相关论文: Novel continuum modeling of crystal surface evolut…
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 kinetics of monoatomic steps in diffusion-controlled crystal growth and evaporation processes are investigated analytically using a Green's function approach. Integro-differential equations of motion for the steps are derived; and a…
Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
Motivated by results of the topological theory of glasses accounting for geometric frustration, we develop the simplest possible continuum mechanical model of defect dynamics in metallic glasses that accounts for topological, energetic, and…
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 analytically and numerically study a fourth order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long time dynamics for the PDE model. The PDE, originally…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
We study a model for the movement of surfaces, namely the conserved, restricted solid-on-solid model. The surface configurations are restricted such that the difference between the heights at adjacent sites is no more than one. In addition…
Mound formation on flat and miscut crystal surfaces exhibits distinct growth behaviors. While mound structures are the predominant feature on flat surfaces, miscut surfaces display a smooth transition from meandered patterns to…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface diffusion and…
A miscut (vicinal) crystal surface can be regarded as an array of meandering but non-crossing steps. Interactions between the steps are shown to induce a faceting transition of the surface between a homogeneous Luttinger liquid state and a…
A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the…
We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is…
We consider a simple model for the growth of isolated steps on a vicinal crystal surface. It incorporates diffusion and drift of adatoms on the terrace, and strong step and kink edge barriers. Using a combination of analytic methods and…
We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…
Phase field crystal (PFC) models constitute a field theoretical approach to solidification, melting and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
This paper discusses a continuum approach to track the evolution of permeability in granular rocks by accounting for the combined effect of porosity changes, grain breakage and cement bond damage. To account for such a broad range of…