相关论文: Percolation Threshold, Fisher Exponent, and Shorte…
We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori…
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 $R\to\infty$.
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…
This is the first of two papers on the critical behaviour of bond percolation models in high dimensions. In this paper, we obtain strong joint control of the critical exponents eta and delta, for the nearest-neighbour model in very high…
We investigate the behaviour of the mean size of directed compact percolation clusters near a damp wall in the low-density region, where sites in the bulk are wet (occupied) with probability $p$ while sites on the wall are wet with…
We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$.…
The analysis of extensive numerical data for the percolation probabilities of incipient spanning clusters in two dimensional percolation at criticality are presented. We developed an effective code for the single-scan version of the…
A rewriting code construction for flash memories based upon lattices is described. The values stored in flash cells correspond to lattice points. This construction encodes information to lattice points in such a way that data can be written…
We generate point configurations (PCs) by thresholding the local energy of the Ashkin-Teller model in two dimensions (2D) and study the percolation transition at different values of $\lambda$ along the critical Baxter line by varying the…
Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system…
We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence…
In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of proximity graphs and are…
We continue our study of the chemical (graph) distance inside large critical percolation clusters in dimension two. We prove new estimates, which involve the three-arm probability, for the point-to-surface and point-to-point distances. We…
Stencil computations on low dimensional grids are kernels of many scientific applications including finite difference methods used to solve partial differential equations. On typical modern computer architectures, such stencil computations…
Extended-range percolation on various regular lattices, including all eleven Archimedean lattices in two dimensions, and the simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) lattices in three dimensions, is…
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…
The brain constructs population codes to represent stimuli through widely distributed patterns of activity across neurons. An important figure of merit of population codes is how much information about the original stimulus can be decoded…
As shown in [28], one of the five isomorphism types of optimal binary subspace codes of size 77 for packet length v=6, constant dimension k=3 and minimum subspace distance d=4 can be constructed by first expurgating and then augmenting the…
Extensive Monte-Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered…
We study how to restore site percolation on a damaged square lattice with nearest neighbor (N$^2$) interactions. Two strategies are suggested for a density $x$ of destroyed sites by a random attack at $p_c$. In the first one, a density $y$…