Related papers: Quantized Scaling of Growing Surfaces
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 present simulation results of deposition growth of surfaces in 2, 3 and 4 dimensions for ballistic deposition where overhangs are present, and for restricted solid on solid deposition where there are no overhangs. The values of the…
We investigate the average frequency of positive slope $\nu_{\alpha}^{+} $, crossing the height $\alpha = h- \bar h$ in the surface growing processes. The exact level crossing analysis of the random deposition model and the…
We contrast analytical results of a variety of growth models involving subdiffusion, thermal noise and quenched disorder with simulations of these models, concluding that the assumed self-affinity property is more an exception than a rule.…
We study the fourth order normalized cumulant of height fluctuations governed by $1+1$ dimensional Kardar-Parisi-Zhang (KPZ) equation for a growing surface. Following a diagrammatic renormalization scheme, we evaluate the kurtosis $Q$ from…
Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes…
Ballistic deposition (BD) is considered to be a paradigmatic discrete growth model that represents the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we question this connection by rigorously deriving a formal continuum…
We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width $W^2(L,t)$ and the interface height $h(x,t)$ in the (1+1)-dimensional…
We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)-< h(t)>, which is depicted as being subordinated to a standard…
We study the mode-coupling approximation for the KPZ equation in the strong coupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension…
Recently Jeong and Kim [Phys. Rev. E {\bf 66}, 051605 (2002)] investigated the scaling properties of equilibrium self-flattening surfaces subject to a restricted curvature constraint. In one dimension (1D), they found numerically that the…
Discrete and continuous models belonging to a universality class share the same linearities and (or) nonlinearities. In this work, we propose a new approach to calculate coarse grained coefficients of the continuous differential equation…
We show that the one-dimensional Kuramoto-Sivashinsky (KS) equation features a scaling regime characterized by the dynamical exponent $z=1$ at intermediate scales between the large-scale Kardar-Parisi-Zhang (KPZ) scaling with $z=3/2$ and…
We introduce the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any…
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,…
We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up to d=7+1. To this end, we study the restricted solid - on - solid growth model,…
Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its…
In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that…
We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this…
Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behavior quite different from that of their equilibrium counterparts. Here we demonstrate a surprising…