Related papers: Surface pattern formation and scaling described by…
Depinning of elastic systems advancing on disordered media can usually be described by the quenched Edwards-Wilkinson equation (qEW). However, additional ingredients such as anharmonicity and forces that can not be derived from a potential…
We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes…
Aiming to investigate the upper critical dimension, $d_u$, of the KPZ class, in [EPL 103 (2013) 10005] some growth models were numerically analyzed using Cayley trees (CTs) as substrates, as a way to access their behavior in the…
We address the dynamics of adsorbed molecules (a fundamental issue in surface physics) within the framework of a Master Equation scheme, and study the diffusion of particles in a finite cubic lattice whose boundaries are at the $z=1$ and…
In this work, a study of epitaxial growth was carried out by means of wavelets formalism. We showed the existence of a dynamic scaling form in wavelet discriminated linear MBE equation where diffusion and noise are the dominant effects. We…
We introduce an off-lattice model with continuous particle distances and pair-potential interactions which allows for the efficient simulation of strained heteroepitaxial growth by means of kinetic Monte Carlo (KMC) simulations. We discuss…
The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its…
Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks.…
The conserved Kuramoto-Sivashinsky (CKS) equation, u_t = -(u+u_xx+u_x^2)_xx, has recently been derived in the context of crystal growth, and it is also strictly related to a similar equation appearing, e.g., in sand-ripple dynamics. We show…
Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). We introduce a discrete stochastic model that allows us to interpret these experimental…
We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1…
We use a three-dimensional lattice Boltzmann model to investigate the spreading of mesoscale droplets on homogeneous and heterogeneous surfaces. On a homogeneous substrate the base radius of the droplet grows with time as $t^{0.28}$ for a…
We consider the growth of a polymer layer on a flat surface in a good solvent by in-situ polymerization. This is viewed as a modified form of diffusion-limited aggregation without branching. We predict theoretically the formation of a…
The evolution of large-scale density perturbations is studied in a stably stratified, two-dimensional flow governed by the Boussinesq equations. As is known, intially smooth density (or temperature) profiles develop into fronts in the very…
Two-component submonolayer growth on triangular lattice is qualitatively studied by kinetic Monte Carlo techniques. The hopping barrier governing surface diffusion of the atoms is estimated with an improved formula and using realistic pair…
Driven surface diffusion occurs, for example, in molecular beam epitaxy when particles are deposited under an oblique angle. Elastic phase transitions happen when normal modes in crystals become soft due to the vanishing of certain elastic…
Passive random walker dynamics is introduced on a growing surface. The walker is designed to drift upward or downward and then follow specific topological features, such as hill tops or valley bottoms, of the fluctuating surface. The…
We consider the Kardar-Parisi-Zhang (KPZ) equation for a circular interface in two dimensions, unconstrained by the standard small-slopes and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate…
The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic…
We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that…