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Properties of screw dislocation dynamics : time estimates on boundary and interior collisions
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Hudson, Thomas E. (Edward) and Morandotti, Marco (2017) Properties of screw dislocation dynamics : time estimates on boundary and interior collisions. SIAM Journal on Applied Mathematics, 77 (5). pp. 1678-1705. doi:10.1137/17M1119974 ISSN 0036-1399.
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Official URL: http://epubs.siam.org/doi/abs/10.1137/17M1119974
Abstract
In this paper, the dynamics of a system of a finite number of screw dislocations is studied. Under the assumption of antiplane linear elasticity, the two-dimensional dynamics is determined by the renormalized energy. The interaction of one dislocation with the boundary and of two dislocations of opposite Burgers moduli are analyzed in detail, and estimates on the collision times are obtained. Additionally, we obtain sufficient conditions that can be used to guarantee that the first collision to occur will be between a specific dislocation and the boundary, or between a specific pair of dislocations. Some exactly solvable cases and numerical simulations show agreement with the estimates obtained.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Crystallography, Mathematical | ||||||||
| Journal or Publication Title: | SIAM Journal on Applied Mathematics | ||||||||
| Publisher: | Society for Industrial and Applied Mathematics | ||||||||
| ISSN: | 0036-1399 | ||||||||
| Official Date: | 21 September 2017 | ||||||||
| Dates: |
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| Volume: | 77 | ||||||||
| Number: | 5 | ||||||||
| Page Range: | pp. 1678-1705 | ||||||||
| DOI: | 10.1137/17M1119974 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 3 October 2017 | ||||||||
| Date of first compliant Open Access: | 4 October 2017 | ||||||||
| Funder: | Leverhulme Trust (LT), France. Agence nationale de la recherche (ANR), European Research Council (ERC) | ||||||||
| Grant number: | ANR-10-LABX-0098 (ANR), Grant agreement no.: 290888, Grant agreement no.: 306274, (ERC) |
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