JournalsifbVol. 11, No. 1pp. 61–118

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

  • Andrea Braides

    Università di Roma Tor Vergata, Italy
  • Caterina Ida Zeppieri

    SISSA, Trieste, Italy
Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy cover
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Abstract

The combined effect of fine heterogeneities and small gradient perturbations is analyzed by means of an asymptotic development by Γ\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 ({\em small or large perturbations} of a homogeneous situation) and their relative period as compared with the characteristic length of the phase transitions ({\em slow or fast oscillations}).

Cite this article

Andrea Braides, Caterina Ida Zeppieri, Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy. Interfaces Free Bound. 11 (2009), no. 1, pp. 61–118

DOI 10.4171/IFB/204