相关论文: Interfaces with a single growth inhomogeneity and …
The roughening behavior of a one-dimensional interface fluctuating under quenched disorder growth is examined while keeping an anchored boundary. The latter introduces detailed balance conditions which allows for a thorough analysis of…
The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near…
We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from…
A set of one dimensional interfaces involving attachment and detachment of $k$-particle neighbors is studied numerically using both large scale simulations and finite size scaling analysis. A labeling algorithm introduced by Barma and Dhar…
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…
A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions…
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
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…
A simple model for an interface moving in a disordered medium is presented. The model exhibits a transition between the two universality classes of interface growth phenomena. Using this model, it is shown that the application of…
The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions,…
We discuss the steady state dynamics of interfaces with periodic boundary conditions arising from body-centered solid-on-solid growth models in $1+1$ dimensions involving random aggregation of extended particles (dimers,…
We study numerically a stochastic differential equation describing an interface driven along the hard direction of an anisotropic random medium. The interface is subject to a homogeneous driving force, random pinning forces and the surface…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is…
We consider three models of evolving interfaces intimately related to the weakly asymmetric simple exclusion process with $N$ particles on a finite lattice of $2N$ sites. Our Model 1 defines an evolving bridge on $[0,1]$, our Model 1-w an…
We propose a one-dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter, the adsorption rate. At a special value of this parameter, the model has some interesting features. For example, the spectrum is…
A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum…
The asymptotic shape of randomly growing radial clusters is studied. We pose the problem in terms of the dynamics of stochastic partial differential equations. We concentrate on the properties of the realizations of the stochastic growth…