Related papers: Percolation with long-range correlated disorder
We calculate the scaling exponents of the two-dimensional correlated percolation cluster's hull and unscreened perimeter. Correlations are introduced through an underlying correlated random potential, which is used to define the state of…
Herein, we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the…
We investigate a critical scaling law for the cluster heterogeneity $H$ in site and bond percolations in $d$-dimensional lattices with $d=2,...,6$. The cluster heterogeneity is defined as the number of distinct cluster sizes. As an…
We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective…
We consider a $d$-dimensional correlated percolation problem of sites {\em not} visited by a random walk on a hypercubic lattice $L^d$ for $d=3$, 4 and 5. The length of the random walk is ${\cal N}=uL^d$. Close to the critical value…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
We consider a correlated site percolation problem on a cubic lattice of size $L^3$, with $16\le L\le 512$. The sites of an initially full lattice are removed by a random walk of ${\cal N}=uL^3$ steps. When the parameter $u$ crosses a…
We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as function of the correlation…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…
We study the critical behavior of various geometrical and transport properties of percolation in 6 dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up…
Using Monte-Carlo simulations, we determine the scaling form for the probability distribution of the shortest path, $\ell$, between two lines in a 3-dimensional percolation system at criticality; the two lines can have arbitrary positions,…
Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order…
We extend our previous model, avalanche-burst invasion percolation (AIP) by introducing long-range correlations between sites described by fractional Brownian statistics. In our previous models with independent, random site strengths, we…
We study the statistics of the backbone cluster between two sites separated by distance $r$ in two-dimensional percolation networks subjected to spatial long-range correlations. We find that the distribution of backbone mass follows the…
Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two…