Durga Prasad Challa

On the Justification of the Foldy--Lax Approximation for the Acoustic Scattering by Small Rigid Bodies of Arbitrary Shapes

We are concerned with the acoustic scattering problem by many small rigid obstacles of arbitrary shapes. We give a sufficient condition on the number

Inverse scattering by point-like scatterers in the Foldy regime

M

Multiscale analysis of the acoustic scattering by many scatterers of impedance type

and the diameter

A cluster of many small holes with negative imaginary surface impedances may generatea negative refraction index

a

Extraction of the index of refraction by embedding multiple small inclusions

of the obstacles as well as the minimum distance

The equivalent mass density for the elastic scattering by many small rigid bodies and applications

d

Location and size estimation of small rigid bodies using elastic far-fields

between them under which the Foldy--Lax approximation is valid. Precisely, if we use single layer potentials for the representation of the scattered fields, as is done sometimes in the literature, then this condition is

Mathematical imaging using electric or magnetic nanoparticles as contrast agents

(M-1)\frac{a}{d^2} <c

The Foldy-Lax approximation of the scattered waves by many small bodies for the Lamé system

, with an appropriate constant

Multiple scattering of electromagnetic waves by finitely many point-like obstacles

c