The combined effect of fine heterogeneities and small gradient perturbations is analyzed by means of an asymptotic development by Gamma-convergence for a family of energies related to (one-dimensional) phase transformations. We show that multi-scale effects add up to the usual sharp-interface limit, due to the homogenization of microscopic interfaces, internal and external boundary layers, optimal arrangements of microscopic oscillations, etc. Several regimes are analyzed depending on the "size" of the heterogeneity (small or large perturbations of a homogeneous situation) and their relative period as compared with the characteristic length of the phase transitions (slow or fast oscillations).

Braides, A., Zeppieri, C. (2009). Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy. INTERFACES AND FREE BOUNDARIES, 11(1), 61-118.

Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy

BRAIDES, ANDREA;
2009-01-01

Abstract

The combined effect of fine heterogeneities and small gradient perturbations is analyzed by means of an asymptotic development by Gamma-convergence for a family of energies related to (one-dimensional) phase transformations. We show that multi-scale effects add up to the usual sharp-interface limit, due to the homogenization of microscopic interfaces, internal and external boundary layers, optimal arrangements of microscopic oscillations, etc. Several regimes are analyzed depending on the "size" of the heterogeneity (small or large perturbations of a homogeneous situation) and their relative period as compared with the characteristic length of the phase transitions (slow or fast oscillations).
2009
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Gamma-convergence; Gamma-development; phase transitions; homogenization
58
http://digitallibrary.sissa.it/bitstream/handle/1963/3666/BZ07.pdf?sequence=2
Braides, A., Zeppieri, C. (2009). Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy. INTERFACES AND FREE BOUNDARIES, 11(1), 61-118.
Braides, A; Zeppieri, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/26763
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