One of the most cited papers in Applied Mechanics is the work of Eshelby from 1957 who
showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in an …

In this chapter, we are interested in finding coefficients of the second-order hyperbolic
operator:(8.0. 1) a0∂ 2 t u+ Au= f in Q= Ω×(0, T) given the initial data (8.0. 2) u= u0,∂ tu= u1 …

This book has grown out of lecture notes for a course on mathematical methods in
biomedical imaging at Ecole Polytechnique. Biomedical imaging is a fascinating research …

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 …

This book is the first introductory and self-contained presentation of a method for the
analysis of singularly perturbed boundary value problems that we have called the Functional …

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 …

The aim of this paper is to give a mathematical justification of cloaking due to anomalous
localized resonance (CALR). We consider the dielectric problem with a source term in a …

A Transformer-based deep direct sampling method is proposed for electrical impedance
tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A …