Related papers: Coarsening in surface growth models without slope …
The coarsening dynamics of three-dimensional islands on a growing film is discussed. It is assumed that the origin of the initial instability of a planar surface is the Ehrlich-Schwoebel step-edge barrier for adatom diffusion. Two…
We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The…
We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…
We demonstrate, using well-established nonequilibrium limited-mobility solid-on-solid growth models, that mound formation in the dynamical surface growth morphology does not necessarily imply the existence of a surface edge diffusion bias…
Homoepitaxial growth is unstable towards the formation of pyramidal mounds when interlayer transport is reduced due to activation barriers to hopping at step edges. Simulations of a lattice model and a continuum equation show that a small…
We present models of surfaces of crystals in an environment where molecular beam epitaxy (MBE) and related methods of crystal growth like atomic layer epitaxy (ALE) can be performed. Besides detailed models of reconstructed (001) surfaces…
We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding…
A high-symmetry crystal surface may undergo a kinetic instability during the growth, such that its late stage evolution resembles a phase separation process. This parallel is rigorous in one dimension, if the conserved surface current is…
The phenomenon of salt creeping along a free surface remains only partially understood, particularly with respect to its dynamics. In this work, combining a theoretical model with controlled experiments, we identify three distinct kinetic…
A discrete solid-on-solid model of epitaxial growth is introduced which, in a simple manner, takes into account the effect of an Ehrlich-Schwoebel barrier at step edges as well as the local relaxation of incoming particles. Furthermore a…
The theory of growth kinetics developed previously is extended to the asymmetric case of off-critical quenches for systems with a conserved scalar order parameter. In this instance the new parameter $M$, the average global value of the…
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…
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density,…
We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication…
In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of…
Flat surface phases are unstable during growth and known to become rough. This does not exclude the possibility that surface reconstruction order persists in rough growing surfaces, in analogy with so-called equilibrium reconstructed rough…
We study the meandering instability during growth of an isolated nanostructure, a crystalline cone, consisting of concentric circular steps. The onset of the instability is studied analytically within the framework of the standard…
We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties…
We investigate the dynamical evolution of a thermodynamically unstable crystal surface into a hill-and-valley structure. We demonstrate that, for quasi one-dimensional ordering, the equation of motion maps exactly to the modified…
It is the first time invariance of specific mass increments of crystalline structures that co-exist in the case of non-equilibrium growth is grounded using the maximum entropy production principle. Based on the hypothesis of the existence…