Unique determination of acoustic properties from thermoacoustic data Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/ft848s492

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  • The extent to which thermoacoustic data determines the acoustic properties of an object was studied. In the case of one dimensional thermoacoustic imaging it was shown that constant acoustic profiles are uniquely specified from measurements. For a radial thermoacoustic problem we have shown that if the acoustic source is radial then constant acoustic speeds are uniquely determined from the data. The case of a radial thermoacoustic setup with a non-radial source was investigated. It was shown that constant acoustic profiles are uniquely determined within a special class of radial acoustic speeds. An investigation of the interior transmission problem was carried out. A variational form for this problem was found for a new class of refractive indexes, existence of an infinite discrete set of transmission eigenvalues was established. The study of the unique determination of the acoustic profiles used a relation between data generated from two distinct sound speeds and the spectrum of the transmission problem. The general transmission problem with a new class of refractive indexes was analyzed using Hardy's inequality. Results in the one dimensional and radial cases relate the transmission spectrum to the spectrum of an eigenvalue problem associated to a system of Sturm-Liouville equations. Asymptotic expansions of solutions to the Sturm-Liouville equations were used, together with a special boundary condition, to study this spectrum and derive the uniqueness results.
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