螺位错动力学：广义最小运动方案方法
Dynamics of screw dislocations: a generalised minimising-movements scheme approach
摘要：
本文用广义最小运动格式研究了文献[CG 99]中螺位错动力学模型的梯度流结构。有限数量的可用滑移方向的假设，连同控制运动方程的“最大耗散准则”，导致求解微分包含而不是常微分方程。本文讨论了[CG 99]中的模型如何连接到时间离散演化方案，该方案明确限制位错沿着单个滑移方向移动每个时间步长。证明了文献[CG 99]中的时间连续模型在时间步长收敛到0时是这些时间离散最小位移格式的极限。这里介绍的研究是迈向[AGS08，第一章]中设定的普遍化的第一步。2和3]，允许耗散，这是不能描述的度量。
英文摘要：
The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the "maximal dissipation criterion" that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in [CG99] is connected to a time-discrete evolution scheme which explicitly confines dislocations to move each time step along a single glide direction. It is proved that the time-continuous model in [CG99] is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalisation of the setting in [AGS08, Chap. 2 and 3] that allows for dissipations which cannot be described by a metric.
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