Related papers: Invasion Percolation Between two Sites
To establish the bond-site duality of explosive percolations in 2 dimension, the site and bond explosive percolation models are carefully defined on a square lattice. By studying the cluster distribution function and the behavior of the…
Hydraulic fracturing (fracking) using high pressures and a low viscosity fluid allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high…
We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p_c of attractive sites. The percolation cluster is characterized by a…
The average number $S_N(t)$ of distinct sites visited up to time t by N noninteracting random walkers all starting from the same origin in a disordered fractal is considered. This quantity $S_N(t)$ is the result of a double average: an…
We study percolation transition of run and tumble particles (RTPs) on a two dimensional square lattice. RTPs in these models run to the nearest neighbour along their internal orientation with unit rate, and to other nearest neighbours with…
Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven…
We consider two-species random sequential adsorption (RSA) in which species A and B adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When the probability $x_A$ of choosing an A…
We study the Gierer-Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let $p$ be the site occupation probability of the square lattice. For $p$ greater than a critical value $p_c$, the steady state consists of…
We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2-D networks, and its variants. The capacities add hierarchically down the clusters.…
In Poisson percolation each edge becomes open after an independent exponentially distributed time with rate that decreases in the distance from the origin. As a sequel to our work on the square lattice, we describe the limiting shape of the…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
We report the critical point for site percolation for the "explosive" type for 2D square lattices using Monte Carlo simulations and compare it to the classical well known percolation. We use similar algorithms as have been recently reported…
Invasion bond percolation (IBP) is mapped exactly into Prim's algorithm for finding the shortest spanning tree of a weighted random graph. Exploring this mapping, which is valid for arbitrary dimensions and lattices, we introduce a new IBP…
We compare the probabilities of arm events in two-dimensional invasion percolation to those in critical percolation. Arm events are defined by the existence of a prescribed color sequence of invaded and non-invaded connections from the…
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…
We study the critical case of first-passage percolation in two dimensions. Letting $(t_e)$ be i.i.d. nonnegative weights assigned to the edges of $\mathbb{Z}^2$ with $\mathbb{P}(t_e=0)=1/2$, consider the induced pseudometric (passage time)…
We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of such a system at the percolation threshold has the continuous…
Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting…
Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in…
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…