2008/11/30 by Amir Haji‐Akbari, Amir Haji-Akbari, Robert M. Ziff · 1 citation
Mathematics · Physics and Astronomy · #Checkerboard #Combinatorics #Complex Network Analysis Techniques #Connection (principal bundle) #Continuum percolation theory #Critical exponent #Geometry #Limit (mathematics) #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Physics #Polygon mesh #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topology (electrical circuits) #Triangle mesh #Zero (linguistics) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.021118
to appear, Physical Review E. Small changes from first version
arxiv created 2009/01/28 · openalex publication_date 2009/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the subnet 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.