相关论文: Model for Diffusion Limited Crystal Growth with an…

We couple a free solute diffusion model to a model of crystal surface growth represented by, but not limited to, a (2 + 1)-dimensional solid-on-solid (SOS) model confined by a flat surface. We use kinetic Monte Carlo (KMC) with dissolution…

We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication…

We study the existence and uniqueness of the solution of a non-linear coupled system constituted of a degenerate diffusion-growth-fragmentation equation and a differential equation, resulting from the modeling of bacterial growth in a…

We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is…

This application note describes how to model diffusion-limited crystal growth from vapor using QuickField - a commercial finite-element analysis code. The crystal growth problem is cast into the format of a steady-state heat diffusion…

The crystal size distribution in polynuclear growth is numerically studied using a coupled map lattice model. The width of the size distribution depends on c/D, where c is the growth rate at interface sites and $D$ is the diffusion…

We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

Guidelines for growing insulin crystals of a uniform size are formulated and tested experimentally. A simple theoretical model based on the balance of matter predicts the time evolution of the crystal size and supersaturation. The time…

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…

Aqueous foams and a wide range of related systems are believed to coarsen by gas diffusion between neighboring domains into a statistically self-similar scaling state, after the decay of initial transients, such that dimensionless size and…

A model for diffusion-controlled spherical particle growth is presented and solved numerically, showing how, on cooling at sufficient rate from a given fraction solid, growth velocity first increases, and then decreases rapidly when solute…

We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

We present measurements of the diffusion-limited growth of ice crystals from water vapor at different supersaturation levels in air at a temperature of -15 C. Starting with thin, c-axis ice needle crystals, the subsequent growth…

Using a self-similar approach a general nonsteady theory is elaborated for the case of the diffusion growth of a gas bubble in a supersaturated solution of gas in liquid. Due to the fact that the solution and the bubble in it are physically…

We consider a model of individual clustering with two specific reproduction rates and small diffusion parameter in one space dimension. It consists of a drift-diffusion equation for the population density coupled to an elliptic equation for…

We describe a numerical model of faceted crystal growth using a cellular automata method that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in the medium surrounding the crystal. The model was developed…