English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We formally deduce closed-form expressions for the transmitted effectivewavenumber 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 andwithout restriction on the frequency. We show that the multi-species effectivewavenumber is not a straightforward extension of expressions for a singlespecies. Comparisons are drawn with state-of-the-art models in acoustics bypresenting numerical results for a concrete and a water-oil emulsion in twodimensions. The limit of when one species is much smaller than the other isalso discussed and we determine the background medium felt by the largerspecies in this limit. Surprisingly, we show that the answer is not theintuitive result predicted by self-consistent multiple scattering theories. Thederivation presented here applies to the scalar wave equation with cylindricalor spherical inclusions, with any distribution of sizes, densities, and wavespeeds. The reflection coefficient associated with a half-space ofmulti-species cylindrical inclusions is also formally derived.

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