# On the stability of Bravais lattices and their Cauchy–Born approximations

Thomas Hudson; Christoph Ortner

- Volume: 46, Issue: 1, page 81-110
- ISSN: 0764-583X

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topHudson, Thomas, and Ortner, Christoph. "On the stability of Bravais lattices and their Cauchy–Born approximations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 46.1 (2012): 81-110. <http://eudml.org/doc/273191>.

@article{Hudson2012,

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.},

author = {Hudson, Thomas, Ortner, Christoph},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Bravais lattice; Cauchy–Born model; stability; Cauchy-Born model},

language = {eng},

number = {1},

pages = {81-110},

publisher = {EDP-Sciences},

title = {On the stability of Bravais lattices and their Cauchy–Born approximations},

url = {http://eudml.org/doc/273191},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Hudson, Thomas

AU - Ortner, Christoph

TI - On the stability of Bravais lattices and their Cauchy–Born approximations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 1

SP - 81

EP - 110

AB - 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.

LA - eng

KW - Bravais lattice; Cauchy–Born model; stability; Cauchy-Born model

UR - http://eudml.org/doc/273191

ER -

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