论文标题
连续脱位动力学的原子起源
Atomistic origins of continuum dislocation dynamics
论文作者
论文摘要
本文着重于四个随机模型和确定性模型之间的连接，以进行直螺钉位错的运动。从将螺钉位错运动作为晶格上的随机行走的描述开始，我们证明了该模型解决方案之间的距离，一个用于位错位置的SDE系统以及描述错位密度的两个确定性平均场模型。这些估计值的证明使用了分析和概率理论中各种技术的集合，包括一种在空间离散模型上建立chaos的新方法。这些估计值在四个参数方面是非质子的，并且是显式的：晶格间距，位错数，位错核心大小和温度。这项工作是探索此参数空间的第一步，其最终目的是连接和量化文献中存在的许多不同错位模型之间的关系。
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.
