Related papers: A Simple Model for Anisotropic Step Growth
The formation of three-dimensional structures during the epitaxial growth of films is associated to the reflection of diffusing particles in descending terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier. We…
We study the dynamics of adatoms in a model of vicinal (11m) fcc metal surfaces. We examine the role of different diffusion mechanisms and their implications to surface growth. In particular, we study the effect of steps and kinks on adatom…
We studied phase separation in a particle interacting system under a large drive along x. We here identify the basic growth mechanisms, and demonstrate time self-similarity, finite-size scaling, as well as other interesting features of both…
We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small…
We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We study several one dimensional step flow models. Numerical simulations show that the slope of the profile exhibits scaling in all cases. We apply a scaling ansatz to the various step flow models and investigate their long time evolution.…
In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step--edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting…
In this paper we would like give a short review of our recent works and current investigation in modeling of solid film surfaces growth based on computer Monte Carlo simulations. We also discuss effect of some simplification in growth rules…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory,…
As a departure from existing continuum approaches for describing the stability and evolution of surfaces of crystalline materials, this article provides a description of surface evolution based on the physics of the main feature imposed by…
The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on…
We study vicinal crystal surfaces within the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of…
The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force…
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…
Two kinds of configurations involving steps on surfaces are reviewed. The first one results from an initially planar vicinal surface, i.e. slightly deviating from a high-symmetry (001) or (111) orientation. In some cases, these surfaces…
We present a simple three-dimensional model to describe the autonomous expansion of a substrate which grows driven by the local mean curvature of its surface. The model aims to reproduce the nest construction process in arboreal…
We describe a numerical model of faceted crystal growth using a cellular automata method that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in the medium surrounding the crystal. The model was developed…