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Abstract. This paper presents a new algorithm for conductivity imaging. Our idea is to extract more information about the conductivity distribution from data that have been enriched by coupling impedance electrical measurements to localized elastic perturbations. Using asymptotics of the elds in the presence of small volume inclusions, we relate the pointwise values of the energy density to the measured data, through a nonlinear PDE. Our algorithm is based on this PDE and takes full advantage of the enriched data. We give numerical examples that illustrate the performance and the accuracy of our approach.

If a body of dielectric material is coated by a plasmonic structure of negative dielectric constant with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. The aim of this paper is to investigate this phenomenon in two and three dimensions when the coated structure is radial, and the core, shell and matrix are isotropic materials. In two dimensions, we show that if the real part of the permittivity of the shell is −1 (under the assumption that the permittivity of the background is 1), then CALR takes place. If it is different from −1, then CALR does not occur. In three dimensions, we show that CALR does not occur. The analysis of this paper reveals that occurrence of CALR is determined by the eigenvalue distribution of the Neumann-Poincaré-type operator associated with the structure.

Layer potential techniques in spectral analysis / Habib Ammari, Hyeonbae Kang, Hyundae Lee. p. cm.-(Mathematical surveys and monographs ; v. 153) Includes bibliographical references and index.

Abstract. We consider the problem of locating perfectly conducting cracks and estimating their geometric features from multi-static response matrix measurements at a single or multiple frequencies. A main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal-to-noise ratios. In this paper we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength-to-crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks. A central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multi-static response matrix measurements. We present numerical experiments to illustrate some of our main findings.