Statistical Topology of Three-Dimensional Poisson-Voronoi Cells and Cell Boundary Networks
arXiv:1401.1736 · doi:10.1103/PhysRevE.88.063309
Abstract
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 250,000,000 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.
15 pages, 19 figures, Supplemental Material included
References in corpus (2)
Cited by in corpus (16)
- A Topological Framework for Local Structure Analysis in Condensed Matter
- Geometric and topological properties of the canonical grain growth microstructure
- Voronoi cell analysis: The shapes of particle systems
- Characterization of maximally random jammed sphere packings: Voronoi correlation functions
- Topological metric detects hidden order in disordered media
- An extension to VORO++ for multithreaded computation of Voronoi cells
- Topological Characterization of Rigid-Nonrigid Transition across the Frenkel Line
- Distribution of Cell Area in Bounded Poisson Voronoi Tessellations with Application to Secure Local Connectivity
- Topological generalization of the rigid-nonrigid transition in soft-sphere and hard-sphere fluids
- Voronoi chains, blocks, and clusters in perturbed square lattices
- On non-Poissonian Voronoi tessellations
- The Universe as a Cellular System
- Pair correlation function based on Voronoi topology
- Many-faced cells and many-edged faces in 3D Poisson-Voronoi tessellations
- Exact asymptotic statistics of the n-edged face in a 3D Poisson-Voronoi tessellation
- Large-n conditional facedness m_n of 3D Poisson-Voronoi cells