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.

中文翻译：

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连续位错动力学的原子起源

本文重点研究直螺旋位错运动的四种随机和确定性模型之间的联系。从将螺旋位错运动描述为晶格上相互作用的随机游走开始，我们证明了对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分析和概率论中各种技术的集合，包括一种在空间离散模型上建立混沌传播的新方法。就四个参数而言，估计是非渐近的和明确的：晶格间距、位错数量、位错核心尺寸和温度。