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Ground states in complex bodies

Published online by Cambridge University Press:  30 May 2008

Paolo Maria Mariano  and
Giuseppe Modica
Paolo Maria Mariano
Affiliation:
DICeA, University of Florence, via Santa Marta 3, 50139 Firenze, Italy; [email protected]
Giuseppe Modica
Affiliation:
Dipartimento di Matematica Applicata “G. Sansone”, University of Florence, via Santa Marta 3, 50139 Firenze, Italy; [email protected]
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Abstract

A unified framework for analyzing the existence of ground states in wideclasses of elastic complex bodies is presented here. The approach makes useof classical semicontinuity results, Sobolev mappings and Cartesiancurrents. Weak diffeomorphisms are used to represent macroscopicdeformations. Sobolev maps and Cartesian currents describe the innersubstructure of the material elements. Balance equations for irregularminimizers are derived. A contribution to the debate about the role of thebalance of configurational actions follows. After describing a list ofpossible applications of the general results collected here, a concretediscussion of the existence of ground states in thermodynamically stablequasicrystals is presented at the end.

Keywords

Cartesian currentscomplex bodiesground statesmultifieldtheories
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 2 , April 2009 , pp. 377 - 402
Copyright
© EDP Sciences, SMAI, 2008

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