Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph.D.)--Brown University, 2005. / Vita. Thesis advisor: William A. Curtin. Includes bibliographical references (leaves 153-164). Also available online.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 291-301).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 200-205). Available also in a digital version from Dissertation Abstracts.

The work of this thesis is concerned, with the investigation and attempted improvement of an integral method for solving the two dimensional, incompressible laminar boundary layer equations of fluid dynamics. The method which is based on a theoretical two parameter representation of well-known boundary layer properties was first produced by Professor S. N. Curle. Its range of application, reliability and accuracy rely on four universal functions which have been derived from known exact solutions to the boundary layer equations, and are given tabulated in terms of a pressure gradient parameter λ. This thesis seeks to improve these properties by making adjustments to the tabulated functions and also considers the extension of the method to certain compressible boundary layer problems. The first chapter contains the development of, and background to the method and gives a critical assessment of the existing functions. This analysis indicates that the method may be improved by supplying more data for certain ranges of λ from which the functions may be calculated; by improving the fitting process; and by the provision for small values of λ of an analytic form for a shape parameter H which the method involves. To supply more data two new solutions for the flows u₁ = U₀ (1+ξ) and u₁ = u₀ (ξ+ξ³) where ξ is a non-dimensional co-ordinate in the direction of the flow, are investigated. The resulting work produces some interesting examples of the use of series expansions in boundary layer theory and these, and the results produced, are given in the second chapter. The fitting of the functions is carried out in chapter three. Polynomial models in terms of λ are fitted by least squares techniques to data from seven solutions and are adjusted to ensure an analytic form for H for small values of λ. A comparison of results using new and old tables Indicates that an improvement has been made. The transformation relating certain compressible and incompressible flows is next examined and the extension of the method to such problems considered. An idea due to Stewartson for assessing the relative accuracies of methods under such circumstances indicates that the method should be highly accurate, a result confirmed by the calculation of the compressible flow u₁ = u₀ (1-ξ) at a leading edge Mach number of four. The thesis is concluded with a review of the work carried out and the results obtained.

No description available.

This dissertation investigates the Patient Input Program, the context from which it arose and the struggles that it evokes for rare disease patients. By drawing on the concepts of boundary work, boundary object, public involvement and needs talk, the dissertation explores a local application of patient involvement as a construction of social participation and site where the needs of rare disease patients are contested among the actors, groups and institutions involved in the Health Technology Assessment (HTA) network. A case study approach was chosen to explain the intrinsic aspects of the Patient Input Program, showing the shaping of the Program and its shaping effect on societal agents and knowledge forms, particularly with respect to rare disease patients. Their experience in the Patient Input Program provides insights on the complexities and controversies rooted within the program, and links more broadly to certain system inadequacies.

Doctor of Philosophy / Department of Mathematics / Ivan Blank / In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator L and at any point [chi]₀ in the domain, there exists a nested family of sets { D[subscript]r([chi]₀) } where the average over any of those sets is related to the value of the function at [chi]₀. Although it is known that the { D[subscript]r([chi]₀) } are nested and are comparable to balls in the sense that there exists c, C depending only on L such that B[subscript]cr([chi]₀) ⊂ D[subscript]r([chi]₀) ⊂ B[subscript]Cr([chi]₀) for all r > 0 and [chi]₀ in the domain, otherwise their geometric and topological properties are largely unknown. In this work we begin the study of these topics and we prove a few results about the geometry of these sets and give a couple of applications of the theorems.

No description available.