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-2 | Engels |
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Pagina's (van-tot) | 2557-2618 |
Aantal pagina's | 62 |
Tijdschrift | Mathematical Models and Methods in Applied Sciences |
Volume | 30 |
Nummer van het tijdschrift | 13 |
DOI's | |
Status | Gepubliceerd - 15 dec. 2020 |
Financiering
TH gratefully acknowledges support from an Early Career Fellowship awarded by the Leverhulme Trust (ECF-2016-526). PvM gratefully acknowledges support from the International Research Fellowship of the Japanese Society for the Promotion of Science and the associated JSPS KAKENHI grant 15F15019. MAP gratefully acknowledges support from NWO project 613.001.552, Large Deviations and Gradient Flows: Beyond Equilibrium.
Financiers | Financiernummer |
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Japan Society for the Promotion of Science | |
Leverhulme Trust | ECF-2016-526 |
Japan Society for the Promotion of Science | 15F15019 |
Nederlandse Organisatie voor Wetenschappelijk Onderzoek | 613.001.552 |