Cones with convoluted geometry that always scatter or radiate
Inverse Problems, ISSN: 1361-6420, Vol: 38, Issue: 12
2022
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Article Description
We investigate fixed energy scattering from conical potentials having an irregular cross-section. The incident wave can be an 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.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85140336659&origin=inward; http://dx.doi.org/10.1088/1361-6420/ac963c; https://iopscience.iop.org/article/10.1088/1361-6420/ac963c; https://dx.doi.org/10.1088/1361-6420/ac963c; https://validate.perfdrive.com/fb803c746e9148689b3984a31fccd902/?ssa=bc65d646-458d-4989-bfdd-4a51ddddcfb3&ssb=37853243700&ssc=https%3A%2F%2Fiopscience.iop.org%2Farticle%2F10.1088%2F1361-6420%2Fac963c&ssi=cf365111-8427-4b01-80e1-ff5ab24e68d8&ssk=support@shieldsquare.com&ssm=727198136857206441313890662659523466&ssn=22e81b4cf3da213933134ddabd8ed09b42a2a842bdc0-9b7b-4e59-bc6c10&sso=4a0800fa-9e3578620ac468b2639c0d43ad8bdc7f3cc8b468c8cc7763&ssp=30448357531719955058172055087162252&ssq=27493577652689670887541132912478317704347&ssr=NTIuMy4yMTcuMjU0&sst=com.plumanalytics&ssu=&ssv=&ssw=&ssx=eyJfX3V6bWYiOiI3ZjYwMDBiM2EzMDFlNy1mMjVlLTRkMzktOTQ0Yi1hYjlhOGY0NDkwYzYxNzE5OTQxMTMyNTY0NjM1MzkzOTU0LTJlZDY3NTRhM2I2ODUxNDIxMzEzODMiLCJyZCI6ImlvcC5vcmciLCJ1em14IjoiN2Y5MDAwZWQ3OGYyMmMtODkyYi00NTZhLWFmZTItMzg4OWE4YzkyNDE0OS0xNzE5OTQxMTMyNTY0NjM1MzkzOTU0LWU5ODJkM2JhNjYyOGEyMTQxMzEzODMifQ==
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