The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This is the first book to provide a systematic exposition of promising techniques for the
reconstruction of small inhomogeneities from boundary measurements. In particular …

In multistatic imaging one uses waves to probe for information about an unknown medium.
These waves can be acoustic, elastic, or electromagnetic. They can be at zero-frequency …

Since the early part of the twentieth century, the use of integral equations has developed into
a range of tools for the study of partial differential equations. This includes the use of single …

The fields of photonics and phononics encompass the fundamental science of light and
sound propagation and interactions in complex structures, as well as its technological …

In this paper we provide a mathematical framework for localized plasmon resonance of
nanoparticles. Using layer potential techniques associated with the full Maxwell equations …

In this paper we consider the localization of a collection of small, three-dimensional
bounded homogeneous inclusions via time-harmonic electromagnetic means, typically …

Mathematical analysis and numerical solutions of problems with unknown shapes or
geometrical domains is a challenging and rich research field in the modern theory of the …

The topological derivative method is recognized as a robust numerical technique in
engineering applications such as topology optimization, inverse problems, imaging …

The aim of this study is an extension and employment of the concept of topological
derivative as it pertains to the nucleation of infinitesimal inclusions in a reference (ie …