Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals.

  title={Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals.},
  author={Hsiao-Ping Hsu and M. C. Huang},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  volume={60 6 Pt A},
  • H. HsuM. Huang
  • Published 1 December 1999
  • Mathematics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
The bond-percolation process is studied on periodic planar random lattices and their duals. The thresholds and critical exponents of the percolation transition are determined. The scaling functions of the percolating probability, the existence probability of the appearance of percolating clusters, and the mean cluster size are also calculated. The simulation result of the percolation threshold is p(c)=0.3333+/-0.0001 for planar random lattices, and 0.6670+/-0.0001 for the duals of planar random… 

Percolation Thresholds, Critical Exponents, And Scaling Functions On Spherical Random Lattices And Their Duals

Bond-percolation processes are studied for random lattices on the surface of a sphere, and for their duals. The estimated threshold is 0.3326 ± 0.0005 for spherical random lattices and 0.6680 ±

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We analyze statistical and scaling properties of the fracture of two-dimensional (2D) central-force spring lattices with strong disorder by means of computer simulation. We run fracture simulations

Percolation thresholds on planar Euclidean relative-neighborhood graphs.

  • O. Melchert
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
The asymptotic degree and diameter of RNGs are determined and estimated and the common percolation critical exponents from the RNG data are deduced to verify that the associated universality class is that of standard 2D percolations.

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Effect of disorder strength on the fracture pattern in heterogeneous networks

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Universality class of explosive percolation in Barabási-Albert networks

This work study explosive percolation in Barabási-Albert network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process finds that the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR.

Cluster size distribution of voids in a polymer melt

By extending a recently developed Bethe lattice theory, we calculate the cluster size distribution and average cluster size of voids in the presence of polymers. Because of the presence of



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