Related papers: Stabilization by rough noise for an epitaxial grow…
We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that…
Nanoscale ferroelectric topologies such as vortices, anti-vortices, bubble patterns etc. are stabilized in thin films by a delicate balance of both mechanical and electrical boundary conditions. A systematic understanding of the phase…
The paper presents results from kinetic Monte Carlo simulations of kinetic surface roughening using an important and experimentally relevant model of epitaxial growth -- the solid-on-solid model with Arrhenius dynamics. A restriction on…
We consider a continuum phase field model for crystal growth via molecular beam epitaxy, with the goal of determining stable numerical time integration methods for the dynamics. We parametrize a class of semi-implicit methods that are…
In this paper we briefly review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. This model allows to understand many experiments of thin film deposition. In the first…
The growth mechanism of pentacene film formation on SiO2 substrate was investigated with a combination of atomic force microscopy measurements and numerical modeling. In addition to the diffusion-limited aggregation (DLA) that has already…
In this work a simple solid-on-solid (SOS) model of inhomogeneous films epitaxial growth is presented. The results of the computer simulations based on the random deposition (RD) enriched by a local relaxation which tends to maximize the…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We propose a mathematical model that combines elastic, viscous and porous effects with growth or shrinkage due to microstructural changes. This phenomenon is important in tissue or tumor growth, as well as in dermal contraction. Although…
In this paper we present a generalization of a simple solid-on-solid epitaxial model of thin films growth, when surface morphology anisotropy is provoked by anisotropy in model control parameters: binding energy and/or diffusion barrier.…
The stabilisation by noise on the boundary of the Chafee-Infante equation with dynamical boundary conditions subject to a multiplicative It\^o noise is studied. In particular, we show that there exists a finite range of noise intensities…
We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang equation and the Lai-Das Sarma equation) and related atomistic models of epitaxial growth…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
Unstable homoepitaxy on rough substrates is treated within a linear continuum theory. The time dependence of the surface width $W(t)$ is governed by three length scales: The characteristic scale $l_0$ of the substrate roughness, the terrace…
We demonstrate epitaxial growth of copper selenide (Cu$_{2-x}$Se) thin films in both cubic and rhombohedral phases, achieved via molecular beam epitaxy on Al$_2$O$_3$ (001) substrates. Remarkably, the high-temperature cubic phase -- which…
We consider following fourth-order parabolic equation with gradient nonlinearity on the two-dimensional torus with and without advection of an incompressible vector field in the case $2<p<3$: \begin{equation*} \partial_t u + (-\Delta)^2 u =…
We consider patterns generated by adding large number of sand grains at a single site in an abelian sandpile model with a periodic initial configuration, and relaxing. The patterns show proportionate growth. We study the robustness of these…
An extension of the Truscott-Brindley model (Bull. Math. Biol. {\bf 56}, 981 (1994)) is derived to account for the effect of demographic fluctuations. In the presence of seasonal forcing, and sufficiently shallow water conditions, the…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
The subtle balance of electronic correlations, crystal field splitting and spin--orbit coupling in layered Ir$^{4+}$ oxides can give rise to novel electronic and magnetic phases. Experimental progress in this field relies on the synthesis…