Related papers: Directed Percolation has Colors and Flavors
The model of a one-dimensional kinetic contact process with parallel update is studied by the Monte Carlo simulations and finite-size scaling. The goal was to reveal the structure of the hidden percolative patterns (order parameters) in the…
The general epidemic process is a paradigmatic model in non-equilibrium statistical physics displaying a continuous phase transition between active and absorbing states.The dynamic isotropic percolation universality class captures its…
Network percolation has recently been proposed as a method to characterize the global structure of an urban system form the bottom-up. This paper proposes to extend urban network percolation in a multi-dimensional way, to take into account…
Understanding the nature of traffic heterogeneity is of major importance, given the widespread adoption of micromobility in cities. Based on massive field data and a nonequilibrium model, we demonstrate that heterogeneous, multispecies…
We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as $p_{\downarrow}= p \cdot…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has…
We propose a model for evolution aiming to reproduce statistical features of fossil data, in particular the distributions of extinction events, the distribution of species per genus and the distribution of lifetimes, all of which are known…
Percolation offers acknowledged models of random media when the relevant medium characteristics can be described as a binary feature. However, when considering habitat modeling in ecology, a natural constraint comes from nearest-neighbor…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…
We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth…
Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
The direct bond percolation process (Gribov process) is studied in the presence of irrotational velocity fluctuations with long-range correlations. The perturbative renormalization group is employed in order to analyze the effects of finite…
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean…
Using perturbative renormalization group we investigate the influence of random velocity field on the critical behavior of directed bond percolation process near its second-order phase transition between absorbing and active phase.…
Many research fields, reaching from social networks and epidemiology to biology and physics, have experienced great advance from recent developments in random graphs and network theory. In this paper we propose to view percolation on a…
We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability…