Finite-size scaling analysis of percolation in three-dimensional correlated binary Markov chain random fields.

@article{Harter2005FinitesizeSA,
  title={Finite-size scaling analysis of percolation in three-dimensional correlated binary Markov chain random fields.},
  author={Thomas Harter},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2005},
  volume={72 2 Pt 2},
  pages={
          026120
        }
}
  • T. Harter
  • Published 18 August 2005
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
Percolation and finite-size scaling properties in three-dimensional binary correlated Markov-chain random fields on a cubic lattice are computed by extensive Monte Carlo simulation. At short correlation scales, the percolation threshold in correlated random fields decreases as the correlation scale increases. The rate of decrease rapidly diminishes for correlation lengths larger than 2-3 lattice sites. At correlation scales of 4-6 lattice sites, the percolation threshold is found to be 0.126… 

Figures and Tables from this paper

Point to point continuum percolation in two dimensions

The outcome of the classic percolation approach is several power-law curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical

Studying the effect of correlation and finite‐domain size on spatial continuity of permeable sediments

The percolation of high‐permeability cells in geo‐reservoir models is affected by cluster correlation and by lattice size. These affects are studied using an analytical methodology, presented as a

Fracture dynamics of correlated percolation on ionomer networks.

A random network model is presented to the study fracture dynamics on a scaffold of charged and elastic ionomer bundles that constitute the stable skeleton of a polymer electrolyte membrane to analyze fracture regimes as a function of the stress and the effective range of stress transfer.

Scale Dependence of Effective Hydraulic Conductivity Distributions in 3D Heterogeneous Media: A Numerical Study

Upscaling procedures and determination of effective properties are of major importance for the description of flow in heterogeneous porous media. In this context, we study the statistical properties

Geological entropy and solute transport in heterogeneous porous media

We propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer, which we fully characterize with two measurable parameters: the variance of the log K
...

References

SHOWING 1-10 OF 23 REFERENCES

Annealed percolation: Determination of exponents in a correlated-percolation problem.

A two-dimensional correlated-percolation model, in which attractive interactions between near-neighbor occupied sites produce a structure reminiscent of discontinuous metal films, is described.

Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Scaling properties of a percolation model with long-range correlations.

  • SahimiMukhopadhyay
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
The results of Monte Carlo simulations of a percolation model with long-range correlations in two and three dimensions are presented, finding the exponents to be mostly nonuniversal and dependent on a parameter that characterizes the nature of the correlations.

Cluster-size statistics of site-bond-correlated percolation models

We consider the cluster-size statistics of two types of site-bond-correlated percolation. In model A ~B! @see Phys. Rev. B 40, 10 986 ~1989!#, the activation of a bond between two first-neighbor

Long-range correlated percolation

This paper is a study of the percolation problem with long-range correlations in the site or bond occupations. An extension of the Harris criterion for the relevance of the correlations is derived

The effect of spatially correlated blocking-up of some bonds or nodes of a network on the percolation threshold

The differential operator and the turning band methods have been used to simulate homogeneous random fields and their values, calculated at the nodes or at the bond centers of the networks, define an order for the blocking-up of these bonds or nodes.

Structural and dynamical properties of long-range correlated percolation.

An algorithm for generating long-range correlations in the percolation problem is developed and it is found that the fractal dimensions of the backbone and the red bonds are quite different from uncorrelatedPercolation and vary with \ensuremath{\lambda}, the strength of the correlation.