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Statistical Mechanics of Discrete Multicomponent Fragmentation
Version 1
: Received: 7 September 2020 / Approved: 8 September 2020 / Online: 8 September 2020 (11:13:13 CEST)
A peer-reviewed article of this Preprint also exists.
Matsoukas, T. Statistical Mechanics of Discrete Multicomponent Fragmentation. Condens. Matter 2020, 5, 64. Matsoukas, T. Statistical Mechanics of Discrete Multicomponent Fragmentation. Condens. Matter 2020, 5, 64.
Abstract
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.
Keywords
discrete fragmentation; multicomponent; partition function; multiplicity of distribution
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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