Atomistic origins of continuum dislocation dynamics
Atomistic origins of continuum dislocation dynamics
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DOI：
10.1142/s0218202520500505
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发表时间：
2020-12-15
影响因子：
3.5
通讯作者：
Peletier, Mark
中科院分区：
文献类型：
--
作者：
Hudson, Thomas;van Meurs, Patrick;Peletier, Mark
本文重点讨论了直螺位错运动的四种随机和确定性模型之间的联系。从描述螺旋位错运动为晶格上相互作用的随机漫步开始，我们证明了该模型解之间距离的显式估计，位错位置的SDE系统，以及描述位错密度的两个确定性平均场模型。这些估计的证明使用了各种分析和概率论技术的集合，包括在空间离散模型上建立混沌传播的新方法。估计是非渐近的和明确的四个参数：晶格间距，位错的数量，位错的核心尺寸，和温度。这项工作是探索这个参数空间的第一步，最终目的是连接和量化文献中许多不同位错模型之间的关系。
This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove explicit estimates of the distance between solutions of this model, an SDE system for the dislocation positions, and two deterministic mean-field models describing the dislocation density. The proof of these estimates uses a collection of various techniques in analysis and probability theory, including a novel approach to establish propagation-of-chaos on a spatially discrete model. The estimates are non-asymptotic and explicit in terms of four parameters: the lattice spacing, the number of dislocations, the dislocation core size, and the temperature. This work is a first step in exploring this parameter space with the ultimate aim to connect and quantify the relationships between the many different dislocation models present in the literature.