Multiple scattering by multiple spheres: A new proof of the Lloyd- Berry formula for the effective wavenumber

摘要

We provide the first classical derivation of the Lloyd-Berry formula for the effective wavenumber of an acoustic medium filled with a sparse random array of identical small scatterers. Our approach clarifies the assumptions under which the Lloyd-Berry formula is valid. More precisely, we derive an expression for the effective wavenumber which assumes the validity of Lax's quasi-crystalline approximation but makes no further assumptions about scatterer size, and then we show that the Lloyd-Berry formula is obtained in the limit as the scatterer size tends to zero.