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A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities…
We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs…
We study a hierarchy of directed percolation (DP) processes for particle species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When the DP critical points at all levels coincide, multicritical behavior emerges, with…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry.…
We study the effects of spatially inhomogeneous diffusion on the non-equilibrium phase transition in the contact process. The directed-percolation critical point in the contact process is known to be stable against the addition of a…
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…
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 and solve a model of hardcore particles on a one dimensional periodic lattice which undergoes an active-absorbing state phase transition at finite density. In this model an occupied site is defined to be active if its left…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP). In higher dimensions these models give rise to directed surfaces,…
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…
Directed percolation is one of the most prominent universality classes of nonequilibrium phase transitions and can be found in a large variety of models. Despite its theoretical success, no experiment is known which clearly reproduces the…
While for standard percolation directionality is known to increase the combinatorial complexity of percolation, here we show that when connectivity is ensured by paths of length $R\geq 2$, network directionality, impeding backtracking, can…
We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…
Motivated by a series of experiments that revealed a temperature dependence of the dynamic scaling regime of growing surfaces, we investigate theoretically how a nonequilibrium growth process reacts to a sudden change of system parameters.…
We study directed percolation at the upper critical transverse dimension $d=4$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) behavior. Viewing directed percolation as a kinetic process, we address…
The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric…