Browsing by Author "H. T. Banks, Committee Chair"

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    An Electromagnetic Interrogation Technique Utilizing Pressure-dependent Polarization
    (2002-05-28) Raye, Julie Knowles; Kazufumi Ito, Committee Member; H. T. Banks, Committee Chair; Hien T. Tran, Committee Member; Michael Shearer, Committee Member
    This dissertation focuses on an interrogation technique that uses traveling acoustic wavefronts as a virtual reflector for an oncoming electromagnetic wave. Electromagnetic interrogation techniques in general have the potential for wide applicability in practical problems and this technique in particular enjoys that potential. We begin by developing a viable model for pressure-dependent orientational (Debye) polarization. We then incorporate it into a one-dimensional Maxwell system to describe the electromagnetic/acoustic interaction. This system may be generalized to include a wider class of electromagnetic behavior; we establish well-posedness, enhanced regularity, and convergence results for this general system. Under the framework provided by the mathematical theory, we obtain computational results for sample forward and inverse problems relating to the interrogation technique. Our numerical algorithms for the forward problem involve finite difference approximations in time and finite element approximations with piecewise linear basis elements in space. Solving the inverse problem entails least squares minimization using a gradient-free Nelder Mead optimization routine. Finally, as a first step in developing a model in which the pressure wave may be modulated by the electromagnetic wave (unlike the one-way coupling in the model presented here), we consider the system describing an acoustic wave propagating through a layered medium. We derive a weak formulation for this system and present computational findings.
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    Prediction of Life History Traits in Invertebrate Species Exposed to Pesticide
    (2005-04-25) Dick, Lara Kristen; S. L. Campbell, Committee Member; H. T. Tran, Committee Member; H. T. Banks, Committee Chair
    Due to environmental concerns, newer pesticides are becoming less lethal than older pesticides, thus leaving more survivors behind. Evaluating efficacy of a pesticide now requires more than just counting dead species. A deterministic, age-structured matrix model that incorporates a species' life history traits (such as birth rate, death rate and fecundity) has previously been used by ecologists. This model will be presented and discussed along with the continuous, age-structured model we introduce that involves a least-squares technique used to identify unknown parameters. We also discuss a statistical test used to test significance of additional parameters into our estimation.
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    Sensitivity Methods for Dynamical Systems
    (2008-07-25) Ernstberger, Stacey Leigh; H. T. Banks, Committee Chair; Robert H. Martin, Committee Member; Mansoor A. Haider, Committee Member; Hien T. Tran, Committee Member