Related papers: Percolation-like phase transition in a non-equilib…
We study a contact process on a two-dimensional square lattice which is diluted by randomly removing bonds with probability p. For p<1/2 and varying birth rate $\lambda$ the model was shown to exhibit a continuous phase transition which…
In this paper, we investigate the impact of bond-dilution disorder on the critical behavior of the stochastic SIR model. Monte Carlo simulations were conducted using square lattices with first- and second-nearest neighbor interactions.…
The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid state physics and materials science, its percolation properties have received few attention. We investigate several…
We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…
The ranges of transmission of the mobiles in a Mobile Ad-hoc Network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment,…
We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional continuum percolation. To average over the randomness, we apply the replica trick, and interpret the…
We consider neighbor-induced damage percolation, a model describing systems where the inactivation of some elements may damage their neighboring active ones, making them unusable. We present an exact solution for the size of the giant…
Precursor gradients in a reaction-diffusion system are spatially varying coefficients in the reaction-kinetics. Such gradients have been used in various applications, such as the head formation in the Hydra, to model the effect of…
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…
The interacting lattice gas model is used to simulate fluid flow through an open percolating porous medium with the fluid entering at the source-end and leaving from the opposite end. The shape of the steady-state concentration profile and…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
The $q=2$ random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values…
Herein, we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the…
We study two models having an infinite-disorder critical point --- the zero temperature random transverse-field Ising model and the random contact process --- on a star-like network composed of $M$ semi-infinite chains connected to a common…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of…
The intrinsic length scales of a reaction diffusion system (Gierer-Meinhardt model)is varied by quasi-statically changing the diffusion constant of the activator and a transition from rolls to hexagon is detected. The transition is…
The size and shape of the region affected by an outbreak is relevant to understand the dynamics of a disease and help to organize future actions to mitigate similar events. A simple extension of the SIR model is considered, where agents…
We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the…