Scattering of scalar waves by many small particles

TL;DR

This paper derives formulas for wave scattering by many small particles in inhomogeneous media, analyzing the limiting behavior as particle size shrinks and their number increases, leading to effective field equations.

Contribution

It introduces new formulas and equations for the effective field in media with many small particles, extending scattering theory to complex inhomogeneous environments.

Findings

Derived formulas for wave scattering by small particles in various boundary conditions.

Established limiting equations for the effective field as particle size approaches zero.

Analyzed the asymptotic behavior of many-particle scattering systems.

Abstract

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size $a$ of small particles tends to zero while their number tends to infinity at a suitable rate. Equations for the limiting effective (self-consistent) field in the medium are derived.