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Atomistic origins of continuum dislocation dynamics
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Hudson, Thomas E. (Edward), Peletier, Mark and van Meurs, Patrick (2020) Atomistic origins of continuum dislocation dynamics. Mathematical Models and Methods in Applied Sciences, 30 (13). pp. 2557-2618. doi:10.1142/S0218202520500505 ISSN 0218-2025.
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WRAP-Atomistic-origins-continuum-dislocation-dynamics-Hudson-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1122Kb) | Preview |
Official URL: https://doi.org/10.1142/S0218202520500505
Abstract
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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Probabilities, Mean field theory , Spatial systems , Dynamics of a particle -- Mathematical models | ||||||||
| Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||
| ISSN: | 0218-2025 | ||||||||
| Official Date: | 15 December 2020 | ||||||||
| Dates: |
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| Volume: | 30 | ||||||||
| Number: | 13 | ||||||||
| Page Range: | pp. 2557-2618 | ||||||||
| DOI: | 10.1142/S0218202520500505 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | Electronic version of an article published as [Journal, Volume, Issue, Year, Pages] https://doi.org/10.1142/S0218202520500505 © [copyright World Scientific Publishing Company] [Journal URL] | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 17 September 2020 | ||||||||
| Date of first compliant Open Access: | 1 November 2021 | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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