Related papers: Large clusters in a correlated percolation model
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 soft matter system controlling the structure of the amorphous materials have been a key challenge. In this work we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical…
One of the major factors governing the mode of failure in disordered solids is the effective range $R$, over which the stress field is modified following a local rupture event. In random fiber bundle model, considered as a prototype of…
A split tree of cardinality $n$ is constructed by distributing $n$ "balls" in a subset of vertices of an infinite tree which encompasses many types of random trees such as $m$-ary search trees, quad trees, median-of-$(2k+1)$ trees,…
We study the cascading failures in a system composed of two interdependent square lattice networks A and B placed on the same Cartesian plane, where each node in network A depends on a node in network B randomly chosen within a certain…
Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour…
Using finite temperature SU(3) lattice gauge theory in the fixed scale approach we analyze center properties of the local Polyakov loop L(x). We construct spatial clusters of points x where the phase of L(x) is near the same center element…
We study the percolation properties of geometrical clusters defined in the overlap space of two statistically independent replicas of a square-lattice Ising model that are simulated at the same temperature. In particular, we consider two…
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 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…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
In order to investigate the dependence on lattice size of several observables in percolation, the Hoshen-Kopelman algorithm was modified so that growing lattices could be simulated. By this way, when simulating a lattice of size L, lattices…
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 existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
We study site percolation on a square lattice with random compact diamond-shaped neighborhoods. Each site $s$ is connected to others within a neighborhood in the shape of a diamond of radius $r_s$, where $r_s$ is uniformly chosen from the…
A phase diagram for a one dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding dynamics of the model: strength of disorder and system size. We monitor the successive events of fiber rupture in…
We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to p_c with an inverse power, \lambda, of the distance to the origin. Assuming the existence of…
We present a Monte Carlo study of the fractal geometry of clusters formed by discrete-time simple random walks (sRW) of $L^2$ steps on a periodic square $L\times L$ lattice. We verify with high precision that the asymptotic behavior of the…
We study a new geometric bootstrap percolation model, line percolation, on the $d$-dimensional integer grid $[n]^d$. In line percolation with infection parameter $r$, infection spreads from a subset $A\subset [n]^d$ of initially infected…
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…