2004/06/30 by F. Jarai-Szabo, Z. Neda · 1 citation
Physics and Astronomy · #cond-mat.soft #cond-mat.stat-mech
published as F. Jarai-Szabo and Z. Neda, Physica A 385, 518-526, 2007 · 12 pages, 6 figures
arxiv created 2008/02/20 · arxiv updated 2009/12/01
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional spaces there is no exact result known for the size-distribution of Voronoi cells. Motivated by the simple form of the distribution function in the one-dimensional case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size distribution function in the practically important two- and three dimensional cases as well. Denoting the dimensionality of the space by d (d=1,2,3) the f(y)=Const*y(3d-1)/2exp(-(3d+1)y/2) compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the validity of the proposed distribution function is studied and critically discussed.