相关论文: Percolation in random environment
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
We study the $m=3$ bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems…
We consider a percolation process in which $k$ points separated by a distance proportional to system size $L$ simultaneously connect together ($k>1$), or a single point at the center of a system connects to the boundary ($k=1$), through…
The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different…
Numerical simulations by means of Monte Carlo method and finite-size scaling analysis have been performed to study the percolation behavior of linear $k$-mers (also denoted in the literature as rigid rods, needles, sticks) on…
The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition,…
We study the critical behavior of various geometrical and transport properties of percolation in 6 dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up…
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
The fourfold research proposal regards in particular: critical oriented percolation; random walk limit laws; neural networks with long-range connections; the ant in a labyrinth.
We consider anisotropic independent bond percolation models on the slab $\Z^2\times\{0,\dots,k\}$, where we suppose that the axial (vertical) bonds are open with probability $p$, while the radial (horizontal) bonds are open with probability…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…
The number of clusters per site $n(p)$ in percolation at the critical point $p = p_c$ is not itself a universal quantity---it depends upon the lattice and percolation type (site or bond). However, many of its properties, including…
We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging…
Herein, we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the…
Three-dimensional bond or site percolation theory on a lattice can be interpreted as a gauge theory in which the Wilson loops are viewed as counters of topological linking with random clusters. Beyond the percolation threshold large Wilson…