Atomistic origins of continuum dislocation dynamics

Thomas Hudson, Patrick van Meurs, Mark Peletier

Onderzoeksoutput: Bijdrage aan tijdschriftArtikel recenserenpeer review

Samenvatting

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.

Originele taal-2Engels
Pagina's (van-tot)2557-2618
Aantal pagina's62
TijdschriftMathematical Models and Methods in Applied Sciences
Volume30
Nummer van het tijdschrift13
DOI's
StatusGepubliceerd - 15 dec 2020

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