crashing of such materials as ore, stone or flour, polymer degradation, dissolving, fragmentation of organisms, or proliferation of cells, etc
There is a vast literature on fragmentation process, originating from physics of polymer degradation [26]
It has been observed that sufficiently rapid fragmentation may result in the decrease of total mass of the system, even though the mass is conserved in every breakup of a single particle
Summary
The fragmentation phenomenon can be observed commonly in many physical, industrial and biological processes, including grinding and crashing of such materials as ore, stone or flour, polymer degradation, dissolving, fragmentation of organisms, or proliferation of cells, etc. McGrady and Ziff [27] observed that, if the breakup is fast for small particles, some solutions for fragmentation equation, which are formally conservative, do not preserve the total mass of particles. The aim of this paper is to present a general stochastic individual-based fragmentation model with infinitely many particles, in which shattering may appear. The setting of the IPF is quite general thanks to the fact that phase space is a locally compact Polish space This generality allows for the description of moving particles or multitype processes. Some auxiliary definitions and results are stated in the appendix
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