Percolation thresholds on 2D Voronoi networks and Delaunay triangulations

Details Percolation thresholds on 2D Voronoi networks and Delaunay triangulations Percolation thresholds on 2D Voronoi networks and Delaunay triangulations

2009-06-24

arxiv.org/abs/0906.4360v3

Phys. Rev. E 80 (4), 041101 (9 pages) 1 October 2009

Physics

Condensed Matter

Disordered Systems and Neural Networks

Paper split into two and additional simulations to quantify errors added

Scientific paper

10.1103/PhysRevE.80.041101

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.

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