Variational homogenization: old and new

  • Rita Ferreira

    King Abdullah University of Science and Technology (KAUST), CEMSE Division, Thuwal 23955-6900, Saudi Arabia
  • Irene Fonseca

    Department of Mathematical Sciences, Carnegie Mellon University(CMU), Forbes Avenue, Pittsburgh, PA 15213, USA
  • Raghavendra Venkatraman

    Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
Variational homogenization: old and new cover
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This note is a summary of the contributions of the authors to the variational viewpoint on homogenization. After providing a broad context, two recent projects are discussed in detail: one concerning the large-scale behavior of quasicrystals, and the other involving phase transitions in periodically heterogeneous media.