Topological Hausdorff dimension and geodesic metric of critical percolation cluster in two dimensions

2017 ◽  
Vol 381 (33) ◽  
pp. 2665-2672 ◽  
Author(s):  
Alexander S. Balankin ◽  
Baltasar Mena ◽  
M.A. Martínez Cruz
Keyword(s):  
Hausdorff Dimension ◽  
Percolation Cluster ◽  
Two Dimensions ◽  
Critical Percolation ◽  
Geodesic Metric

Estimates of critical percolation probabilities for a set of two-dimensional lattices

1972 ◽  
Vol 71 (1) ◽  
pp. 97-106 ◽  
Author(s):  
D. G. Neal
Keyword(s):  
Monte Carlo ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Site Percolation

AbstractThis paper describes new detailed Monte Carlo investigations into bond and site percolation problems on the set of eleven regular and semi-regular (Archimedean) lattices in two dimensions.

scholarly journals A PERCOLATION MODEL OF DIAGENESIS

2002 ◽  
Vol 13 (03) ◽  
pp. 319-331 ◽  
Author(s):  
S. S. MANNA ◽  
T. DATTA ◽  
R. KARMAKAR ◽  
S. TARAFDAR
Keyword(s):  
Numerical Simulation ◽  
Critical Behavior ◽  
Sedimentary Rocks ◽  
Two Dimensions ◽  
Percolation Model ◽  
Type Model ◽  
Stable Configuration ◽  
Critical Percolation ◽  
Restructuring Process ◽  
Simulation Results

The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in dense environments. Starting from sub-critical states of ordinary percolation the system evolves under the diagenetic rules to critical percolation configurations. Our numerical simulation results in two dimensions indicate that the stable configuration has the same critical behavior as the ordinary percolation.

scholarly journals The percolation process on a tree where infinite clusters are frozen

2000 ◽  
Vol 128 (3) ◽  
pp. 465-477 ◽  
Author(s):  
DAVID J. ALDOUS
Keyword(s):  
Binary Tree ◽  
Percolation Cluster ◽  
Critical Percolation ◽  
Percolation Process ◽  
Infinite Clusters ◽  
The Law

Modify the usual percolation process on the infinite binary tree by forbidding infinite clusters to grow further. The ultimate configuration will consist of both infinite and finite clusters. We give a rigorous construction of a version of this process and show that one can do explicit calculations of various quantities, for instance the law of the time (if any) that the cluster containing a fixed edge becomes infinite. Surprisingly, the distribution of the shape of a cluster which becomes infinite at time t > ½ does not depend on t; it is always distributed as the incipient infinite percolation cluster on the tree. Similarly, a typical finite cluster at each time t > ½ has the distribution of a critical percolation cluster. This elaborates an observation of Stockmayer [12].

Monte Carlo study of self-avoiding walks on a critical percolation cluster

1989 ◽  
Vol 39 (13) ◽  
pp. 9561-9572 ◽  
Author(s):  
Sang Bub Lee ◽  
Hisao Nakanishi ◽  
Y. Kim
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Percolation Cluster ◽  
Critical Percolation ◽  
Self Avoiding Walks

Ideal chain on a two-dimensional critical percolation cluster

1992 ◽  
Vol 25 (8) ◽  
pp. L461-L468 ◽  
Author(s):  
A Giacometti ◽  
H Nakanishi ◽  
A Maritan ◽  
N H Fuchs
Keyword(s):  
Percolation Cluster ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Ideal Chain

scholarly journals Estimating singularity dimension

2014 ◽  
Vol 158 (2) ◽  
pp. 223-238 ◽  
Author(s):  
M. POLLICOTT ◽  
P. VYTNOVA
Keyword(s):  
Hausdorff Dimension ◽  
Euclidean Space ◽  
Efficient Algorithm ◽  
Two Dimensions ◽  
Open Family

AbstractIn this paper we address an interesting question on the computation of the dimension of self-affine sets in Euclidean space. A well-known result of Falconer showed that under mild assumptions the Hausdorff dimension of typical self-affine sets is equal to its Singularity dimension. Heuter and Lalley subsequently presented a smaller open family of non-trivial examples for which there is an equality of these two dimensions. In this article we analyse the size of this family and present an efficient algorithm for estimating the dimension.

scholarly journals Relations between invasion percolation and critical percolation in two dimensions

2009 ◽  
Vol 37 (6) ◽  
pp. 2297-2331 ◽  
Author(s):  
Michael Damron ◽  
Artëm Sapozhnikov ◽  
Bálint Vágvölgyi
Keyword(s):  
Two Dimensions ◽  
Invasion Percolation ◽  
Critical Percolation
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