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Transmission and reflection at an interface between metamaterial and ordinary material

Presented by: 
John Raymond Willis University of Cambridge
Date: 
Wednesday 14th August 2019 - 10:00 to 10:30
Venue: 
INI Seminar Room 1
Abstract: 
A contribution to the subject in the title is made, in the case that the metamaterial has random microstructure. A variational approach permits the development of a system of integral equations which can be replaced by a Wiener-Hopf system.The equations retain information on the metamaterial up to two-point probabilities. The formulation will be developed in detail for a configuration of particular simplicity -- acoustic materials, all with the same modulus but different densities. A special case, for which the problem reduces to a very simple scalar Wiener-Hopf problem, has been solved, giving explicit formulae for transmission and reflection coefficients. It should be possible to develop the analysis further and obtain more general solutions... It is likely that the audience will be able to provide useful input.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons