Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks.
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250000000 cells to provide topological and geometrical statistics of this important class of networks. We also report correlations between some of these topological and geometrical measures. Using these results, we are able to corroborate several conjectures regarding the properties of three-dimensional Poisson-Voronoi networks and refute others. In many cases, we provide accurate fits to these data to aid further analysis. We also demonstrate that topological measures represent powerful tools for describing cellular networks and for distinguishing among different types of networks.
Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA and Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Emanuel A
EA
Lazar
Lawrence Livermore National Laboratory, Livermore, California 94550, USA and Boğaziçi University, Bebek, Istanbul 34342, Türkiye.
Jeremy K
JK
Mason
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, USA.
Robert D
RD
MacPherson
Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
David J
DJ
Srolovitz