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

Kirill Cherednichenko, Yulia Ershova, Alexander V. Kiselev

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11 Citations (SciVal)
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Abstract

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
Volume79
Issue number2
Early online date16 Apr 2019
DOIs
Publication statusPublished - 2019

Funding

\ast Received by the editors May 14, 2018; accepted for publication (in revised form) January 28, 2019; published electronically April 16, 2019. http://www.siam.org/journals/siap/79-2/M118716.html Funding: The work of the first and second authors was supported by the Engineering and Physical Sciences Research Council: grant EP/L018802/2 ``Mathematical Foundations of Metama-terials: Homogenisation, Dissipation and Operator Theory."" The work of the second author was also supported by RFBR grant 19-01-00657-a. The work of the third author was partially supported by RFBR grant 16-01-00443-a.

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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