Statistics of cross sections of Voronoi tessellations

Details Statistics of cross sections of Voronoi tessellations Statistics of cross sections of Voronoi tessellations

2011-10-11

arxiv.org/abs/1110.2337v1

Published on Physical Review E 84, 041107, (2011)

Physics

Condensed Matter

Statistical Mechanics

10 pages and 6 figures

Scientific paper

10.1103/PhysRevE.84.041107

In this paper we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in order to obtain analytical results, Voronoi cells are approximated to spheres. First, the probability density function for the lengths of the radii of the sections is derived and it is shown that it is related to the Meijer $G$-function; its properties are discussed and comparisons are made with the numerical results. Next the probability density function for the areas of cross sections is computed and compared with the results of numerical simulations.

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