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

Kirill Cherednichenko, Yulia Ershova, Alexander V. Kiselev

OAI: oai:purehost.bath.ac.uk:publications/4a208efa-6bd9-47fc-b2dd-cb14234033aa • DOI: https://doi.org/10.1137/18M1187167

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.

Asymptotics Effective properties homogenization Operators Time-dispersive media /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics