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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, Vol.46 (No.1). pp. 81-110. 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 |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | ESAIM: Mathematical Modelling and Numerical Analysis |
| Publisher: | EDP Sciences |
| ISSN: | 0764-583X |
| Date: | January 2012 |
| Volume: | Vol.46 |
| Number: | No.1 |
| Page Range: | pp. 81-110 |
| Identification Number: | 10.1051/m2an/2011014 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/43786 |
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