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Reflection from a multi-species material and its transmitted effective wavenumber.

Published version
Peer-reviewed

Type

Article

Change log

Authors

Parnell, William J 
Abrahams, I David 

Abstract

We formally deduce closed-form expressions for the transmitted effective wavenumber of a material comprising multiple types of inclusions or particles (multi-species), dispersed in a uniform background medium. The expressions, derived here for the first time, are valid for moderate volume fractions and without restriction on the frequency. We show that the multi-species effective wavenumber is not a straightforward extension of expressions for a single species. Comparisons are drawn with state-of-the-art models in acoustics by presenting numerical results for a concrete and a water-oil emulsion in two dimensions. The limit of when one species is much smaller than the other is also discussed and we determine the background medium felt by the larger species in this limit. Surprisingly, we show that the answer is not the intuitive result predicted by self-consistent multiple scattering theories. The derivation presented here applies to the scalar wave equation with cylindrical or spherical inclusions, with any distribution of sizes, densities and wave speeds. The reflection coefficient associated with a halfspace of multi-species cylindrical inclusions is also formally derived.

Description

Keywords

ensemble average, homogenization, multiple scattering, polydisperse, random media, size distribution

Journal Title

Proc Math Phys Eng Sci

Conference Name

Journal ISSN

1364-5021
1471-2946

Volume Title

474

Publisher

The Royal Society
Sponsorship
Engineering and Physical Sciences Research Council (EP/M026205/1)
Engineering and Physical Sciences Research Council (EP/K032208/1)
Engineering and Physical Sciences Research Council (EP/R014604/1)