Percolation in Networks with Voids and Bottlenecks

Abstract

A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the sub-net mesh size goes to zero. The validity of this method is tested for bond percolation on filled checkerboard and "stack-of-triangle" lattices. Thresholds for the checkerboard lattices of different mesh sizes are estimated using the gradient percolation method, while for the triangular system they are found exactly using the triangle-triangle transformation. The values of the thresholds approach the asymptotic values of 0.64222 and 0.53993 respectively as the mesh is made finer, consistent with a direct determination based upon the predicted critical corner-connection probability.

to appear, Physical Review E. Small changes from first version

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Cited by in corpus (11)

• Universal condition for critical percolation thresholds of kagome-like lattices
• How to Quantify and Avoid Finite Size Effects in Computational Studies of Crystal Nucleation: The Case of Heterogeneous Ice Nucleation
• Critical surfaces for general inhomogeneous bond percolation problems
• Critical frontier for the Potts and percolation models on triangular-type and kagome-type lattices II: Numerical analysis
• Polynomial sequences for bond percolation critical thresholds
• Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions
• Double percolation effects and fractal behavior in magnetic/superconducting hybrids
• Dimer Covering and Percolation Frustration
• Random site percolation on honeycomb lattices with complex neighborhoods
• Potts and percolation models on bowtie lattices
• Lower limit of percolation threshold on a square lattice with complex neighborhoods