Time-dispersive behavior as a feature of critical-contrast media

Kirill Cherednichenko, Yulia Ershova, Alexander V. Kiselev

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Motivated by the need to attribute a rigorous mathematical meaning to the term ``metamaterial,"" we propose a novel approach to the homogenization of critical-contrast composites. This is based on the asymptotic analysis of the Dirichlet-to-Neumann map on the interface between different components (``stiff"" and ``soft"") of the medium, which leads to an asymptotic approximation of eigenmodes. This allows us to see that the presence of the soft component makes the stiff one behave as a class of time-dispersive media. By an inversion of this argument, we also offer a recipe for the construction of such media with prescribed dispersive properties from periodic composites.

Original languageEnglish
Pages (from-to)690-715
Number of pages26
JournalSIAM Journal on Applied Mathematics
Issue number2
Early online date16 Apr 2019
Publication statusPublished - 2019


  • Asymptotics
  • Effective properties
  • Homogenization
  • Operators
  • Time-dispersive media

ASJC Scopus subject areas

  • Applied Mathematics


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