Related papers: Scaling of local interface width of statistical gr…
We study (2+1)-dimensional single step model (SSM) for crystal growth including both deposition and evaporation processes parametrized by a single control parameter $p$. Using extensive numerical simulations with a relatively high…
We study numerically some discrete growth models belonging to the class of the nonlinear molecular beam epitaxy equation, or Villain-Lai-Das Sarma (VLDS) equation. The conserved restricted solid-on-solid model (CRSOS) with maximum heights…
Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson (EW) class for linear surface growth. The autocorrelation…
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…
With a nonequilibrium relaxation method, we calculate the dynamic critical exponent z of the two-dimensional Ising model for the Swendsen-Wang and Wolff algorithms. We examine dynamic relaxation processes following a quench from a…
Dynamical roughening of interfaces has received much attention in recent years. However, experiments have been restricted to one dimensional (1d) systems. Moreover, theoretical studies of the two dimensional (2d) case have been highly…
We consider the evolution of a family of 2D dispersive turbulence models. The members of this family involve the nonlinear advection of a dynamically active scalar field, the locality of the streamfunction-scalar relation is denoted by…
We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar--Parisi--Zhang model. The turbulent advecting velocity…
In recent years several local extrema based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work we study systematically the distribution of the…
We apply and test the recently proposed "extended scaling" scheme in an analysis of the magnetic susceptibility of Ising systems above the upper critical dimension. The data are obtained by Monte Carlo simulations using both the…
We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the…
We derive direct representations of the scaling functions of the 3d O(4) model which are relevant for comparisons to other models, in particular QCD. This is done in terms of expansions in the scaling variable z= t/h^{1/Delta}. The…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems.…
The value of the dynamic critical exponent $z$ is studied for two-dimensional superconducting, superfluid, and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find $z\simeq5.6\pm0.3$, a…
We have performed a detailed Monte Carlo study of a diffusionless $(1+1)$-dimensional solid-on-solid model of particle deposition and evaporation that not only tunes the roughness of an equilibrium surface but also demonstrates the need for…
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…
We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the…
The scaling of the growth of CdTe films on glass substrates was investigated by Mata \textit{et al.} [Phys. Rev. B \textbf{78}, 115305 (2008)]. Part of the analysis consisted of the estimation of the correlation length $\xi$ using the decay…
The octahedron model introduced recently has been implemented onto graphics cards, which permits extremely large scale simulations via binary lattice gases and bit coded algorithms. We confirm scaling behaviour belonging to the 2d…