Related papers: Model for Anisotropic Directed Percolation
Connectedness percolation phenomena in the two-dimensional (2D) packing of binary mixtures of disks with different diameters were studied numerically. The packings were produced using random sequential adsorption (RSA) model with…
Microscopic diffusion anisotropy ({\mu}A) has been recently gaining increasing attention for its ability to decouple the average compartment anisotropy from orientation dispersion. Advanced diffusion MRI sequences, such as double diffusion…
While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…
By carefully analyzing the low temperature density dependence of 2D conductivity in undoped high mobility n-GaAs heterostructures, we conclude that the 2D metal-insulator transition in this system is a density inhomogeneity driven…
I consider a one dimensional system of particles which interact through a hard core of diameter $\si$ and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$…
We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in…
The directed percolation (DP) hypothesis for stochastic, range-4 cellular automata with acceptance rule $y \le\sum_{j=-4}^4 s_{i-j} \le 6$, in cases of $y < 6$ was investigated in one and two dimensions. Simulations, mean-field…
To establish the bond-site duality of explosive percolations in 2 dimension, the site and bond explosive percolation models are carefully defined on a square lattice. By studying the cluster distribution function and the behavior of the…
We present simulations of a 3-d percolation model studied recently by K.J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016)], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems…
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…
By event-driven molecular dynamics simulations we investigate magneto-transport in a two-dimensional model with randomly distributed scatterers close to the field-induced localization transition. This transition is generated by percolating…
In this paper, we study the piezoresistive response and its anisotropy for a bond percolation model of granular metals. Both effective medium results and numerical Monte Carlo calculations of finite simple cubic networks show that the…
We consider a four-vertex model introduced by B\'{a}lint T\'{o}th: a dependent bond percolation model on $\mathbb{Z}^2$ in which every edge is present with probability 1/2 and each vertex has exactly two incident edges, perpendicular to…
We introduce and study a dynamic transport model exhibiting Self-Organized Criticality. The novel concepts of our model are the probabilistic propagation of activity and unbiased random repartition of energy among the active site and its…
The results of investigations of main characteristics of a one-dimensional percolation theory (percolation threshold, critical exponents of correlation radius and specific heat, and free energy) are presented for the problem of bonds and…
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…
The influence of anisotropy on the transport current in MgB$_2$ polycrystalline bulk samples and wires is discussed. A model for the critical current density is proposed, which is based on anisotropic London theory, grain boundary pinning…