Related papers: New Epitaxial Thin Film Models and numerical appro…
Two-dimensional effective continuous models are derived for the surface states and thin films of the three-dimensional topological insulator (3DTI). Starting from an effective model for 3DTI based on the first principles calculation [Zhang…
We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based…
The thickness evolution of in-plane magnetization reversal in ultrathin films is studied with a theoretical model that takes account of surface roughness typical of epitaxial growth. Guided by N\'{e}el's model, step edge sites of…
This work presents a mathematical model for the optimal control of thin-film flows over a flexible topography influenced by an external force. Our thin-film model allows for the rupture of films as well as the coalescence of bubbles. The…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
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…
$\beta$-$\mathrm{Ga}_{2}\mathrm{O}_{3}$ has gained intensive interests of research and application as an ultrawide bandgap semiconductor. Epitaxial growth technique of the $\beta$-$\mathrm{Ga}_{2}\mathrm{O}_{3}$ thin film possesses a…
A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…
Properties of complex oxide thin films can be tuned over a range of values as a function of mismatch, composition, orientation, and structure. Here, we report a strategy for growing structured epitaxial thermoelectric thin films leading to…
Accurate and computationally accessible models of liquid film flows allow for optimizing coating processes such as hot-dip galvanization and vertical slot-die coating. This paper extends the classic three-dimensional integral boundary layer…
The retraction of thin films, as described by the Taylor-Culick (TC) theory, is subject to widespread debate, particularly for films at the nanoscale. We use non-equilibrium molecular dynamics simulations to explore the validity of the…
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…
We consider the stochastic thin-film equation with linear deterministic and stochastic It\^o perturbations. The existence of nonnegative weak martingale solutions on the semi-axis is established, and their asymptotic behavior as $t \to…
Epitaxial growth on a surface vicinal to a high-symmetry crystallographic plane occurs through the propagation of atomic steps, a process called step-flow growth. In some instances, the steps tend to form close groups (or bunches), a…
The coarsening dynamics of three-dimensional islands on a growing film is discussed. It is assumed that the origin of the initial instability of a planar surface is the Ehrlich-Schwoebel step-edge barrier for adatom diffusion. Two…
Atomically flat, epitaxial, and stoichiometric thin films of the electronically phase separated compound (La$_{0.5}$Pr$_{0.5}$)$_{0.67}$Ca$_{0.33}$MnO$_{3}$ were grown on as-received and treated NdGaO$_{3}$ substrates by fine tuning of…
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…
We present results from a comprehensive numerical study of {\it morphological phase separation} (MPS) in unstable thin liquid films on a 2-dimensional substrate. We study the quantitative properties of the evolution morphology via several…
We present here a summary of some recent techniques used for atomistic studies of thin film growth and morphological evolution. Specific attention is given to a new kinetic Monte Carlo technique in which the usage of unique labeling schemes…
In this paper we consider a two-phase thin film consisting of two immiscible viscous fluids endowed with a layer of insoluble surfactant on the surface of the upper fluid. The governing equations for the two film heights and the surfactant…