相关论文: Modeling Diffusion-Limited Crystal Growth from Vap…
The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…
I describe an adaptable apparatus for making precision measurements of the growth of faceted ice prisms from water vapor as a function of temperature, supersaturation, and background gas pressure. I also describe procedures for modeling…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of…
We consider both equilibrium and kinetic aspects of the phase separation (``thermal faceting") of thermodynamically unstable crystal surfaces into a hill--valley structure. The model we study is an Ising lattice gas for a simple cubic…
We investigate crystal-growth kinetics in the presence of strong shear flow in the liquid, using molecular-dynamics simulations of a binary-alloy model. Close to the equilibrium melting point, shear flow always suppresses the growth of the…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
We study spherically symmetric bubble growth and droplet decay in first order cosmological phase transitions, using a numerical code including both the complete hydrodynamics of the problem and a phenomenological model for the microscopic…
This paper presents a matrix of 206 snow crystal growth observations as a function of temperature and water vapor supersaturation in air, each illustrating the morphology and size of a crystal forming on the tip of an isolated c-axis ice…
Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…
The crystal plasticity finite element method (CPFEM) is used to investigate the coupling between the cylindrical void growth or collapse and grain refinement in face-centered cubic (FCC) single crystals. A 2D plane strain model with one…
The samples of hcp solid helium (1% $^3$He in $^4$He) are studied by NMR technique. The samples are grown by the blocking capillary method at different growth rates (about 8, 2, and 0.08 mK/s). The NMR technique is used for phase…
The diffusion model has emerged as a powerful tool for generating atomic structures for materials science. This work calls attention to the deficiency of current particle-based diffusion models, which represent atoms as a point cloud, in…
The development of wafer-scale continuous single-crystal graphene layers is key in view of its prospective applications. To this end, here we pave the way for a graphene growth model in the framework of the Langmuir adsorption theory and…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
Polar mesospheric clouds provide clues to physicochemical processes in the mesosphere and lower thermosphere. However, the heterogeneous nucleation and growth processes of water ice under polar mesospheric conditions are poorly understood,…
A study of ice formation in stationary turbulent conditions is carried out in various limit regimes of crystal growth, supercooling and ice entrainment at the water surface. Analytical expressions for the temperature, salinity and ice…
In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in…
Mathematical model that allows for direct tracking of the homoepitaxial crystal growth out of the window etched in the solid, pre-deposited layer on the substrate is described. The growth is governed by the normal (to the crystal-vapor…
A numerical recipe is given for obtaining the density image of an initially compact quantum mechanical wavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that…