Ground states in complex bodies

Paolo Maria Mariano; Giuseppe Modica

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 15, Issue: 2, page 377-402
  • ISSN: 1292-8119

Abstract

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A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end.

How to cite

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Mariano, Paolo Maria, and Modica, Giuseppe. "Ground states in complex bodies." ESAIM: Control, Optimisation and Calculus of Variations 15.2 (2008): 377-402. <http://eudml.org/doc/90918>.

@article{Mariano2008,
abstract = { A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end. },
author = {Mariano, Paolo Maria, Modica, Giuseppe},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Cartesian currents; complex bodies; ground states; multifield theories; existence; semicontinuity; Sobolev mappings; thermodynamically stable quasicrystals},
language = {eng},
month = {5},
number = {2},
pages = {377-402},
publisher = {EDP Sciences},
title = {Ground states in complex bodies},
url = {http://eudml.org/doc/90918},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Mariano, Paolo Maria
AU - Modica, Giuseppe
TI - Ground states in complex bodies
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/5//
PB - EDP Sciences
VL - 15
IS - 2
SP - 377
EP - 402
AB - A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end.
LA - eng
KW - Cartesian currents; complex bodies; ground states; multifield theories; existence; semicontinuity; Sobolev mappings; thermodynamically stable quasicrystals
UR - http://eudml.org/doc/90918
ER -

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