Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks

2019 ◽  
Vol 383 (10) ◽  
pp. 957-966 ◽  
Author(s):  
Alexander S. Balankin ◽  
M.A. Martínez-Cruz ◽  
M.D. Álvarez-Jasso ◽  
M. Patiño-Ortiz ◽  
J. Patiño-Ortiz
Keyword(s):  
Percolation Threshold ◽  
Site Percolation ◽  
Regular Lattices ◽  
Connectivity Degree

Exact site-percolation probability on the square lattice

2021 ◽  
Author(s):  
Stephan Mertens
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Percolation Threshold ◽  
Percolation Cluster ◽  
Square Lattice ◽  
Site Percolation ◽  
Exact Probability ◽  
Percolation Probability ◽  
A Site ◽  
Time And Space Complexity

Abstract We present an algorithm to compute the exact probability $R_{n}(p)$ for a site percolation cluster to span an $n\times n$ square lattice at occupancy $p$. The algorithm has time and space complexity $O(\lambda^n)$ with $\lambda \approx 2.6$. It allows us to compute $R_{n}(p)$ up to $n=24$. We use the data to compute estimates for the percolation threshold $p_c$ that are several orders of magnitude more precise than estimates based on Monte-Carlo simulations.

scholarly journals Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation

2015 ◽  
Vol 145 (3) ◽  
pp. 481-512 ◽  
Author(s):  
Patrick W. Dondl ◽  
Michael Scheutzow ◽  
Sebastian Throm
Keyword(s):  
Percolation Threshold ◽  
Elastic Medium ◽  
Driving Force ◽  
Percolation Cluster ◽  
Nearest Neighbour ◽  
Site Percolation ◽  
Kinetic Relation ◽  
Force Velocity ◽  
Linear Force ◽  
Neighbour Site

For a model of a driven interface in an elastic medium with random obstacles we prove the existence of a stationary positive supersolution at non-vanishing driving force. This shows the emergence of a rate-independent hysteresis through the interaction of the interface with the obstacles despite a linear (force = velocity) microscopic kinetic relation. We also prove a percolation result, namely, the possibility to embed the graph of an only logarithmically growing function in a next-nearest neighbour site percolation cluster at a non-trivial percolation threshold.

Site percolation threshold for honeycomb and square lattices

1982 ◽  
Vol 15 (8) ◽  
pp. L405-L412 ◽  
Author(s):  
Z V Djordjevic ◽  
H E Stanley ◽  
A Margolina
Keyword(s):  
Percolation Threshold ◽  
Site Percolation

scholarly journals ON SITE PERCOLATION ON THE CORRELATED SIMPLE CUBIC LATTICE

2003 ◽  
Vol 14 (10) ◽  
pp. 1405-1412 ◽  
Author(s):  
YURIY YU. TARASEVICH ◽  
ELENA N. MANZHOSOVA
Keyword(s):  
Percolation Threshold ◽  
Size Distribution ◽  
Cluster Size ◽  
Cluster Size Distribution ◽  
Site Percolation ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We consider site percolation on a correlated bi-colored simple cubic lattice. The correlated medium is constructed from a strongly alternating bi-colored simple cubic lattice due to anti-site disordering. The percolation threshold is estimated. The cluster size distribution is obtained. A possible application to the double 1:1 perovskites is discussed.

PRECISE NUMERICAL DETERMINATION OF THE SUPERCONDUCTING EXPONENT OF PERCOLATION IN THREE DIMENSIONS

1990 ◽  
Vol 01 (02n03) ◽  
pp. 207-214 ◽  
Author(s):  
J. M. NORMAND ◽  
H. J. HERRMANN
Keyword(s):  
Percolation Threshold ◽  
Three Dimensions ◽  
Numerical Determination ◽  
Site Percolation ◽  
Random Mixture ◽  
Purpose Computer ◽  
Special Purpose Computer

We present data obtained on the special purpose computer "Percola" determining the exponent [Formula: see text] of the random mixture of superconducting and normal conducting elements at the percolation threshold. The extrapolation is done for bond and site percolation and gives [Formula: see text] with a correction exponent ω = 1.85 ± 0.20.

ANTI-RED BOND CALCULATION ALGORITHM IN PERCOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 267-272 ◽  
Author(s):  
OLIVIER SCHOLDER
Keyword(s):  
Fractal Dimension ◽  
Percolation Threshold ◽  
Lattice Site ◽  
Calculation Algorithm ◽  
Site Percolation ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
The One

This paper presents an algorithm, which computes the number of anti-red bonds in a simple cubic lattice (site percolation) for different sizes and densities. Our interest was the fractal dimension of anti-red bonds at the percolation threshold. The value is found to be 1.18 ± 0.01. Two different theories proposed by Conigilio resp. Gouyet suggested a fractal dimension of 1.25 resp. 0.9. Thus, we can exclude the theory of Gouyet and are consistent with the one by Coniglio.

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