Bond-percolation threshold and lattice structure

1988 ◽  
Vol 38 (7) ◽  
pp. 5039-5041
Author(s):  
N.-C. Chao
Keyword(s):  
Percolation Threshold ◽  
Lattice Structure ◽  
Bond Percolation

An upper bound for the bond percolation threshold of the cubic lattice by a growth process approach

2021 ◽  
Vol 58 (3) ◽  
pp. 677-692
Author(s):  
Gaoran Yu ◽  
John C. Wierman
Keyword(s):  
Percolation Threshold ◽  
Upper Bound ◽  
Triangular Lattice ◽  
Dynamic Process ◽  
Growth Process ◽  
Open Cluster ◽  
Process Approach ◽  
The Body ◽  
Bond Percolation ◽  
Cubic Lattice

AbstractWe reduce the upper bound for the bond percolation threshold of the cubic lattice from 0.447 792 to 0.347 297. The bound is obtained by a growth process approach which views the open cluster of a bond percolation model as a dynamic process. A three-dimensional dynamic process on the cubic lattice is constructed and then projected onto a carefully chosen plane to obtain a two-dimensional dynamic process on a triangular lattice. We compare the bond percolation models on the cubic lattice and their projections, and demonstrate that the bond percolation threshold of the cubic lattice is no greater than that of the triangular lattice. Applying the approach to the body-centered cubic lattice yields an upper bound of 0.292 893 for its bond percolation threshold.

A test of scaling near the bond percolation threshold

1978 ◽  
Vol 11 (8) ◽  
pp. L189-L197 ◽  
Author(s):  
H Nakanishi ◽  
H E Stanley
Keyword(s):  
Percolation Threshold ◽  
Bond Percolation

scholarly journals Aperiodic Non-Isomorphic Lattices with Equivalent Percolation and Random-Cluster Models

10.37236/320 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Klas Markström ◽  
John C. Wierman
Keyword(s):  
Percolation Threshold ◽  
Cluster Model ◽  
Large Scale ◽  
Threshold Value ◽  
Bond Percolation ◽  
Random Cluster Model ◽  
Random Cluster ◽  
Random Cluster Models ◽  
Percolation Thresholds ◽  
Scale Properties

We explicitly construct an uncountable class of infinite aperiodic plane graphs which have equal, and explicitly computable, bond percolation thresholds. Furthermore for both bond percolation and the random-cluster model all large scale properties, such as the values of the percolation threshold and the critical exponents, of the graphs are equal. This equivalence holds for all values of $p$ and all $q\in[0,\infty]$ for the random-cluster model. The graphs are constructed by placing a copy of a rotor gadget graph or its reflection in each hyperedge of a connected self-dual 3-uniform plane hypergraph lattice. The exact bond percolation threshold may be explicitly determined as the root of a polynomial by using a generalised star-triangle transformation. Related randomly oriented models share the same bond percolation threshold value.

On Polya random walks, lattice Green functions, and the bond percolation threshold

1983 ◽  
Vol 16 (2) ◽  
pp. L67-L71 ◽  
Author(s):  
M Sahimi ◽  
B D Hughes ◽  
L E Scriven ◽  
H T Davis
Keyword(s):  
Random Walks ◽  
Percolation Threshold ◽  
Bond Percolation ◽  
Green Functions

scholarly journals How clustering affects the bond percolation threshold in complex networks

2010 ◽  
Vol 81 (6) ◽  
Author(s):  
James P. Gleeson ◽  
Sergey Melnik ◽  
Adam Hackett
Keyword(s):  
Complex Networks ◽  
Percolation Threshold ◽  
Bond Percolation

A geometrical approach to percolation through random fractured rocks

1985 ◽  
Vol 122 (2) ◽  
pp. 157-162 ◽  
Author(s):  
N. Rivier ◽  
E. Guyon ◽  
E. Charlaix
Keyword(s):  
Percolation Threshold ◽  
Percolation Theory ◽  
Fractured Rocks ◽  
Statistical Characteristics ◽  
Bond Percolation ◽  
Geometrical Approach ◽  
Random Lattice ◽  
Voronoi Partition ◽  
Percolation Problem

AbstractThe permeability of rocks fractured by random, planar cracks, is expressed as a classical bond percolation problem on a random lattice, by Voronoi partition of space. The percolation threshold is determined as a function of the statistical characteristics of the cracks, or of their traces on an arbitrary face of the rock, by using an empirical quasi-invariant of percolation theory.

Universal Mass Ratios of Non-Unique Spanning Clusters in Percolation

1997 ◽  
Vol 08 (05) ◽  
pp. 1169-1173 ◽  
Author(s):  
Parongama Sen ◽  
Amnon Aharony
Keyword(s):  
Fractal Dimension ◽  
Percolation Threshold ◽  
Lattice Structure ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Mass Ratios ◽  
Different Shapes ◽  
The Masses

We find that when two or more spanning clusters exist at the percolation threshold, the mass of each scales with the same fractal dimension D=1.89 in two dimensions and D=2.53 in three dimensions. We also determine the ratios of the masses of the spanning clusters. In two dimensions, this is done for different lattices of different shapes. In the case of two spanning clusters, the ratio of the larger spanning cluster to the smaller lies around 1.4 for two dimensions, almost independent of lattice structure and shape.

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