Geometric statistics and dynamic fragmentation

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Abstract
The present study is focused on the distributions in particle size produced in dynamic fragmentation processes. Previous work on this subject is reviewed. We then examine the one‐dimensional fragmentation problem as a random Poisson process and provide comparisons with expanding ring fragmentation data. Next we explore the two‐dimensional (area) and, less extensively, the three‐dimensional (volume) fragmentation problem. Mott’s theory of random area fragmentation is developed, and we propose an alternative application of Poisson statistics which leads to an exponential distribution in fragment size. Both theoretical distributions are compared with analytic and computer studies of random area geometric fragmentation problems, including those suggested by Mott, the Voronoi construction, a variation of the Johnson–Mehl construction, and several methods of our own. We find that size distributions from random geometric fragmentation are construction dependent, and that a conclusive choice between the two distributions cannot be made. A tentative application of the maximum entropy principle to fragmentation is discussed. The statistical theory is extended to include a concept of statistical heterogeneity in the fragmentation process. Finally, comparisons are made with various, dynamic fragmentation data.

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