Multiple scattering by multiple scatterers

Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401-1887, USA

Abstract

Acoustic scattering by random collections of identical circular cylinders is considered. Two classes of methods are used. The first is usually associated with the names of Foldy and Lax. Such methods require a “closure assumption”, in addition to the governing equations. The second class is based on iterative approximations to integral equations of Lippmann–Schwinger type. Such methods do not use a closure approximation. Both methods are reviewed. In particular, when each cylinder is penetrable, with a sound-speed that is close to that in the exterior (the scattering is said to be “weak”), we show that both approaches lead to exactly the same formulas for the effective wavenumber, correct to second order in scattering strength and second order in filling fraction.