Related papers: Many universality classes in an interface model re…
Consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half-line $x\geq 0$. The interface is initially flat, $h(x,t=0)=0$, and driven by a Neumann boundary condition $\partial_x…
The Raise and Peel model is a recently proposed one-dimensional statistical model describing a fluctuating interface. The evolution of the model follows from the competition between adsorption and desorption processes. The model is…
Interfaces of phase-separated systems roughen in time due to capillary waves. Because of fluxes in the bulk, their dynamics is nonlocal in real space and is not described by the Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) equations, nor…
Critical wetting transitions under nonequilibrium conditions are studied numerically and analytically by means of an interface-displacement model defined by a Kardar-Parisi-Zhang equation, plus some extra terms representing a limiting,…
A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which…
We analyse by numerical simulations and scaling arguments the avalanche statistics of 1-dimensional elastic interfaces in random media driven at a single point. Both global and local avalanche sizes are power-law distributed, with universal…
We study single-channel continuum models of one-dimensional insulators induced by periodic potential modulations which are either terminated by a hard wall (the boundary model) or feature a single region of dislocations and/or impurity…
We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically…
The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural…
The Edwards-Wilkinson (EW) growth of $1+1$ interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a…
We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal…
Consider the Ising model at low-temperatures and positive external field $\lambda$ on an $N\times N$ box with Dobrushin boundary conditions that are plus on the north, east, and west boundaries and minus on the south boundary. If $\lambda =…
We propose a new type of SPDEs, singular or with regularized noises, motivated by a study of the fluctuation of the density field in a microscopic interacting particle system. They include a large scaling parameter $N$, which is the ratio…
We report on an extensive numerical investigation of the Kardar-Parisi-Zhang equation describing non-equilibrium interfaces. Attention is paid to the dependence of the growth exponents on the details of the distribution of the noise. All…
Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of $\mathbb{Z}$ and stick to the interface at the first point of contact, causing it to grow. We…
We study the pinning phase transition for discrete surface dynamics in random environments. A renormalization procedure is devised to prove that the interface moves with positive velocity under a finite size condition. This condition is…
Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood.…
This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the…
It has recently been proposed that fluctuating ``pulled'' fronts propagating into an unstable state should not be in the standard KPZ universality class for rough interface growth. We introduce an effective field equation for this class of…
We study a restricted solid-on-solid (RSOS) model involving deposition and evaporation with probabilities p and 1-p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang…