Thesis (M.S.)--Virginia Polytechnic Institute, 1966. / Vita. Abstract. Includes bibliographical references (leaf 42). Also available via the Internet.

Let Ω be an arbitrary open set in IR³. Let || • || denote the L²(Ω) norm, and let [formula omitted] denote the completion of [formula omitted] in the Dirichlet norm || ∇•||. The pointwise bound [forumula omitted] is established for all functions [formula omitted] with Δ u є L² (Ω). The constant [formula omitted] is shown to be the best possible. Previously, inequalities of this type were proven only for bounded smooth domains or convex domains, with constants depending on the regularity of the boundary. A new method is employed to obtain this sharp inequality. The key idea is to estimate the maximum value of the quotient ⃒u(x)⃒/ || ∇u || ½ || Δ u || ½, where the point x is fixed, and the function u varies in the span of a finite number of eigenfunctions of the Laplacian. This method admits generalizations to other elliptic operators and other domains. The inequality is applied to study the initial-boundary value problem for Burgers' equation: [formula omitted] in arbitrary domains, with initial data in [formula omitted]. New a priori estimates are obtained. Adapting and refining known theory for Navier-Stokes equations, the existence and uniqueness of bounded smooth solutions are established. As corollaries of the inequality and its proof, pointwise bounds are given for eigenfunctions of the Laplacian in terms of the corresponding eigenvalues in two- and three-dimensional domains. / Science, Faculty of / Mathematics, Department of / Graduate

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Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: heterostructure; semiconductor; quantum engineering; self consistency. Includes bibliographical references (p. 30-33).

by Fan Xuqian. / "August 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 84-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Thesis (Ph.D.)--University of Missouri-Columbia, 2005. / 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 (January 25, 2007) Vita. Includes bibliographical references.

The performance of peristaltic pumps is mainly governed by their tubing or hose materials. Research and development in this area is therefore very important for peristaltic pump manufacturers to keep in front of the competition and to open up new applications to enable further market penetration. Another aspect of this is of course price; performance and cost have to be in balance. As an approach to fabricate a new tube material, the field of negative Poisson's ratio (or: auxetic) materials is explored. The combined deformations of tensile, compression and shear in a peristaltic pump tube may well benefit from the specific characteristics of auxetic materials. Materials can be designed to keep their dimensions constant in directions perpendicular to an applied load. This is referred to as “auxetic balancing”. Finite element modelling shows that lowering the Poisson's ratio will rapidly decrease the maximum stresses in the cross-section of an occluded tube. Optimum values for the Poisson's ratio are found to be between −0.1 and +0.1, preferentially being 0. The re-entrant honeycomb structure is selected for initial trials, but manufacturing of this structure at the desired dimension proved to be too difficult at this time. Instead, electrospun nanofibre membranes are selected as the reinforcement structure. A liquid silicone elastomer is used as the matrix material. Key characteristics for the new material are derived from baseline test results on existing tubing. Laminates are manufactured from electrospun nylon6 nanofibre membranes coated with a liquid silicone rubber. Compression moulding is used to cure the nylon6-silicone rubber laminate, to give two effects: it ensures impregnation of the membrane and the compression deforms the nanofibre structure in such a way that it will become auxetic through-the-thickness. Flat sheet laminates of 2 mm thickness are manufactured with 14 layers of reinforcement. A reinforcing effect and substantial lowering of the through-the-thickness Poisson's ratio is observed for the laminates at low strains. At higher strains (>50%) the effect of the reinforcement diminishes and the Poisson's ratio of the laminate and pure silicone rubber equalises. Finally, tubular laminates are manufactured and the resulting tubes are tested in a peristaltic pump with some promising results (>1 million occlusions before failure). Tube performance is not yet at the required level, but with further optimisation of the laminating process, mould design and (post-)curing large steps forward can be made.

Thesis (Ph. D.)--Michigan State University. Applied Mathematics, 2008. / Title from PDF t.p. (viewed on July 8, 2009) Includes bibliographical references (p. 123-131). Also issued in print.

Yes / The Poisson's equation is an essential entity of applied mathematics for modelling many phenomena of importance. They include the theory of gravitation, electromagnetism, fluid flows and geometric design. In this regard, finding efficient solution methods for the Poisson's equation is a significant problem that requires addressing. In this paper, we show how it is possible to generate approximate solutions of the Poisson's equation subject to various boundary conditions. We make use of the discrete finite difference operator, which, in many ways, is similar to the standard finite difference method for numerically solving partial differential equations. Our approach is based upon the Laplacian averaging operator which, as we show, can be elegantly applied over many folds in a computationally efficient manner to obtain a close approximation to the solution of the equation at hand. We compare our method by way of examples with the solutions arising from the analytic variants as well as the numerical variants of the Poisson's equation subject to a given set of boundary conditions. Thus, we show that our method, though simple to implement yet computationally very efficient, is powerful enough to generate approximate solutions of the Poisson's equation. / Supported by the European Union’s Horizon 2020 Programme H2020-MSCA-RISE-2017, under the project PDE-GIR with grant number 778035.

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