Coexistence of the infinite (*) clusters: ? A remark on the square lattice site percolation

1982 ◽  
Vol 61 (1) ◽  
pp. 75-81 ◽  
Author(s):  
Yasunari Higuchi
Keyword(s):  
Lattice Site ◽  
Square Lattice ◽  
Site Percolation ◽  
Infinite Clusters

Substitution Method Critical Probability Bounds for the Square Lattice Site Percolation Model

1995 ◽  
Vol 4 (2) ◽  
pp. 181-188 ◽  
Author(s):  
John C. Wierman
Keyword(s):  
Upper Bound ◽  
Lattice Site ◽  
Percolation Model ◽  
Square Lattice ◽  
Critical Probability ◽  
Site Percolation ◽  
Substitution Method ◽  
Probability Bounds

The square lattice site percolation model critical probability is shown to be at most .679492, improving the best previous mathematically rigorous upper bound. This bound is derived by extending the substitution method to apply to site percolation models.

scholarly journals Square-lattice site percolation at increasing ranges of neighbor bonds

2005 ◽  
Vol 71 (1) ◽  
Author(s):  
Krzysztof Malarz ◽  
Serge Galam
Keyword(s):  
Lattice Site ◽  
Square Lattice ◽  
Site Percolation

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.

Percolation on Penrose Tilings

1998 ◽  
Vol 41 (2) ◽  
pp. 166-177 ◽  
Author(s):  
A. Hof
Keyword(s):  
Large Class ◽  
Arbitrary Dimension ◽  
Bond Percolation ◽  
Critical Probability ◽  
Site Percolation ◽  
Aperiodic Tilings ◽  
Infinite Clusters ◽  
Almost All ◽  
Percolation Processes ◽  
Penrose Tilings

AbstractIn Bernoulli site percolation on Penrose tilings there are two natural definitions of the critical probability. This paper shows that they are equal on almost all Penrose tilings. It also shows that for almost all Penrose tilings the number of infinite clusters is almost surely 0 or 1. The results generalize to percolation on a large class of aperiodic tilings in arbitrary dimension, to percolation on ergodic subgraphs of ℤd, and to other percolation processes, including Bernoulli bond percolation.

DIFFUSION UNDER CROSSED LOCAL AND GLOBAL BIASES IN DISORDERED SYSTEMS

2000 ◽  
Vol 11 (07) ◽  
pp. 1357-1369 ◽  
Author(s):  
SITANGSHU BIKAS SANTRA ◽  
WILLIAM A. SEITZ
Keyword(s):  
Relaxation Time ◽  
Disordered Systems ◽  
Maximum Rate ◽  
Rate Of Change ◽  
Square Lattice ◽  
Site Percolation ◽  
Local Bias ◽  
Random Walker ◽  
Percolation Clusters ◽  
Global Bias

Diffusion on 2D site percolation clusters at p = 0.7, 0.8, and 0.9 above pc on the square lattice in the presence of two crossed bias fields, a local bias B and a global bias E, has been investigated. The global bias E is applied in a fixed global direction whereas the local bias B imposes a rotational constraint on the motion of the diffusing particle. The rms displacement Rt ~ tk in the presence of both biases is studied. Depending on the strength of E and B, the behavior of the random walker changes from diffusion to drift to no-drift or trapping. There is always diffusion for finite B with no global bias. A crossover from drift to no-drift at a critical global bias Ec is observed in the presence of local bias B for all disordered lattices. At the crossover, value of the rms exponent changes from k = 1 to k < 1, the drift velocity vt changes from constant in time t to decreasing power law nature, and the "relaxation" time τ has a maximum rate of change with respect to the global bias E. The value of critical bias Ec depends on the disorder p as well as on the strength of local bias B. Phase diagrams for diffusion, drift, and no-drift are obtained as a function of bias fields E and B for these systems.

scholarly journals INFINITE NETWORKS OF IDENTICAL CAPACITORS

2010 ◽  
Vol 24 (07) ◽  
pp. 695-705 ◽  
Author(s):  
J. H. ASAD ◽  
R. S. HIJJAWI ◽  
A. J. SAKAJI ◽  
J. M. KHALIFEH
Keyword(s):  
Lattice Site ◽  
Superposition Principle ◽  
Square Lattice ◽  
Simple Cubic ◽  
Infinite Grid ◽  
Infinite Networks

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors each of capacitance C is calculated. The method is generalized to infinite Simple Cubic (SC) lattice of identical capacitors each of capacitance C. We make use of the superposition principle and the symmetry of the infinite grid.

scholarly journals Site-Percolation Models Including Heterogeneous Particles on a Square Lattice

1999 ◽  
Vol 40 (11) ◽  
pp. 1314-1318 ◽  
Author(s):  
Ryoji Sahara ◽  
Hiroshi Mizuseki ◽  
Kaoru Ohno ◽  
Yoshiyuki Kawazoe
Keyword(s):  
Square Lattice ◽  
Site Percolation
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