相关论文: Percolation thresholds on 2D Voronoi networks and …
The values obtained experimentally for the conductivity critical exponent in numerous percolation systems, in which the interparticle conduction is by tunnelling, were found to be in the range of $t_0$ and about $t_0+10$, where $t_0$ is the…
We consider boundary roughness for the ``droplet'' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least $l^2$, for large $l$. The…
An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with non-zero clustering is presented. The networks are generated using a…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond…
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we…
We present a general method for predicting bond percolation thresholds and critical surfaces for a broad class of two-dimensional periodic lattices, reproducing many known exact results and providing excellent approximations for several…
We prove that the standard Russo-Seymour-Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result…
We study a large class of Bernoulli percolation models on random lattices of the half- plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact value of the site percolation threshold…
Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius…
The probability that the cluster of the origin in critical site percolation on the triangular grid has diameter larger than $R$ is proved to decay like $R^{-5/48}$ as $R\to\infty$.
In this paper, the 60-year-old concept of long-range interaction in percolation problems introduced by Dalton, Domb, and Sykes, is reconsidered. With Monte Carlo simulation -- based on Newman-Ziff algorithm and finite-size scaling…
We use the connection between bond percolation and SIR epidemics to establish lower bounds for the critical percolation probability in $2$ and $3$ dimensions as the range becomes large. The bound agrees with the conjectured asymptotics for…
Series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction. The percolation threshold $p_c$ is found to be the same as…
Kesten showed the exponential decay of percolation probability in the subcritical phase for the two-dimensional percolation model. This result implies his celebrated computation that $p_c=0.5$ for bond percolation in the square lattice, and…
The site percolation problem is one of the core topics in statistical physics. Evaluation of the percolation threshold, which separates two phases (sometimes described as conducting and insulating), is useful for a range of problems from…
In this paper, site percolation on random $\Phi^{3}$ planar graphs is studied by Monte-Carlo numerical techniques. The method consists in randomly removing a fraction $q=1-p$ of vertices from graphs generated by Monte-Carlo simulations,…
We derive three critical exponents for Bernoulli site percolation on the on the Uniform Infinite Planar Triangulation (UIPT). First we compute explicitly the probability that the root cluster is infinite. As a consequence, we show that the…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…