Cones with convoluted geometry that always scatter or radiate

Abstract We investigate fixed energy scattering from conical potentials having an irregular cross-section. The incident wave can be arbitrary non-trivial Herglotz wave. show that a large number of such local scatterers scatter all waves, meaning the far-field will always non-zero. In essence there are no waves for which these would seem transparent at any given energy. more specifically is collection star-shaped cones whose geometries produce scattered fact, except countable set, family deformations between circular and cone Our methods based on use spherical harmonics deformation argument. also related problem sources. particular if support source locally thin cone, with cross-section, then it non-zero far-field.