Related papers: New Epitaxial Thin Film Models and numerical appro…
We consider a class of stochastic partial differential equations arising as a model for amorphous thin film growth. Using a spectral Galerkin method, we verify the existence of stationary mild solutions, although the specific nature of the…
The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak…
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 perform a mass constrained phase-field approximation for a model that describes the epitaxial growth of a two-dimensional thin film on a substrate in the context of linearised elasticity. The approximated model encodes a variable on the…
We present the first analytical study of phase transitions in ferroelastic-ferroelectric epitaxial thin films on exactly solvable model. The emerging domain structure with domains of equal width (which may be exponentially large on a "soft"…
Transition metal spinel oxides comprised of Earth-abundant Mn and Co have long been explored for their use in catalytic reactions and energy storage. However, understanding of functional properties can be challenging due to differences in…
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…
Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale…
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…
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 propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
The evolution in the surface morphology of epitaxial graphene films and 6H-SiC(0001) substrates is studied by electron channeling contrast imaging. Whereas film thickness is determined by growth temperature only, increasing growth times at…
When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid…
We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and…
Many biological materials such as cervical mucus and collagen gel possess a fibrous micro-structure. This micro-structure affects the emergent mechanical properties of the material, and hence the functional behaviour of the system. We…
Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general…
A solid-on-solid model of epitaxial growth in 1+1 dimensions is investigated in which slope dependent upward and downward particle currents compete on the surface. The microscopic mechanisms which give rise to these currents are the…
Synchrotron-based x-ray reflectivity is increasingly employed as an \textit{in situ} probe of surface morphology during thin film growth, but complete interpretation of the results requires modeling the growth process. Many models have been…
In this work, we show the short-time existence of solutions of the evolution equations that represent the solid state dewetting of thin films through evaporation-condensation as a two dimensional sharp interface variational model. The…
Immense interests in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth with an aim to design and control film's surface morphology. Oftentimes, smooth surface is…