Percolation in Networks with Voids and Bottlenecks

Amir Haji-Akbari; Robert M. Ziff

doi:10.1103/physreve.79.021118

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arXiv · 0811.4575

Percolation in Networks with Voids and Bottlenecks

Amir Haji-Akbari·Robert M. Ziff

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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.

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BibTeX RIS

Amir Haji-Akbari, Robert M. Ziff. 2009-01-28. Percolation in Networks with Voids and Bottlenecks. https://doi.org/10.1103/physreve.79.021118

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