Related papers: Nonlocal growth processes and conformal invariance
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…
The raise and peel model is a one-dimensional stochastic model of a fluctuating interface with nonlocal interactions. This is an interesting physical model. It's phase diagram has a massive phase and a gapless phase with varying critical…
The raise and peel model (RPM) is a nonlocal stochastic model describing the space and time fluctuations of an evolving one dimensional interface. Its relevant parameter $u$ is the ratio between the rates of local adsorption and nonlocal…
We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption…
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…
Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter $u$ (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating…
We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter $u$ controls the ratio of the local backwards and nonlocal forwards hopping…
We study a two parameter ($u,p$) extension of the conformally invariant raise and peel model. The model also represents a nonlocal and biased-asymmetric exclusion process with local and nonlocal jumps of excluded volume particles in the…
We investigate a non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For specific values of adsorption ($u_a$) and desorption($u_d$) rates…
We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one…
We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
The local scale invariance has been investigated in the nonequilibrium kinetic Ising model exhibiting absorbing phase transition of PC type in 1+1 dimension. Numerical evidence has been found for the satisfaction of this symmetry and…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We study the growth of slip line in a plastically deforming crystal by numerical simulation of a double-ended pile-up model with a dislocation source at one end, and an absorbing wall at the other end. In presence of defects, the pile-up…
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent theta or a dynamical exponent z. For a given value of theta, we construct local scale transformations which can…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects.…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…