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Journal article
EXAMPLES OF NON-SCATTERING INHOMOGENEITIES
Inverse problems and imaging (Springfield, Mo.)
01 Jan 2025
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencies exist, i.e., for which at some frequencies there are incident fields which produce null scattered fields outside of the inhomogeneity. We show in particular that certain domains with corners or even cusps can support non-scattering frequencies. We relate the latter, for some inclusions, to resonance frequencies for Dirichlet or Neumann cavities. We also find situations where incident non-scattering fields solve the Helmholtz equation in a neighbourhood of the inhomogeneity and not in the whole space. In relation with invisibility, we give examples of inclusions of anisotropic materials which are non-scattering for all real frequencies. We prove that corresponding material indices must have a special structure on the boundary.
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Details
- Title
- EXAMPLES OF NON-SCATTERING INHOMOGENEITIES
- Creators
- Lucas Chesnel - Universidade da MadeiraHoussem Haddar - École Nationale Supérieure de Techniques AvancéesHongjie Li - Tsinghua UniversityJingni Xiao - Drexel University
- Publication Details
- Inverse problems and imaging (Springfield, Mo.)
- Publisher
- Amer Inst Mathematical Sciences-Aims
- Number of pages
- 25
- Grant note
- 12401561 / NSFC; National Natural Science Foundation of China (NSFC) DMS-2307737 / NSF; National Science Foundation (NSF) 5333100432 / Research Start Fund
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001405965700001
- Scopus ID
- 2-s2.0-105006674700
- Other Identifier
- 991022024210404721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical