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Directed percolation is one of the generic universality classes for dynamic processes. We study the crossover from isotropic to directed percolation by representing the combined problem as a random cluster model, with a parameter $r$…
In a recent work [Shao $et$ $al$ 2009 Phys. Rev. Lett. \textbf{108} 018701], a nonconsensus opinion (NCO) model was proposed, where two opinions can stably coexist by forming clusters of agents holding the same opinion. The NCO model on…
Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order…
Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few…
We study a plant population model introduced recently by J. Wallinga [OIKOS {\bf 74}, 377 (1995)]. It is similar to the contact process (`simple epidemic', `directed percolation'), but instead of using an infection or recovery rate as…
Following the approach outlined in [18], convergence to SLE6 of the Exploration Processes for the correlated bond-triangular type models studied in [7] is established. This puts the said models in the same universality class as the standard…
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Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken…
We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This…
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 define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting…
We introduce a stochastic model of binary opinion dynamics in one dimension. The binary opinions $\pm 1$ are analogous to up and down Ising spins and in the equivalent spin system, only the spins at the domain boundary can flip. The…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
The probability distributions of the order parameter for two models in the directed percolation universality class were evaluated. Monte Carlo simulations have been performed for the one-dimensional generalized contact process and the…
A general model of opinion dynamics is introduced in which each individual's opinion is measured on a bounded continuous spectrum. Each opinion is influenced heterogeneously by every other opinion in the population. It is demonstrated that…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
This is a brief survey of recent experimental studies on out-of-equilibrium scaling laws, focusing on two prominent situations where non-trivial universality classes have been identified theoretically: absorbing-state phase transitions and…
We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability p at every time instance. We observe that such kind of coupling stabilizes the local…
We introduce a dynamical model of coupled directed percolation systems with two particle species. The two species $A$ and $B$ are coupled asymmetrically in that $A$ particles branch $B$ particles whereas $B$ particles prey on $A$ particles.…
We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the…