Acoustic Scattering from Corners, Edges and Circular Cones

Acoustic Scattering from Corners, Edges and Circular Cones Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions and a planar corner point in two dimensions. The opening angles of cones and edges are allowed to be any number in $${(0,2\pi)\backslash\{\pi\}}$$ ( 0 , 2 π ) \ { π } . We prove that such an obstacle scatters any incoming wave non-trivially (that is, the far field patterns cannot vanish identically), leading to the absence of real non-scattering wavenumbers. Local and global uniqueness results for the inverse problem of recovering the shape of penetrable scatterers are also obtained using a single incoming wave. Our approach relies on the singularity analysis of the inhomogeneous Laplace equation in a cone. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

Acoustic Scattering from Corners, Edges and Circular Cones

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-017-1202-4
Publisher site
See Article on Publisher Site

Abstract

Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions and a planar corner point in two dimensions. The opening angles of cones and edges are allowed to be any number in $${(0,2\pi)\backslash\{\pi\}}$$ ( 0 , 2 π ) \ { π } . We prove that such an obstacle scatters any incoming wave non-trivially (that is, the far field patterns cannot vanish identically), leading to the absence of real non-scattering wavenumbers. Local and global uniqueness results for the inverse problem of recovering the shape of penetrable scatterers are also obtained using a single incoming wave. Our approach relies on the singularity analysis of the inhomogeneous Laplace equation in a cone.

Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Dec 27, 2017

References

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