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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