Upscaling a Model for the Thermally-Driven Motion of Screw Dislocations

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• 作者：T. Hudson
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：224
• 期：1
• 页码：291-352
• 全文大小：1024KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0673
• 卷排序：224

文摘

We formulate and study a stochastic model for the thermally-driven motion of interacting straight screw dislocations in a cylindrical domain with a convex polygonal cross-section. Motion is modelled as a Markov jump process, where waiting times for transitions from state to state are assumed to be exponentially distributed with rates expressed in terms of the potential energy barrier between the states. Assuming the energy of the system is described by a discrete lattice model, a precise asymptotic description of the energy barriers between states is obtained. Through scaling of the various physical constants, two dimensionless parameters are identified which govern the behaviour of the resulting stochastic evolution. In an asymptotic regime where these parameters remain fixed, the process is found to satisfy a Large Deviations Principle. A sufficiently explicit description of the corresponding rate functional is obtained such that the most probable path of the dislocation configuration may be described as the solution of Discrete Dislocation Dynamics with an explicit anisotropic mobility which depends on the underlying lattice structure.