Statistical Distributions of Poisson Voronoi Cells in Two and Three Dimensions
نویسندگان
چکیده
Statistical distributions of geometrical characteristics concerning the Poisson Voronoi cells, namely, Voronoi cells for the homogeneous Poisson point processes, are numerically obtained in twoand three-dimensional spaces based on the computer experiments. In this paper, ten million and five million independent samples of Voronoi cells in twoand three-dimensional spaces, respectively, are generated. Geometrical characteristics such as the cell volume, cell surface area and so on, are fitted to the generalized gamma distribution. Then, maximum likelihood estimates of parameters of the generalized gamma distribution are given.
منابع مشابه
Temporal evolution of the domain structure in a Poisson-Voronoi nucleation and growth transformation: results for one and three dimensions.
The distribution of spatial domain structures originated during one- and three-dimensional Poisson-Voronoi transformations are computed analytically extending the recently obtained results for the two-dimensional case. The presented method gives a full description of the developed microstructure and is valid for tessellations of any dimensionality. The temporal and spatial dependences of the do...
متن کاملSymmetry-Break in Voronoi Tessellations
We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional streng...
متن کاملFrom symmetry break to Poisson point process in 2D Voronoi tessellations: the generic nature of hexagons
We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions is perturbed through...
متن کاملHeuristic theory for many-faced d-dimensional Poisson-Voronoi cells
We consider the d-dimensional Poisson-Voronoi tessellation and investigate the applicability of heuristic methods developed recently for two dimensions. Let pn(d) be the probability that a cell have n neighbors (be ‘n-faced’) and mn(d) the average facedness of a cell adjacent to an n-faced cell. We obtain the leading order terms of the asymptotic large-n expansions for pn(d) and mn(3). It appea...
متن کاملProbabilistic Model for Polycrystalline Microstructures with Application to Intergranular Fracture
A two part probabilistic model for polycrystalline microstructures is described. The model utilizes a Poisson–Voronoi tessellation for the grain geometry and a vector random field model for the crystallographic orientation. The grain geometry model is calibrated to experimental data through the intensity of the Poisson point field underlying the Poisson–Voronoi tessellation and the orientation ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004