连续位错动力学的原子起源
Atomistic origins of continuum dislocation dynamics
摘要：
本文着重讨论了直螺位错运动的四种随机模型与确定性模型之间的联系。从相互作用的随机游动的晶格上的螺旋位错运动的描述，我们证明了明确的估计，这个模型的解决方案之间的距离，一个系统的位错位置，和两个确定性的平均场模型描述的位错密度。这些估计的证明使用了各种技术的分析和概率论，包括一种新的方法来建立传播的混沌空间离散模型的集合。的估计是非渐近和明确的四个参数：晶格间距，位错的数量，位错核心的大小，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存在的许多不同的位错模型之间的关系。
英文摘要：
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.
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