Many-body wave scattering by small bodies and applications II

TL;DR

This paper investigates the behavior of wave scattering by many small bodies, deriving asymptotic formulas for the case where the bodies are very small and numerous, with applications to material design and wave manipulation.

Contribution

It introduces new asymptotic methods for analyzing wave scattering by a large number of small bodies as their size approaches zero.

Findings

Derived asymptotic formulas for wave scattering in the small-body limit

Analyzed the distribution of small bodies as their size tends to zero

Provided insights into controlling wave propagation with small scatterers

Abstract

The many-body wave scattering problem is studied in the case where the bodies are small, $ka \ll 1$, where $a$ is the characteristic size of a body. The limiting case when $a \to 0$ and the total number of the small bodies is $M = O (a^{2-\kappa})$ is studied, $\kappa\in (0,1)$ is a parameter, the distance $d$ between neighboring bodies is $d=O(a^{(2-\kappa)/3}$.