The magnetic spherical pendulum is a mechanical system consisting of a pendulum whereof the bob is electrically charged, moving under the influence of gravitation and the magnetic field induced by a magnetic monopole deposited at the origin. Physically not directly realizable, it turns out to be equivalent to a reduction of the Lagrange top. This work is essentially the logbook of our attempts at understanding the simplest contemporary approaches to the magnetic spherical pendulum.

Research Doctorate - Doctor of Philosophy (PhD) / Permeability is an important property that arises in many fields of study. The ability to predict the permeability for a particular material is necessary as it affects the design of many materials handling and storage solutions. There are an abundance of equations that predict permeability for specific applications, but the underlying theory for these equations remains constant. Key factors affecting permeability that appear in many equations are the pore space, individual pore size, and pore connectivity. Many existing equations seek to quantify these factors in some form, with void ratio, particle diameter and tortuosity the most commonly used. Each of these factors is investigated throughout this thesis to further investigate their influence on permeability. These factors are investigated with specific reference to two equations; the Ergun equation and the Kozeny-Carman equation, and with specific reference to two types of materials; spherical particle mixtures and fibrous particle mixtures. Numerical simulation methods are used to build assemblies of spherical and fibrous particles. The assemblies of particles are used to extract fundamental information regarding the pore size and connectivity. The average size of the individual voids can be found as well as the average length the flowing fluid takes through the voids of the material. The use of the simulated assemblies to find material properties such as these allows for new insight into the structure of these types of packed beds. This new insight allows for an improvement in the way permeability is characterised for the materials studied in this thesis.

Thesis--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (p.192-193).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Hamid Garmestani, FAMU-FSU College of Engineering, Dept. of Mechanical Engineering. Title and description from dissertation home page (viewed Sept. 19, 2006). Document formatted into pages; contains xiii, 101 pages. Includes bibliographical references.

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (p. 51).

Clustering text documents is a fundamental task in modern data analysis, requiring approaches which perform well both in terms of solution quality and computational efficiency. Spherical k-means clustering is one approach to address both issues, employing cosine dissimilarities to perform prototype-based partitioning of term weight representations of the documents. This paper presents the theory underlying the standard spherical k-means problem and suitable extensions, and introduces the R extension package skmeans which provides a computational environment for spherical k-means clustering featuring several solvers: a fixed-point and genetic algorithm, and interfaces to two external solvers (CLUTO and Gmeans). Performance of these solvers is investigated by means of a large scale benchmark experiment. (authors' abstract)

Condition monitoring of epicyclic gearboxes through vibration signature analysis, with particular focus on time domain methods and the use of adaptive filtering techniques for the purpose of signal enhancement, is the central theme of this work. Time domain filtering methods for the purpose of removal of random noise components from periodic, but not necessarily stationary or cyclostationary, signals are developed. Damage identification is accomplished through vibration signature analysis by nonstationary timefrequency methods, belonging to Cohen’s general class of time-frequency distributions, strictly based in the time domain. Although a powerful and commonly used noise reduction technique, synchronous averaging requires alternate sensors in addition to the vibration pickup. For this reason the use of time domain techniques that employ only the vibration data is investigated. Adaptive filters may be used to remove random noise from the nonstationary signals considered. The well-known Least Mean Squares algorithm is employed in an adaptive line enhancer configuration. To counter the much discussed convergence difficulties that are often experienced when the least mean squares algorithm is applied, a new unconditionally convergent algorithm based on the spherical quadratic steepest descent method is presented. The spherical quadratic steepest descent method has been shown to be unconditionally convergent when applied to a quadratic objective function. Time-frequency methods are succinctly employed to analyse the vibration signals simultaneously in the time and frequency domains. Transients covering a wide frequency range are a clear and definite indication of impacting events as gear teeth mate, and observation of such events on a timefrequency distribution are used to indicate damage to the transmission. The pseudo Wigner-Ville distribution and the Spectrogram, both belonging to Cohen’s general class of time-frequency distributions are comparatively used to the end of damage identification. It is shown that an unconditionally convergent adaptive filtering technique used in conjunction with time-frequency methods can indicate a damaged condition in an epicyclic gearbox, where the non-adaptively filtered data did not present clear indications of damage. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / MEng / MEng / unrestricted

This thesis will focus on spherical near-field antenna measurements and the methods developed or modified for the work of this thesis to estimate the uncertainty in a particular far-field radiation pattern. We will discuss the need for error assessment in spherical near-field antenna measurements. A procedure will be proposed that, in an automated fashion, can be used to determine the overall uncertainty in the measured far-field radiation pattern of a particular antenna. This overall uncertainty will be the result of a combination of several known sources of error common to SNF measurements. This procedure will consist of several standard SNF measurements, some newly developed tests, and several stages of post-processing of the measured data. The automated procedure will be tested on four antennas of various operating frequencies and directivities to verify its functionality. Finally, total uncertainty data will be presented to the reader in several formats.

Le programme des modèles minimaux (MMP) est l'une des grandes théories développée en géométrie algébrique en vue de classifier les variétés algébriques complexes. Pour certaines familles d'exemples, le MMP est très bien connu. Notamment, pour les variétés toriques et horosphériques, la théorie se résume à une étude assez simple de familles de polytopes, dits polytopes moments, et elle s'étend même à des variétés plus singulières que dans le cas général. Le but de cette thèse est d'étendre ces résultats à des compactifications sphériques d'un groupe. On décrit dans un premier temps ces variétés, et on classifie tous les polytopes moments attachés à de telles compactifications. Puis on démontre que le MMP appliqué sur ces compactifications sphériques se traduit en termes de polytopes moments. Enfin on donne un programme codé en SageMath qui permet de donner les polytopes apparaissant dans le MMP d'une compactification sphérique d'un groupe simple. / The Minimal Model Program (MMP) is one of the greatest theories in Algebraic Geometry developped to classify algebraic varieties. For some families of algebraic varieties, the MMP has been studied in depth. In particular, for toric and horospherical varieties, it comes down to a quite easy study of families of polytopes, called moment polytopes, and it could be adapted to weaker hypothesis of singularities. The goal of this thesis is to show that this reduction can be extended to spherical compactifications of a group. First of all we describe these varieties and classify all moment polytopes of such compactifications. Then we prove that the MMP applied on this spherical compactifications reduces to a study of a families of this moment polytopes. Finaly we give a computer program, coded in SageMath, which gives all polytopes appearing in the MMP of a simple group's spherical compactification.