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A Monte Carlo study of size and angular properties of a three-dimensional Poisson-Delaunay cell

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Abstract

On the basis of simulation of 1.2×106 three-dimensional Poisson-Delaunay cells, the statistical properties of their size and angular parameters have been studied. The moments of the volume, face area, and edge length distributions are found to be equal to those obtained from the exact expressions of Miles and of Moller. The volume, surface area, and face area distributions can be described by the two-parameter gamma distribution. The normal distribution can be used to describe the distributions of the total edge length of a cell and the perimeter of a face. The edge length distribution has also been studied. The distribution of the angle in a face is found to be in accordance with its theoretical distribution.

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Authors and Affiliations

  1. Materials Science and Engineering, University of Cincinnati, 45221-0012, Cincinnati, Ohio

    Susmit Kumar

  2. Materials Research Laboratory, Pennsylvania State University, 16802, University Park, Pennsylvania

    Stewart K. Kurtz

  3. Electrical and Computer Engineering, Pennsylvania State University, 16802, University Park, Pennsylvania

    Stewart K. Kurtz

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  1. Susmit Kumar
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Kumar, S., Kurtz, S.K. A Monte Carlo study of size and angular properties of a three-dimensional Poisson-Delaunay cell. J Stat Phys 75, 735–748 (1994). https://doi.org/10.1007/BF02186878

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