Thesis (M.S.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; contains xi, 107 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 87-89).

Thesis (Ph. D.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; contains xviii, 224 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 201-208).

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographic references (p.118-121).

No description available.

No description available.

We study Schrödinger operators perturbed by non-compact (spatially extended) defects. We consider two models: a one-dimensional (1D) dimer structure with a global phase shift, and a two-dimensional (2D) honeycomb structure with a line-defect or "edge''. In both the 1D and 2D settings, the non-compact defects are modeled by adiabatic, domain wall modulations of the respective dimer and honeycomb structures. Our main results relate to the rigorous construction of states via bifurcations from continuous spectra. These bifurcations are controlled by asymptotic effective (homogenized) equations that underlie the protected or non-protected character of the states. In 1D, the states we construct are localized solutions. In 2D, they are "edge states'' - time-harmonic solutions which are propagating (plane-wave-like) parallel to a line-defect or "edge'' and are localized transverse to it. The states are described as protected if they persist in the presence of spatially localized (even strong) deformations of the global phase defect (in 1D) or edge (in 2D). The protected states bifurcate from "Dirac points'' (linear/conical spectral band-crossings) in the continuous spectra and are seeded by an effective Dirac equation. The (more conventional) non-protected states bifurcate from spectral band edges are seeded by an effective Schrödinger equation. Our 2D model captures many aspects of the phenomenon of topologically protected edge states observed in honeycomb structures such as graphene and "artificial graphene''. The protected states we construct in our 1D dimer model can be realized as highly robust TM- electromagnetic modes for a class of photonic waveguides with a phase-defect. We present a detailed computational study of an experimentally realizable photonic waveguide array structure.

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No description available.

Thesis (M.S.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on April 9, 2009) Includes bibliographical references.

In the production of iron chromium honeycombs, iron oxide and chromium oxide mixtures are reduced by hydrogen at elevated temperatures to produce a metallic alloy. The complete reduction of the iron oxide occurs prior to the reduction of the chromium oxide. The reduction of the chromium oxide particles within the iron matrix is affected by factors that include the diffusion of the reduced chromium away from the chromium oxide particle into the iron matrix, the diffusion of the gaseous reactants and products to and from the chromium oxide particles, and the porosity of the iron matrix, which changes as a result of sintering. The type of heat-treatment used, (isothermal or non-isothermal, i.e., holding at a specific temperature versus using a steadily increasing temperature) plays a vital role in how these factors will affect chromium oxide reduction. Experimental data were used in conjunction with sintering and dissolution models to obtain an understanding of the environment in which the chromium oxide particles reduce as a function of heat-treatment. This understanding will assist in the development of more effective processing steps for the reduction of metallic honeycombs from oxide mixtures.