Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

In recent years, considerable attention has been focused on the application of orthogonal expansions to system analysis, parameter identification, model reduction and control system design. However, little research has been done in applying their useful properties to Power System analysis and control. This research attempts to make some inroads in applying the so called " orthogonal expansion approach " to analysis and control of Power systems, especially the latter. A set of orthogonal functions commonly called Walsh functions in system science after it's discoverer J.L. Walsh [1923] have been successfully used for parameter identification in the presence of severe nonlinearities. The classical optimal control problem is applied to a synchronous machine infinite bus system via the orthogonal expansion approach and a convenient method outlined for designing PID controllers which can achieve prespecified closed loop response characteristics. The latter is then applied for designing a dynamic series capacitor controller for a single machine infinite bus system. / Graduation date: 1993

Thesis (Ph. D.)--University of Washington. / Includes bibliographies.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 124-130). Also available in electronic version. Access restricted to campus users.

Introduction. Statement of problem: The primary purpose of this study is to indicate the manner in which a Boundary Value problem in Physics leads to the solution in generalized Fourier Series. The conditions to be met in problems of this sort are generally the Partial Differential Equation and several unique physical conditions which are imposed on the distribution sought after. The problem is solved when a mathematical solution of the Differential Equation is found which satisfies all of the restrictions levied by the physical considerations. The secondary purpose of this study is to obtain a view of the generalized problem which leads ultimately to the Sturm-Liouville theory.

The Givens orthogonalization algorithm is an efficient alternative to the normal equations method for solving many adjustment problems in photogrammetry. The Givens method is one of a class of methods for solving linear systems known generally as orthogonalization or QR methods. It allows for sequential processing and greatly simplifies the computation of statistics on the observations and residuals. The underlying reason for these advantages is the immediate availability of the orthogonal Q matrix, which is computed as the data are processed and is intimately related to the statistics needed for blunder detection. One of these statistics, the F statistic computed from externally studentized residuals, is both easily obtained and well-suited for blunder detection. The Givens method requires nearly four times the number of computations as compared to the normal equations approach in order to reach a solution. However, depending on the size of the problem, blunder detection through the normal equations requires far more computer time than is required when starting with a Givens decomposition. The method allows a user to review intermediate results, test residuals and modify the solution without having to compute a full solution. Adjustments of a level net and a single-photo resection are used to demonstrate the method. Because of the advantage in computational time, the Givens method is superior to the normal equations approach when rigorous blunder detection is required. / Master of Science

Since an extratropical transition (ET) of a decaying tropical cyclone (TC) often results in a fast-moving, rapidly developing extratropical cyclone and amplification of synoptic-scale systems far downstream, proper forecasting of ET events is critical to forecast accuracy over large ocean regions. Past studies have linked forecast accuracy to the phasing of a decaying TC with favorable midlatitudes conditions. Because ET events are sensitive to the analyzed initial conditions, this phasing is examined using 11 member ensemble predictions available four times daily from the National Centers for Environmental Prediction, which were combined into a single 44 member ensemble based on a common forecast verification time. Recurring ET patterns within the 44 member ensemble were objectively identified using a combination of EOF and cluster analysis. Ensemble spread first appears near the point where the TC moves into the midlatitudes and then propagates downstream. Although ensemble spread in the forecast fields was large at extended forecast intervals, the ensemble spread, and the number of ET patterns identified in successive EPS predictions, decreased as the ET process became better defined. Within 48 hours of the ET event, the ensemble prediction system properly identified the ET pattern with a minimum ensemble spread. Similar to Klein et al. (2002), the shifts in the initial position of the TC and the subsequent dynamical coupling can explain differences between weak and strong ET reintensifications.

In this thesis we focus on two problems. First we propose a numerical method for generating optimized Wannier functions with desired properties. Second we perform the state of the art density functional plus dynamical mean-field calculations in pyrochlore iridates, to investigate the physics induced by the cooperation of spin-orbit coupling and electron correlation. We begin with the introduction for maximally localized Wannier functions and other related extensions. Then we describe the current research in the field of spin-orbit coupling and its interplay with correlation effects, followed by a brief introduction of the `hot' materials of iridates. Before the end of the introduction, we discuss the numerical methods employed in our work, including the density functional theory; dynamical mean-field theory and its combination with the exact diagonalization impurity solver. Then we propose our approach for constructing an optimized set of Wannier functions, which is a generalization of the functionality of the classic maximal localization method put forward by Marzari and Vanderbilt. Our work is motivated by the requirement of the effective description of the local subspace of the Hamiltonian by the beyond density functional theory methods. In extensions of density functional theory such as dynamical mean-field theory, one may want highly accurate description of particular local orbitals, including correct centers and symmetries; while the basis for the remaining degrees of freedom is unimportant. Therefore, we develop the selectively localized Wannier function approach which allows for a greater localization in the selected subset of Wannier functions and at the same time allows us to fix the centers and ensure the point symmetries. Applications in real materials are presented to demonstrate the power of our approach. Next we move to the investigation of pyrochlore iridates, focussing on the metal-insulator transition and material dependence in these compounds. We perform combined density functional plus dynamical mean-field calculations in Lu$_2$Ir$_2$O$_7$, Y$_2$Ir$_2$O$_7$, Eu$_2$Ir$_2$O$_7$, with spin-orbit coupling included and both single-site and cluster approximations appiled. A broad range of Weyl metal is predicted as the intervening phase in the metal-insulator transition. By comparing to experiments, we find that the single-site approximation fails to predict the gap values and substantial difference between the Y and Eu-compound, demonstrating the inadequacy of this approximation and indicating the key role played by the intersite effects. Finally, we provide a more accurate description of the vicinity of the metal-insulator and topological transitions implied by density functional plus cluster dynamical mean-field calculations of pyrochlore iridates. We find definitive evidence of the Weyl semimetal phase, the electronic structure of which can be approximately described as ``Weyl rings" with an extremely flat dispersion of one of the Weyl bands. This Weyl semimetal phase is further investigated by the $k\cdot p$ analysis fitting to the numerical results. We find that this unusual structure leads to interesting behavior in the optical conductivity including a Hall effect in the interband component, and to an enhanced susceptibility.

University of Macau / Faculty of Science and Technology / Department of Mathematics