A curve shortening equation with time-dependent mobility related to grain boundary motions

The Role of Symmetry and Separation in Surface Evolution and Curve Shortening

With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated solutions is the exact curve shortening flow of a closed, convex "oval"-shaped curve and another is the smoothing of an initial periodic curve that is close to a square wave. The types of anisotropic evaporation coefficient are found for which the evaporation-condensation evolution does or does not have solutions that are analogous to the basic solutions of the…

与晶界运动相关的Łojasiewicz-Simon不等式及其应用

The Łojasiewicz-Simon inequality related to grain boundary motion and its applications

本文研究了晶界运动数学模型中的Łojasiewicz-Simon梯度不等式，推导了具有时间依赖移动性的曲线缩短方程，并讨论了该不等式在晶界能量中的应用。

A stochastic model of grain boundary dynamics: A Fokker-Planck perspective

Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The energetics and connectivities of the grain boundaries play an essential role in defining the effective properties of materials across multiple scales. In this paper we derive a Fokker-Planck model for the evolution of the planar grain boundary network. The proposed model considers anisotropic grain boundary energy which depends on lattice misorientation and takes into account mobility of the triple juncti…