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Interval exchange transformations: Applications of Keane's construction and disjointness
This thesis is divided into two parts. The first part uses a family of Interval Exchange Transformations constructed by Michael Keane to show that IETs can have some particular behavior including: (1) IETs can be topologically ...
Spectral Properties of Limit-Periodic Schrodinger Operators
We investigate spectral properties of limit-periodic SchrÃ¶dinger operators in [cursive l] 2 ([Special characters omitted.] ). Our goal is to exhibit as rich a spectral picture as possible. We regard limit-periodic potentials ...
Optimization of shell structure acoustics
This thesis analyzes a mathematical model for shell structure acoustics, and develops and implements the adjoint equations for this model. The adjoint equations allow the computation of derivatives with respect to large ...
Ritz values and Arnoldi convergence for non-Hermitian matrices
This thesis develops ways of localizing the Ritz values of non-Hermitian matrices. The restarted Arnoldi method with exact shifts, useful for determining a few desired eigenvalues of a matrix, employs Ritz values to refine ...
Complex flow and transport phenomena in porous media
This thesis analyzes partial differential equations related to the coupled surface and subsurface flows and develops efficient high order discontinuous Galerkin (DG) methods to solve them numerically. Specifically, the ...