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

Thomas Hudson; Christoph Ortner

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- 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 46.1 (2011): 81-110. <http://eudml.org/doc/222137>.

@article{Hudson2011,

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},

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

language = {eng},

month = {7},

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/222137},

volume = {46},

year = {2011},

}

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

DA - 2011/7//

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/222137

ER -

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