相关论文: Novel continuum modeling of crystal surface evolut…

Due to particle conservation, Canonical Molecular Dynamics (MD) simulations fail in the description of surface phase transitions involving coverage or lateral density changes. However, a step on the surface can act effectively as a source…

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…

The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force…

This is a review of recent theoretical work on complex dynamical behavior of steps on crystal surfaces. The first part of the article is devoted to the electromigration-driven motion of islands and voids, and the second part addresses step…

We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away…

The problem addressed here can be concisely formulated as follows: given a stable surface orientation with a known reconstruction and given a direction in the plane of this surface, find the atomic structure of the steps oriented along that…

We study the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. With computational experiments and theoretical arguments we are able to…

This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…

The growth of crystal surfaces, under non-equilibrium conditions, involves the displacement of mono-atomic steps by atom diffusion and atom incorporations into steps. The time-evolution of the growing crystal surface is thus governed by a…

An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…

We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding…

We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure evolution and solidification that have been…

The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling…

We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or…

We study the effect of crystal symmetry and step-edge diffusion on the surface current governing the evolution of a growing crystal surface. We find there are two possible contributions to anisotropic currents, which both lead to the…

Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…

The evolution of interfaces is intrinsic to many physical processes ranging from cavitation in fluids to recrystallization in solids. Computational modeling of interface motion entails a number of challenges, many of which are related to…

We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the…

An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction--diffusion process on the surface,…

We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…