相关论文: Modeling Diffusion-Limited Crystal Growth from Vap…
Atomically thin transition metal dichalcogenides (TMDs) have recently attracted great attention since the unique and fascinating physical properties have been found in various TMDs, implying potential applications in next-generation…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical Thermodynamics. The resulting system of equations captures all…
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
We extend an infrared-deformed soft-wall anti de-Sitter/QCD model at zero temperature to a model at finite temperature and perform hydrodynamics. To have the infalling boundary condition to make the hydrodynamic analysis possible, we treat…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
Frozen water might appear opaque since gas bubbles can get trapped in the ice during the freezing process. They nucleate and then grow near the advancing solidification front, due to the formation of a gas supersaturation region in its…
Fabrication of devices designed to fully harness the unique properties of quantum mechanics through their coupling to quantum bits (qubits) is a prominent goal in the field of quantum information processing (QIP). Among various qubit…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem,…
In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas-liquid-dendrite system is proposed through considering…
We present measurements of growth rates of the (0001) facet surface of ice as a function of water vapor supersaturation over the temperature range $-2$ $\geq T\geq -40$ C. From these data we infer the temperature dependence of premelting on…
An essential parameter for crystal growth is the kinetic coefficient given by the proportionality between super-cooling and average growth velocity. Here we show that this coefficient can be computed in a single equilibrium simulation using…
We report a simple, reliable method to grow high quality BaFe$_{2-x}$Co$_x$As$_2$ single crystal samples without using any fluxing agent. The starting materials for the single crystal growth come from well-crystallized polycrystalline…
We solve the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow…
We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in…
The temperature in natural convection problems is, under mild data assumptions, uniformly bounded in time. This property has not yet been proven for the standard finite element method (FEM) approximation of natural convection problems with…