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Asymptotic analysis of boundary layers in a repulsive particle system
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Hall, Cameron L., Hudson, Thomas E. (Edward) and van Meurs, Patrick (2018) Asymptotic analysis of boundary layers in a repulsive particle system. Acta Applicandae Mathematicae, 153 (1). pp. 1-54. doi:10.1007/s10440-017-0119-0 ISSN 0167-8019.
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Official URL: https://doi.org/10.1007/s10440-017-0119-0
Abstract
This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. This setting covers, for instance, pile-ups of dislocations, dislocation dipoles and dislocation walls. The main challenge in characterising the boundary behaviour is to control the nonlocal nature of the pairwise particle interactions. Using matched asymptotic expansions for the particle positions and rigorous development of an appropriate energy via Γ-convergence, we obtain the equilibrium equation solved by the boundary layer correction, associate an energy with an appropriate scaling to this correction, and provide decay rates into the bulk.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QC Physics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Particles -- Mathematical models | ||||||||
Journal or Publication Title: | Acta Applicandae Mathematicae | ||||||||
Publisher: | Springer Netherlands | ||||||||
ISSN: | 0167-8019 | ||||||||
Official Date: | February 2018 | ||||||||
Dates: |
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Volume: | 153 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 1-54 | ||||||||
DOI: | 10.1007/s10440-017-0119-0 | ||||||||
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: | 8 September 2018 | ||||||||
Funder: | Science Foundation Ireland (SFI), France. Agence nationale de la recherche (ANR), Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Netherlands Organisation for Scientific Research] (NWO), Nihon Gakujutsu Shinkōkai [Japan Society for the Promotion of Science] (JSPS) | ||||||||
Grant number: | 12/IA/1683 (SFI), ANR-10-LABX-0098 (ANR), Grant 645.000.01 (NWO), Grant 15F15019 (JSPS) |
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