ensemble averaging

Materials comprising randomly distributed particles, or inclusions, occur frequently in the world around us. Common examples include composites, emulsions, suspensions, complex gases, etc... This paper is the first to clearly prove that, contrary to the belief of most in the community, multiple effective waves propagate in particulate materials (in an ensemble-average sense).

We show that in general there is not only one effective wave, but there is a series of effective waves in an ensemble averaged particulate material. By particulate material we mean a medium filled with randomly placed particles and consider waves …

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 …