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- W4286905686 abstract "We investigate fixed energy scattering from conical potentials having an irregular cross-section. The incident wave can be any arbitrary non-trivial Herglotz wave. We show that a large number of such local conical scatterers scatter all incident waves, meaning that the far-field will always be non-zero. In essence there are no incident waves for which these potentials would seem transparent at any given energy. We show more specifically that there is a large collection of star-shaped cones whose local geometries always produce a scattered wave. In fact, except for a countable set, all cones from a family of deformations between a circular and a star-shaped cone will always scatter any non-trivial incident Herglotz wave. Our methods are based on the use of spherical harmonics and a deformation argument. We also investigate the related problem for sources. In particular if the support of the source is locally a thin cone, with an arbitrary cross-section, then it will produce a non-zero far-field." @default.
- W4286905686 created "2022-07-25" @default.
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- W4286905686 date "2021-10-12" @default.
- W4286905686 modified "2023-09-26" @default.
- W4286905686 title "Cones with convoluted geometry that always scatter or radiate" @default.
- W4286905686 doi "https://doi.org/10.48550/arxiv.2110.06044" @default.
- W4286905686 hasPublicationYear "2021" @default.
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