Related papers: Numerical Methods for Coupled Surface and Grain Bo…
Coupled grain boundary (GB) motion has been studied in a two-dimensional tricrystal where a cylindrical grain is embedded at the center of the planar GB of a large bicrystal. Kinetic relations for GB dynamics, grain orientations, and…
A novel continuum theory of incoherent interfaces with triple junctions is applied to study three-dimensional coupled grain boundary (GB) motion in polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
Grain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by…
The evolution of two grains, which lie on a substrate and are in contact with each other, can be roughly described by a model in which the exterior surfaces of the grains evolve by surface diffusion and the grain boundary, namely the…
Grain boundary (GB) kinetics is important for many applications in 2d materials and metal thin films. To study how the substrate shape affects GB mobility and kinetics, we develop a kinetic Monte Carlo (kMC) simulation method and an…
A mesoscopic model of a diblock copolymer is used to study the motion of a grain boundary separating two regions of perfectly ordered lamellar structures under an oscillatory but uniform shear flow. The case considered is a grain boundary…
We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved…
This work is based upon a coupled, lattice-based continuum formulation that was previously applied to problems involving strong coupling between mechanics and mass transport; e.g. diffusional creep and electromigration. Here we discuss an…
A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in Ref. [48]. The model is based on the motion and reaction of the constituent…
In this work, we investigate the shape evolution of rotated, embedded, initially cylindrical grains (with [001] cylinder axis) in Ni under an applied synthetic driving force via molecular dynamics simulations and a continuum,…
A numerical investigation of grain-boundary grooving by means of a Level Set method is carried out. An idealized polygranular interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average…
In this work, we consider parabolic models with dynamic boundary conditions and parabolic bulk-surface problems in 3D. Such partial differential equations based models describe phenomena that happen both on the surface and in the…
Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasi-continuum method links atomistic and…
We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or…
We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity…
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…
A discrete model and the regular solution approximation are applied to describe the effect of grain boundary motion on grain boundary phase transformations in a binary alloy. The model predicts all thermodynamic properties of the grain…
We consider a system of three surfaces, graphs over a bounded domain in ${\mathbb R}^2$, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to…
In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion…