Related papers: Numerical Methods for Coupled Surface and Grain Bo…
Synthetic driving force molecular dynamics simulations were utilized to survey grain boundary mobility in three classes of incoherent {\Sigma}3 twin boundaries: <112>, <110>, and <111> tilt boundaries. These boundaries are faceted on low…
Previous simulation and experimental studies have shown that some grain boundaries (GBs) can couple to applied shear stresses and be moved by them, producing shear deformation of the lattice traversed by their motion. While this coupling…
Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…
Motion by (weighted) mean curvature is a geometric evolution law for surfaces, representing steepest descent with respect to (an)isotropic surface energy. It has been proposed that this motion could be computed by solving the analogous…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
We describe numerical solutions of two non potential models of pattern formation in nonequilibrium systems to address the motion and decay of grain boundaries separating domains of stripe configurations of different orientations. We first…
With the increasing availability of experimental and computational data concerning the properties and distribution of grain boundaries in polycrystalline materials, there is a corresponding need to efficiently and systematically express…
We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg…
We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing…
Motion by weighted mean curvature is a geometric evolution law for surfaces and represents steepest descent with respect to anisotropic surface energy. It has been proposed that this motion could be computed numerically by using a…
We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation appropriate for hexagonal patterns, a multiple scale analysis leads to an analytical…
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make…
Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters…
Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is a recent embedding method that has been used to solve a…
We propose a two dimensional frame-invariant phase field model of grain impingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. We are…
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…
We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a…
We use the sixth order linear parabolic equation \begin{equation} \frac{\partial y}{\partial t}=B\left(\alpha\frac{\partial^{6}y}{\partial x^{6}}-\frac{\partial^{4}y}{\partial x^{4}}\right),\ x\in \mathbb{R}_{+},\ t>0,\nonumber…
In this paper, we deal with the parabolic KWC system, associated with the mathematical model of grain boundary motion. The goal of this paper is to guarantee the well-posedness of the parabolic KWC system. However, such results have not…