# Ground states in complex bodies

Paolo Maria Mariano; Giuseppe Modica

ESAIM: Control, Optimisation and Calculus of Variations (2009)

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

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topMariano, Paolo Maria, and Modica, Giuseppe. "Ground states in complex bodies." ESAIM: Control, Optimisation and Calculus of Variations 15.2 (2009): 377-402. <http://eudml.org/doc/245447>.

@article{Mariano2009,

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; Cartesian currents; existence; semicontinuity; Sobolev mappings; thermodynamically stable quasicrystals},

language = {eng},

number = {2},

pages = {377-402},

publisher = {EDP-Sciences},

title = {Ground states in complex bodies},

url = {http://eudml.org/doc/245447},

volume = {15},

year = {2009},

}

TY - JOUR

AU - Mariano, Paolo Maria

AU - Modica, Giuseppe

TI - Ground states in complex bodies

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2009

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; Cartesian currents; existence; semicontinuity; Sobolev mappings; thermodynamically stable quasicrystals

UR - http://eudml.org/doc/245447

ER -

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