The reciprocity gap method for a cavity in an inhomogeneous medium

The factorization method for a cavity in an inhomogeneous medium

We consider the inverse scattering problem for a cavity that is bounded by a penetrable anisotropic inhomogeneous medium of compact support and seek to determine the shape of the cavity from internal measurements on a curve or surface inside the cavity. We derive a factorization method which provides a rigorous characterization of the support of the cavity in terms of the range of an operator w...

A new method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium

A new method is presented for solving the inverse scattering problem of determining the speed of sound in an inhomogeneous medium from the far-field data. If F (a; k , 6 ) are the far-field data corresponding to an incident plane wave with wavenumber k moving in the direction & and F j , ( f ; k , &) are the far-field data for a ball no containing the inhomogeneous region and satisfying an impe...

Casimir stress in an inhomogeneous medium

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz’s theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wi...

Wave Propagation in an Inhomogeneous Medium

Reflected Waves in an Inhomogeneous Excitable Medium

Propagation can be encumbered in an excitable cable in which intrinsic properties change abruptly. A sudden increase in diameter or a decrease in conductivity or excitability can lead to propagation block or delay in propagation with or without reflection. We study such transient phenomena from a geometric point of view. A simple two-cell caricature, with one cell enlarged to mimic diameter inc...