Atomistic origins of continuum dislocation dynamics

Thomas Hudson, Patrick van Meurs, Mark Peletier

Research output: Contribution to journalReview articleAcademicpeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2557-2618
Number of pages62
JournalMathematical Models and Methods in Applied Sciences
Issue number13
Publication statusPublished - 15 Dec 2020


  • discrete-to-continuum limit
  • Dislocations
  • mean-field limit
  • particle system
  • SDE


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