Comparative study of spanning cluster distributions in different dimensions

The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the universal scaling functions are shown to have simple power law variations with the dimensionality. The cases where multiple spanning clusters occur are discussed separately and compared.Comment: 8 pages, latex, 4 eps figures included, to appear in Int. Journal of Modern Physics

Probability of Incipient Spanning Clusters in Critical Square Bond Percolation

The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold $p_c=1/2$. It is found that the probability of k and more Incipient Spanning Clusters (ISC) has the values $P(k>1) \approx 0.00658(3)$ and $P(k>2) \approx 0.00000148(21)$ provided that the limit of these probabilities for infinite lattices exists. The probability $P(k>3)$ of more than three ISC could be estimated to be of the order of 10^{-11} and is beyond the possibility to compute a such value by nowdays computers. So, it is impossible to check in simulations the Aizenman law for the probabilities when $k>>1$. We have detected a single sample with 4 ISC in a total number of about 10^{10} samples investigated. The probability of single event is 1/10 for that number of samples.Comment: 7 pages, 1 table, 5 figures (1PS+4*Latex),uses epsf.sty Int.J.Mod.Phys. C (submitted to

Effects of boundary conditions on the critical spanning probability

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 find $p_c = 0.311605(5)$ in the cubic lattice.Comment: 8 pages Latex, To appear in Int. J. Mod. Phys.

Fractal geometry of critical Potts clusters

Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are presented. The data are found consistent with the recently derived corrections-to-scaling theory. However, the approach to the asymptotic region is slow, and the present range of the data does not allow a unique identification of the exact correction exponentsComment: 7 pages, 8 figures, Late

Are the Tails of Percolation Thresholds Gaussians ?

The probability distribution of percolation thresholds in finite lattices were first believed to follow a normal Gaussian behaviour. With increasing computer power and more efficient simulational techniques, this belief turned to a stretched exponential behaviour, instead. Here, based on a further improvement of Monte Carlo data, we show evidences that this question is not yet answered at all.Comment: 7 pages including 3 figure

Characterization of seedling and adult-plant resistance to stem rust race Ug99 in Iranian bread wheat landraces

The full-length infectious cDNA clone was constructed and sequenced from the strain DM of echovirus 9, which was recently isolated from a 6-week-old child at the clinical onset of type 1 diabetes. Parallel with the isolate DM, the full-length infectious cDNA clone of the prototype strain echovirus 9 Barty (Barty-INF), was constructed and sequenced. Genetic relationships of the sequenced echo 9 viruses to the other members of the human enterovirus type B species were studied by phylogenetic analyses. Comparison of capsid protein sequences showed that the isolate DM was closely related to both prototype strains: Hill and Barty-INF. The only exception was the inner capsid protein VP4 where serotype specificity was not evident and the isolate DM clustered with the strain Hill and the strain Barty-INF with echovirus 30 Bastianni. Likewise, the nonstructural protein coding region, P2P3, of isolate DM was more similar to strain Hill than to strain Barty-INF. However, like echovirus 9 Barty, the isolate DM contained the RGD-motif in the carboxy terminus of capsid protein VP1. By blocking experiments using an RGD-containing peptide and a polyclonal rabbit antiserum to the alpha(v)beta(3)-integrin, it was shown that this molecule works as a cellular receptor for isolate DM. By using primary human islets, it was shown that the isolate DM is capable of infecting insulin-producing beta-cells like the corresponding prototype strains did. However, only isolate DM was clearly cytolytic for beta-cells. The infectious clones that were made allow further investigations of the molecular features responsible for the diabetogenicity of the isolate DM

Beyond Blobs in Percolation Cluster Structure: The Distribution of 3-Blocks at the Percolation Threshold

The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block is a graph that cannot be separated into disconnected subgraphs by cutting the graph at 2 or fewer vertices. Clusters, blobs, and 3-blocks are special cases of $k$-blocks with $k=1$, 2, and 3, respectively. We study bond percolation clusters at the percolation threshold on 2-dimensional square lattices and 3-dimensional cubic lattices and, using Monte-Carlo simulations, determine the distribution of the sizes of the 3-blocks into which the blobs are decomposed. We find that the 3-blocks have fractal dimension $d_3=1.2\pm 0.1$ in 2D and $1.15\pm 0.1$ in 3D. These fractal dimensions are significantly smaller than the fractal dimensions of the blobs, making possible more efficient calculation of percolation properties. Additionally, the closeness of the estimated values for $d_3$ in 2D and 3D is consistent with the possibility that $d_3$ is dimension independent. Generalizing the concept of the backbone, we introduce the concept of a ``$k$-bone'', which is the set of all points in a percolation system connected to $k$ disjoint terminal points (or sets of disjoint terminal points) by $k$ disjoint paths. We argue that the fractal dimension of a $k$-bone is equal to the fractal dimension of $k$-blocks, allowing us to discuss the relation between the fractal dimension of $k$-blocks and recent work on path crossing probabilities.Comment: All but first 2 figs. are low resolution and are best viewed when printe

Exact results at the 2-D percolation point

We derive exact expressions for the excess number of clusters b and the excess cumulants b_n of a related quantity at the 2-D percolation point. High-accuracy computer simulations are in accord with our predictions. b is a finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula for the number of clusters per site n_c in the infinite system limit; the bn correct bulk cumulants. b and b_n are universal, and thus depend only on the system's shape. Higher-order corrections show no apparent dependence on fractional powers of the system size.Comment: 12 pages, 2 figures, LaTeX, submitted to Physical Review Letter

Efficient Monte Carlo algorithm and high-precision results for percolation

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 occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at occupation probability 0.59274621(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.Comment: 8 pages, including 3 postscript figures, minor corrections in this version, plus updated figures for the position of the percolation transitio

Percolation on two- and three-dimensional lattices

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent and critical concentration are obtained for the square, simple cubic, HCP and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.Comment: 15 pages, 6 figures, 3 table