Fragmenting the Universe. 3: The constructions and statistics of 3-D Voronoi tessellations

Details Fragmenting the Universe. 3: The constructions and statistics of 3-D Voronoi tessellations Fragmenting the Universe. 3: The constructions and statistics of 3-D Voronoi tessellations

Mar 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...283..361v&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 283, no. 2, p. 361-406

Statistics

Computation

38

Astronomical Models, Computational Astrophysics, Cosmology, Galactic Clusters, Galactic Evolution, Mathematical Models, Statistical Analysis, Three Dimensional Models, Universe, Algorithms, Boundary Conditions, Computerized Simulation, Galactic Nuclei, Histograms, Monte Carlo Method, Poisson Equation, Spatial Distribution

Scientific paper

In this paper we present a study of the statistical properties of three-dimensional Voronoi tessellations. This unique tiling of space into polyhedral cells generated by a random distribution of seeds is a phenomological model for a cell-like or sponge-like distribution of galaxies. By means of a Monte Carlo study we subsequently turn towards an extensive statistical analysis of several geometrical aspects of three dimensional Voronoi tessellations. To assess the dependence of its geometrical properties on the underlying distribution of nuclei three different distributions are investigated. We generate for each of these distributions four different realizations of tessellations, each of 1000 cells, inside a box with periodic boundary conditions. The first part of this study concerns the moments and distributions of geometrical properties of the tessellations and their building blocks, the cells. In the second part we turn to the properties of planar and linear sections through these three-dimensional tessellations.

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