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ACMD Seminar: Eigenvalue problems in scattering theory and their application to nondestructive testing of materials

Samuel Cogar
Department of Mathematical Sciences, University of Delaware

Tuesday, May 29, 2018 15:00 - 16:00
Building 227 Room A202

Tuesday, May 29, 2018 13:00 - 14:00
Building 1 Room 4072

Host: Ryan Evans

Abstract: The problem of nondestructive testing of materials is complicated by the observation that an anisotropic inhomogeneous medium is not uniquely determined by its scattering data. However, as the aim of nondestructive testing is to detect only a change in a tested object relative to some reference object, a viable alternative is to use a target signature: a set of numbers that depends on the material properties of the medium. This idea has received considerable interest in the context of transmission eigenvalues in recent years, but due to their connection with the physical parameter of frequency, transmission eigenvalues fail to serve as a practical target signature. In particular, their detection requires the collection of scattering data for multiple frequencies, and they may only be detected for materials with negligible absorption. We discuss a recently developed class of methods which overcomes these defects by modifying the far field operator in order to generate new eigenvalue problems with artificial eigenparameters. After a brief introduction to some of the eigenvalue problems developed, we focus on so-called modified transmission eigenvalues for acoustic scattering, and we show that they possess the desired properties of a target signature for the case of both far field measurements and internal measurements in a cavity surrounded by an anisotropic medium. We conclude with a series of numerical examples and a remark on the application of these ideas to Maxwell's nist-equations.

Bio: Samuel Cogar is a Ph.D. candidate in Applied Mathematics at the University of Delaware under the advisement of David Colton and Peter Monk. His research focuses on the development and study of eigenvalue problems in inverse scattering theory, including investigations of their spectral properties and the computation of eigenvalues both from measured scattering data and using the finite element method. He is a 2016 recipient of the National Defense Science and Engineering Graduate (NDSEG) Fellowship, and his research is supported by the Army Research Office.

Note: Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.

Created May 16, 2018, Updated November 15, 2019