Related papers: Percolation is Odd
In this paper we compute the square lattice random sites percolation thresholds in case when sites from the 4th and the 5th coordination shells are included for neighbourhood. The obtained results support earlier claims, that (a) the…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it…
A model named `Colored Percolation' has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability $p$ and are then colored by one of the $n$ distinct colors…
We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same…
The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from…
Some examples of translation invariant site percolation processes on the $\Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the probability that a site is open given…
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…
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 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…
We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size $L \times L$ sites when considering a plane (the crossing probability in a given direction), a cylinder…
On the lattice $\widetilde{\mathbb Z}^2_+:={(x,y)\in \mathbb Z \times \mathbb Z_+\colon x+y \text{is even}}$ we consider the following oriented (northwest-northeast) site percolation: the lines $H_i:={(x,y)\in \widetilde {\mathbb Z}^2_+…
We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have…
For some m \ge 4, let us color each column of the integer lattice L = Z^2 independently and uniformly into one of m colors. We do the same for the rows, independently from the columns. A point of L will be called blocked if its row and…
This article presents a Monte Carlo study on bond percolation in distorted square and triangular lattices. The distorted lattices are generated by dislocating the sites from their regular positions. The amount and direction of the…
A calculation of site-bond percolation thresholds in many lattices in two to five dimensions is presented. The line of threshold values has been parametrized in the literature, but we show here that there are strong deviations from the…
We consider site percolation on a correlated bi-colored simple cubic lattice. The correlated medium is constructed from a strongly alternating bi-colored simple cubic lattice due to anti-site disordering. The percolation threshold is…
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…
The site percolation problem is studied on d-dimensional generalisations of the Kagome' lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site…
A lattice is called well-rounded, if its lattice vectors of minimal length span the ambient space. We show that there are interesting connections between the existence of well-rounded sublattices and coincidence site lattices (CSLs).…