Journal article
FINITENESS RESULTS CONCERNING NONSCATTERING WAVE NUMBERS FOR INCIDENT PLANE AND HERGLOTZ WAVES
SIAM journal on mathematical analysis, v 53(5), pp 5436-5464
01 Jan 2021
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
In this paper we introduce an approach to establish finiteness results for the set of wave numbers that may lead to vanishing scattering effects. We use this approach to establish two results concerning the two dimensional Helmholtz equation in the context of a penetrable obstacle and (1) incident plane waves as well as (2) incident Herglotz waves. For a smooth, strictly convex, bounded domain, we show that there are at most finitely many positive wave numbers at which a plane wave with a fixed incident direction is nonscattering. For a disk there exist densities such that the corresponding incident Herglotz waves are nonscattering for infinitely many positive wave numbers. Here we show that any small perturbation of the disk to a proper ellipse will lead to at most finitely many such wave numbers.
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Details
- Title
- FINITENESS RESULTS CONCERNING NONSCATTERING WAVE NUMBERS FOR INCIDENT PLANE AND HERGLOTZ WAVES
- Creators
- Michael Vogelius - Rutgers, The State University of New JerseyJingni Xiao - Rutgers Sexual and Reproductive Health and Rights
- Publication Details
- SIAM journal on mathematical analysis, v 53(5), pp 5436-5464
- Publisher
- Siam Publications
- Number of pages
- 29
- Grant note
- DMS-12-11330 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000749346300014
- Scopus ID
- 2-s2.0-85128842983
- Other Identifier
- 991021879785004721
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InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied