Percolation thresholds on 2D Voronoi networks and Delaunay triangulations

Abstract

The site percolation threshold for the random Voronoi network is determined numerically for the first time, with the result p_c = 0.71410 +/- 0.00002, using Monte-Carlo simulation on periodic systems of up to 40000 sites. The result is very close to the recent theoretical estimate p_c = 0.7151 of Neher, Mecke, and Wagner. For the bond threshold on the Voronoi network, we find p_c = 0.666931 +/- 0.000005, implying that for its dual, the Delaunay triangulation, p_c = 0.333069 +/- 0.000005. These results rule out the conjecture by Hsu and Huang that the bond thresholds are 2/3 and 1/3 respectively, but support the conjecture of Wierman that for fully triangulated lattices other than the regular triangular lattice, the bond threshold is less than 2 sin pi/18 = 0.3473.

Paper split into two and additional simulations to quantify errors added

References in corpus (19)

• What do we learn from the local geometry of glass-forming liquids?
• Scaling corrections: site-percolation and Ising model in three dimensions
• Finding Galaxy Clusters using Voronoi Tessellations
• The critical probability for random Voronoi percolation in the plane is 1/2
• Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations
• Critical Percolation in High Dimensions
• Exact bond percolation thresholds in two dimensions
• From symmetry break to Poisson point process in 2D Voronoi tessellations: the generic nature of hexagons
• Determination of the bond percolation threshold for the Kagome lattice
• Topological estimation of percolation thresholds
• Estimation of Bond Percolation Thresholds on the Archimedean Lattices
• Contact process on a Voronoi triangulation
• Universal condition for critical percolation thresholds of kagome-like lattices
• Percolation on random Johnson-Mehl tessellations and related models
• Statistical properties of planar Voronoi tessellations
• New Monte Carlo method for planar Poisson-Voronoi cells
• Asymptotic statistics of the n-sided planar Poisson-Voronoi cell. I. Exact results
• Percolation on dual lattices with k-fold symmetry
• Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics

Cited by in corpus (16)

• Mechanical heterogeneity in tissues promotes rigidity and controls cellular invasion
• Finite-size effects and percolation properties of Poisson geometries
• Critical surfaces for general inhomogeneous bond percolation problems
• Percolation thresholds on planar Euclidean relative neighborhood graphs
• Polynomial sequences for bond percolation critical thresholds
• Universality class of site and bond percolation on multi-multifractal scale-free planar stochastic lattice
• Dimer Covering and Percolation Frustration
• Fragmentation properties of two-dimensional Proximity Graphs considering random failures and targeted attacks
• Complex systems: features, similarity and connectivity
• Site and bond percolation thresholds in $K_{n,n}$-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies
• Numerical evidence against a conjecture on the cover time of planar graphs
• Honeycomb Lattices with Defects
• Explosive dismantling of two-dimensional random lattices under betweenness centrality attacks
• Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects
• Markov models of coarsening in two-dimensional foams with edge rupture
• Path Finding under Uncertainty through Probabilistic Inference