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On the stability of Bravais lattices and their Cauchy–Born approximations
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Hudson, Thomas and Ortner, Christoph (2012) On the stability of Bravais lattices and their Cauchy–Born approximations. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 46 (Number 1). pp. 81-110. doi:10.1051/m2an/2011014 ISSN 0764-583X.
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Official URL: http://dx.doi.org/10.1051/m2an/2011014
Abstract
We investigate the stability of Bravais lattices and their Cauchy–Born approximations under periodic perturbations. We formulate a general interaction law and derive its Cauchy–Born continuum limit. We then analyze the atomistic and Cauchy–Born stability regions, that is, the sets of all matrices that describe a stable Bravais lattice in the atomistic and Cauchy–Born models respectively. Motivated by recent results in one dimension on the stability of atomistic/continuum coupling methods, we analyze the relationship between atomistic and Cauchy–Born stability regions, and the convergence of atomistic stability regions as the cell size tends to infinity.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Lattice theory | ||||||||
Journal or Publication Title: | ESAIM: Mathematical Modelling and Numerical Analysis | ||||||||
Publisher: | EDP Sciences | ||||||||
ISSN: | 0764-583X | ||||||||
Official Date: | January 2012 | ||||||||
Dates: |
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Volume: | Volume 46 | ||||||||
Number: | Number 1 | ||||||||
Page Range: | pp. 81-110 | ||||||||
DOI: | 10.1051/m2an/2011014 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 20 December 2015 | ||||||||
Date of first compliant Open Access: | 20 December 2015 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
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