# Percolation in networks with voids and bottlenecks.

@article{HajiAkbari2008PercolationIN, title={Percolation in networks with voids and bottlenecks.}, author={Amir Haji-Akbari and Robert M. Ziff}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2008}, volume={79 2 Pt 1}, pages={ 021118 } }

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…

## 12 Citations

### Threshold of hierarchical percolating systems.

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The concept of a hierarchical percolating (percolating-within-percolation) system is developed and it is found that the double-level percolation threshold is close to, but definitely larger than, the product of the localPercolation thresholds for the two enclosed single-level systems.

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This work concludes that, due to skewness in the distribution of occupation probabilities visited the average does not converge monotonically to the true percolation threshold, and identifies several alternative metrics which do exhibit monotonic convergence and document their observed convergence rates.

### Potts and percolation models on bowtie lattices.

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The exact critical frontier of the Potts model on bowtie lattices is given, and the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al.

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We present a method of general applicability for finding exact values or accurate approximations of bond percolation thresholds for a wide class of lattices. To every lattice we systematically…

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The scientific novelty of the obtained results is that for different network structures, it was shown that the percolation threshold for the blocking of nodes problem could be represented as an additive set of invariant values, that is, as an algebraic sum, the value of the members of which is stored in the transition from one structure to another.

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Perpendicular magnetic anisotropy ferromagnetic/superconducting (FM/SC) bilayers with a labyrinth domain structure are used to study nucleation of superconductivity on a fractal network, tunable…

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The Merrifield-Simmons index is a topological index used in structural chemistry for quantifying relevant properties of molecular structure. This index, in different names, has been studied on the…

### Polynomial sequences for bond percolation critical thresholds

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In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4, 6, 12) and (34, 6) lattices using the linearity approximation described in Scullard and Ziff (2010 J.…

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