Lazar Emanuel A, Mason Jeremy K, MacPherson Robert D, Srolovitz David J
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.
Lawrence Livermore National Laboratory, Livermore, California 94550, USA and Boğaziçi University, Bebek, Istanbul 34342, Türkiye.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):063309. doi: 10.1103/PhysRevE.88.063309. Epub 2013 Dec 20.
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.
泊松点过程的Voronoi镶嵌被广泛用于对多种物理和生物系统进行建模。在本文中，我们分析了总共包含250000000个细胞的模拟泊松 - Voronoi结构，以提供这类重要网络的拓扑和几何统计信息。我们还报告了其中一些拓扑和几何度量之间的相关性。利用这些结果，我们能够证实关于三维泊松 - Voronoi网络性质的几个猜想，并反驳其他一些猜想。在许多情况下，我们对这些数据提供了精确的拟合以辅助进一步分析。我们还证明，拓扑度量是描述细胞网络和区分不同类型网络的有力工具。
