Award Date

May 2016

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Dieudonne D. Phanord

Second Committee Member

Amei Amei

Third Committee Member

Rohan J. Dalpatadu

Fourth Committee Member

Diejo Assane

Number of Pages

76

Abstract

This thesis solves the scattering problem in which an acoustic plane wave of propagation number K1 is scattered by a soft prolate spheroid. The interior field of the scatterer is characterized by a propagation number K2, while the field radiated by the scatterer is characterized by the propagation number K3. The three fields and their normal derivatives satisfy boundary conditions at the surface of the scatterer. These boundary conditions involve six complex parameters depending on the propagation numbers. The scattered wave also satisfies the Sommerfeld radiation condition at infinity. Through analytical methods, series representations are constructed for the interior field and scattered field for an arbitrary sphere and a prolate spheroid. In addition, results for the reciprocity relations and Energy theorem are derived. Application to detection of whales and submarines are discussed, as well as classification of fish, squid and zoo plankton. In general Ref[ ] is used for reference and the work is done in three dimensions.

Keywords

brace algebra; energy theorem; propagation; reciprocity relations; Twersky; waves

Disciplines

Acoustics, Dynamics, and Controls | Applied Mathematics | Mathematics

Language

English


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