Many-body wave scattering by small bodies and applications

TL;DR

This paper develops a simplified method for analyzing wave scattering by many small particles, deriving effective medium equations, and demonstrating how to engineer materials with specific refraction properties by embedding small particles.

Contribution

It introduces a new approach to reduce many-body wave scattering problems to linear algebraic systems and derives effective equations for media with embedded small particles.

Findings

A linear algebraic system for wave scattering is established.

Effective medium equations are derived for infinitely many small particles.

Materials with tailored refraction coefficients can be created by embedding small particles.

Abstract

A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium is considered and the limiting equation for the field in the medium is derived. The impedance boundary conditions are imposed on the boundaries of small bodies. The case of Neumann boundary conditions (acoustically hard particles) is also considered. Applications to creating materials with a desired refraction coefficient are given. It is proved that by embedding suitable number of small particles per unit volume of the original material with suitable boundary impedances one can create a new material with any desired refraction coefficient. The governing equation is a scalar Helmholtz equation, which one obtains by Fourier transforming the wave equation.