On Non-Poissonian Voronoi Tessellations

Abstract

<p>The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern ”random”, Poisson-Voronoi tessellations (PVT), or ”non-random”, Non Poisson-Voronoi tessellations. In this note we shall consider properties of Voronoi tessellations with centers gener-ated by Sobol quasi random sequences which produce a more ordered disposition of the centers with respect to the PVT case. A probability density function for volumes of these Sobol Voronoi tessellations (SVT) will be proposed and compared with results of numerical simulations. An application will be presented concerning the local struc-ture of gas (CO<sub>2</sub>) in the liquid-gas coexistence phase. Furthermore a probability distribution will be computed for the length of chords resulting from the intersections of random lines with a three-dimensional SVT. The agreement of the analytical formula with the results from a computer simulation will be also investigated. Finally a new type of Voronoi tessellation based on adjustable positions of seeds has been introduced which generalizes both PVT and SVT cases.</p>