Percolation thresholds on two-dimensional Voronoi networks and Delaunay triangulations.
@article{Becker2009PercolationTO, title={Percolation thresholds on two-dimensional Voronoi networks and Delaunay triangulations.}, author={Adam Becker and Robert M. Ziff}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2009}, volume={80 4 Pt 1}, pages={ 041101 } }
The site percolation threshold for the random Voronoi network is determined numerically, with the result pc=0.714 10+/-0.000,02 , using Monte Carlo simulation on periodic systems of up to 40,000 sites. The result is very close to the recent theoretical estimate pc approximately 0.7151 of Neher For the bond threshold on the Voronoi network, we find pc=0.666, 931+/-0.000,005 implying that, for its dual, the Delaunay triangulation pc=0.333 069+/-0.000 005 . These results rule out the conjecture by…
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References
SHOWING 1-10 OF 78 REFERENCES
Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation.
- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006
A correlated bond problem on the hexagonal lattice is solved by use of the star-triangle transformation and the site problem is solved, by a particular choice of correlations derived from a site-to-bond transformation, on the martini lattice.
Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals.
- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999
It is demonstrated explicitly that the idea of a universal scaling function with nonuniversal metric factors in the finite-size scaling theory can be extended to random lattices and their duals for the existence probability, the percolating probability, and the mean cluster size.
Percolation transitions in two dimensions.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008
The amplitude of the power-law correction associated with X_{t2}=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems.
New Monte Carlo method for planar Poisson–Voronoi cells
- Mathematics
- 2006
By a new Monte Carlo algorithm, we evaluate the sidedness probability pn of a planar Poisson–Voronoi cell in the range 3 ⩽ n ⩽ 1600. The algorithm is developed on the basis of earlier theoretical…
Exact bond percolation thresholds in two dimensions
- Mathematics
- 2006
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs,…
Renormalisation group approach to Delaunay percolation networks with topological disorder
- Physics
- 1986
A renormalisation group approach is developed for Delaunay percolating systems in two and three dimensions using a scaling transformation for a finite lattice in real space. Considering various…
Critical percolation in high dimensions.
- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003
Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4-13 dimensions are presented and a scaling law for finite cluster size corrections is proposed.
A bond percolation critical probability determination based on the star-triangle transformation
- Mathematics
- 1984
The bond percolation critical probability of a planar graph with square and triangular faces, obtained by inserting a diagonal in every other face of the square lattice, is the root of…
Asymptotic statistics of the n-sided planar Poisson–Voronoi cell: I. Exact results
- Mathematics
- 2005
We achieve a detailed understanding of the n-sided planar Poisson–Voronoi cell in the limit of large n. Let pn be the probability for a cell to have n sides. We construct the asymptotic expansion of…
Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions
- Mathematics
- 1964
An exact method for determining the critical percolation probability, pc, for a number of two‐dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc…