Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

摘要

Voronoi tessellations of Poisson point processes are widely used for modeling many types of physicalnand biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total ofn250 000 000 cells to provide topological and geometrical statistics of this important class of networks. We alsonreport correlations between some of these topological and geometrical measures. Using these results, we are ablento corroborate several conjectures regarding the properties of three-dimensional Poisson-Voronoi networks andnrefute others. In many cases, we provide accurate fits to these data to aid further analysis. We also demonstratenthat topological measures represent powerful tools for describing cellular networks and for distinguishing amongndifferent types of networks.