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published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

One of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which, the Wang and Yau quasi-local energy has yet to be explored. In this region, the results of this thesis indicate that the Wang and Yau quasi-local energy yields complex values and is essentially equivalent to the previously defined Brown and York quasi-local energy. However, an application of their quasi-local mass is suggested in a dynamical setting, which can potentially give new and meaningful measures. In supporting this thesis, the development of a novel adiabatic isometric mapping algorithm is included. Its purpose is to provide the isometric embedding of convex 2-surfaces with spherical topology into Euclidean 3-space necessary for completing the calculation of quasilocal energy in numerical relativity codes. The innovation of this algorithm is the guided adiabatic pull- back routine. This uses Ricci flow and Newtons method to give isometric embeddings of piecewise simplicial 2-manifolds, which allows the algorithm to provide accuracy of the edge lengths up to a user set tolerance. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

This work focuses on the development of a highly accurate energy-based hysteresismodel for the modeling of magnetic hysteresis phenomena. The model relies on anexplicit representation of the magnetic pinning effect as a dry friction-like force actingon the magnetic polarization. Unlike Preisach and Jiles-Atherton models, this modelis vectorial from the beginning and derives from thermodynamic first principles.Three approaches are considered: the first one, called vector play model, relies on asimplification that allows an explicit, and thus fast, update rule, while the two others,called the variational and the differential approaches, avoid this simplification,but require a non-linear equation to be solved iteratively. The vector play model andthe variational approach were already used by other researchers, whereas the differentialapproach introduced in this thesis, is a new, more efficient, exact implementation,which combines the efficiency of the vector play model with the accuracy of the variationalapproach. The three hysteresis implementations lead to the same result forpurely unidirectional or rotational excitation cases, and give a rather good approximationin all situations in-between, at least in isotropic material conditions.These hysteresis modeling approaches are incorporated into a finite-element code asa local constitutive relation with memory effect. The inclusion is investigated in detailfor two complementary finite-element formulations, magnetic field h or flux densityb conforming, the latter requiring the inversion of the vector hysteresis model,naturally driven by h, for which the Newton-Raphson method is used. Then, at thefinite-element level, once again, the Newton-Raphson technique is adopted to solvethe nonlinear finite-element equations, leading to the emergence of discontinuous differentialreluctivity and permeability tensors, requiring a relaxation technique in theNewton-Raphson scheme. To the best of the author’s knowledge, the inclusion of anenergy-based hysteresis model has never been successfully achieved in a b-conformfinite-element formulation before. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

In many digital signal processing applications, we often need some special function units which can compute complicated arithmetic functions such as reciprocal and logarithm. Conventionally, table-based arithmetic design strategy uses lookup tables to implement these kinds of function units. However, the table size will increase exponentially with respect to the required precision. In this thesis, we propose two methods to reduce the table size: bottom-up non-uniform segmentation and the approach which merges uniform piecewise interpolation and Newton-Raphson method. Experimental results show that we obtain significant table sizes reduction in most cases.

In this thesis, an efficiency method for reducing the rotation ROM size in table-based architecture is proposed. The original rotation can be divided into two stages, coarse stage and fine stage. Our approach modifies the previous two-stage rotation method and proposes a multi-stage architecture and discuses three-stage phase calculation. The effect of table reduction is more apparently for higher accuracy requirement in the three-stage architecture. The total area of the previous two-stage architecture is larger than the proposed table-reduced three-stage architecture because the table size takes a significant ratio of the total area especially when the required bit accuracy is large. In the proposed three-stage design, there are two different types of architectures, depending on the rotation angles in the first and second rotation stages. Comparison of different types of architecture with the previous method shows that our designs indeed reduce the table size and the total area significantly.

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Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2007. / "May, 2007." Title from electronic thesis title page (viewed 4/28/2009) Advisor, Ali Hajjafar; Faculty readers, Linda Marie Saliga, Lala Krishna; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. Description based on print version record. Includes bibliographical references (p. 185-187).