# 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

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topMariano, 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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