Percolation thresholds on two-dimensional Voronoi networks and Delaunay triangulations.

  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},
  volume={80 4 Pt 1},
  • Adam BeckerR. Ziff
  • Published 24 June 2009
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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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