Related papers: Probability distribution of the order parameter in…
We derive a generic expression for the generating function (GF) of the particle-number probability distribution (PNPD) for a simple reaction diffusion model that belongs to the directed percolation universality class. Starting with a single…
Quenched disorder in absorbing phase transitions can disrupt the structure and symmetry of reaction-diffusion processes, offering a more accurate mapping to real physical systems. We developed a temporally quenched disorder method in the…
We study the absorbing-state phase transition in the one-dimensional contact process under the combined influence of spatial and temporal random disorders. We focus on situations in which the spatial and temporal disorders decouple. Couched…
In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…
Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme…
We study epidemic outbreaks on random Delaunay triangulations by applying Asynchronous SIR (susceptible-infected-removed) model kinetic Monte Carlo dynamics coupled to lattices extracted from the triangulations. In order to investigate the…
The properties of template-directed nucleation are studied close to the transition where full nucleation control is lost and additional nucleation occurs beyond the pre-patterned regions. First, kinetic Monte Carlo simulations are performed…
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…
A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier…
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…
We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
We study a (1+1) dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel (DKCA), but in which the update of a given site depends on the state of {\it three} sites at the previous time step. Thus, compared…
We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice with periodic boundary conditions. The finite size scaling relation for the…
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…
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…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one dimensional ring, where the walkers hop to their nearest neighbor with a bias $\epsilon$. For…
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…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…