Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag

Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag

Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in defining the main characteristics of materials across a wide range of scales. In this work, we propose a model for the evolution of the grain boundary network with dynamic boundary conditions at the triple junctions, triple junctions drag, and with dynamic lattice misorientations. Using the energetic variational approach, we derive system of geometric differentia…

Long time behavior for a curvature flow of networks related to grain bundary motion with the effect of lattice misorientations

The mathematical model of grain boundary motion, including lattice misorientations' effect, is considered. When time-dependent lattice misorientations are state variables of the surface tension of the grain boundary, to ensure the energy dissipation law, one can obtain a curvature flow of networks with time-dependent mobilities. This paper studies the solvability and long-time asymptotic behavior of the curvature flow subjected to the Herring condition which ensures that the constituent grain boundary surface tensions are balanced at the triple junction.

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…

带有三结点阻力的网络曲率流

Curvature Flow of Networks with Triple Junction Drag

本文针对带三结点阻力的网络曲率流PDE系统，证明了其抛物型赫尔德类解的存在唯一性，扩展了初始网络适用范围，揭示了网络演化的新型拓扑变化，并探讨了表面张力对静止网络稳定性的影响。

Grain Growth and the Effect of Different Time Scales

Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play a crucial role in determining the grain structure and defining the materials properties across multiple scales. In this work, we consider two models for the motion of grain boundaries with the dynamic lattice misorientations and the triple junctions drag, and we conduct extensive numerical study of the models, as well as present relevant experimental results of grain growth in thin films.

带三叉点阻力的网络曲率流的相场方法

A Phase-Field Method for Curvature Flow of Networks with Triple Junction Drag

本文提出带三叉点阻力网络曲率流的相场方法，从变分视角推导耦合偏微分方程组，验证其收敛性并保留自动处理拓扑变化的特性。