Related papers: Unified continuum approach to crystal surface morp…
We study the continuum limit in 2+1 dimensions of nanoscale anisotropic diffusion processes on crystal surfaces relaxing to become flat below roughening. Our main result is a continuum law for the surface flux in terms of a new…
The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited…
In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1…
We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step free energy. Results are in agreement with experiments and Monte Carlo simulations…
In the continuum theory the time evolution of surfaces eroded by ion bombardment is modelled by stochastic partial differential equations (SPDEs). These determine the scaling regimes and universality classes of the evolving surfaces.…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the…
We present simulations of the relaxation towards equilibrium of one dimensional steps and sinusoidal grooves imprinted on a surface below its roughening transition. We use a generalization of the hypercube stacking model of Forrest and…
A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated…
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…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
As an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations (PDEs). Their {\em heuristic derivation} makes use of inherent symmetries in the…
The decay of a crystalline cone below the roughening transition is studied. We consider local mass transport through surface diffusion, focusing on the two cases of diffusion limited and attachment-detachment limited step kinetics. In both…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
The relaxation process of one dimensional surface modulations is re-examined. Surface evolution is described in terms of a standard step flow model. Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz…
Relationships between sediment flux and geomorphic processes are combined with statements of mass conservation, in order to create continuum models of hillslope evolution. These models have parameters which can be calibrated using available…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
The behavior of a surface energy $\mathcal F(E,u)$, where $E$ is a set of finite perimeter and $u\in L^1(\partial^* E, \mathbb R_+)$ is studied. These energies have been recently considered in the context of materials science to derive a…