Asymptotic Expansions for Resonances in the Presence of Small Anisotropic Imperfections

TL;DR

This paper derives an asymptotic formula to understand how small anisotropic imperfections affect resonance values, enabling the identification of their properties and locations.

Contribution

It introduces a rigorous asymptotic expansion method for perturbations in resonance values caused by small anisotropic imperfections, providing a robust way to recover their characteristics.

Findings

Derived an asymptotic expansion formula for resonance perturbations

Method allows for recovering imperfections' location, shape, and material properties

Provides a rigorous mathematical framework for anisotropic imperfection analysis

Abstract

We provide a rigorous derivation of an asymptotic formula for perturbations in the resonance values caused by the presence of finite number of anisotropic imperfections of small shapes with constitutive parameters different from the background conductivity. The asymptotic expansion is carried out with respect to the size of the imperfections. The main feature of the method is to yield a robust procedure making it possible to recover information about the location, shape, and material properties of the anisotropic imperfections.