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Nonperturbative rates of harmonic generation or frequency mixing and rates of multiphoton ionisation were obtained for atomic hydrogen and for a one-electron model of the negative hydrogen ion, using the Floquet-Sturmian method. The following cases were investigated: elliptically polarised, monochromatic incident field, two-colour incident field with incommensurable frequencies, coherent super position of an incident field and its third harmonic, and superposition of a laser field and a static electric field. For elliptical polarisation, the ellipticity angle of the harmonics differ from the ellipticity of the incident laser and we established that there is an offset angle between the major axis of the incident laser's polarisation ellipse and that of the harmonics generated. The variation is greatest in the plateau region. Resonance-enhanced ionisation was studied when a high frequency field was applied in addition to a fundamental field. In contrast to these changes in the ionisation rate only small variations have been obtained in the harmonic generation rate. Results for frequency-mixing exhibit a difference in the strength of the harmonics, although the behaviour is the same in terms of the length of the plateau and the cut-off order. Also we found a marked change between sum-frequency and difference frequency processes, which depends on the harmonic order. In addition to a strong production of even harmonics, it was found that the variation of the rate of ionisation and harmonic generation in the presence of a static field oscillates as a function of the strength of the latter. In the case of hydrogen, we observed dc-stark shift induced resonance enhancements. The results obtained for H(^-) are in very good agreement with those obtained for two-colour (w, 3w) mixing. We concluded that the application of a static field in general leads to a reduction in the conversion efficiency.

The portion of energy converted by non-linear loads in the modern power system is increasing due to the energy-efficiency and sophistication possible with power electronics. Higher voltage and energy ratings are continuously forthcoming. These devices draw non-linear currents resulting in voltage waveform distortion at the Point of Common Coupling due to non-zero supply impedances between voltage source and the PCC. With the increase in waveform distortion comes the demand for better Quality of Supply management. The verification and quantification of the origin of waveform distortion in a power system is a continuous field of study and forms a critical part of the mitigation design. Methods utilizing single-point measurements, usually taken at the Point of Common Coupling, for the assessment of the harmonic distortion generated by loads are continuously being published. It’s been proven by means of computer simulations and laboratory experiments that in an interconnected network where multiple sources of distortion exist that loads have the ability to exchange harmonic active power between each other. This project investigates the latter statement by conducting practical experiments to conclude that loads have the ability to exchange harmonic active power and that multiple synchronized measurements should be taken to assess the harmonic distortion due to a load. Laboratory experiments are carried utilizing an acknowledged single point measurement method. The results are compared to the direction of harmonic active power obtained from utilizing multiple synchronized measurements. To further the information obtained from the laboratory experiments, practical experiments were conducted utilizing the same methods. The results obtained coincided with the results of previously conducted experiments of which the results were published. From the results obtained it was concluded that in an interconnected network where multiple sources of distortion exist that loads have the ability to exchange harmonic active power between each other. Furthermore it was proven that the single point measurement method investigated presented inconsistent results. Ultimately it was concluded that the reason for the inconsistency was due to the fact that loads have the ability to exchange harmonic active power and that the single point measurement failed to acknowledge this. / Thesis (M.Ing. (Electrical and Electronic Engineering))--North-West University, Potchefstroom Campus, 2012

by Hung Ching Nam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaf 100). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Sobolev spaces of maps into metric space --- p.9 / Chapter 2.1 --- "Lp(Ω,X) spaces" --- p.9 / Chapter 2.2 --- Maps with finite energy --- p.11 / Chapter 2.3 --- Differentiation of maps along a direction --- p.28 / Chapter 2.4 --- Theory of differentiation of maps --- p.35 / Chapter 2.5 --- Trace of maps on Lipschitz domains --- p.48 / Chapter 3 --- Sobolev maps into NPC space --- p.58 / Chapter 3.1 --- NPC space --- p.58 / Chapter 3.2 --- NPC space with curvature bound --- p.69 / Chapter 3.3 --- Sobolev maps into NPC space --- p.71 / Chapter 3.4 --- Tensor inequality for Sobolev maps --- p.77 / Chapter 4 --- Harmonic maps into NPC space --- p.79 / Chapter 4.1 --- Existence and uniqueness of Dirichlet problem --- p.79 / Chapter 4.2 --- Interior Lipschitz continuity of harmonic maps --- p.81 / Chapter 5 --- Equivariant harmonic maps --- p.86 / Chapter 5.1 --- A functional analysis lemma --- p.86 / Chapter 5.2 --- Existence of equivariant harmonic maps --- p.87 / Chapter 5.3 --- Compactification of NPC space --- p.93 / Chapter 5.4 --- Isometric action on CAT(-l) space --- p.96

by Tsui Wai-kwok Ricky. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 58-59). / Abstracts in English and Chinese. / Chapter 1 --- Preliminary --- p.4 / Chapter 1.1 --- Introduction --- p.4 / Chapter 1.2 --- Some basic theorem --- p.7 / Chapter 2 --- Bubble tree Convergence for a sequence of harmonic map --- p.11 / Chapter 3 --- Heat Flow of Harmonic Maps on Riemann Surface --- p.21 / Chapter 3.1 --- Existence of unique solution to the evolution problem --- p.21 / Chapter 3.1.1 --- Some Basic Estimates --- p.22 / Chapter 3.1.2 --- Existence Result --- p.34 / Chapter 3.1.3 --- Behaviour of solutions near singular points --- p.37 / Chapter 3.2 --- Finite time Blow-up --- p.39 / Chapter 3.3 --- Energy Identity --- p.51 / Bibliography --- p.58

Chan Mei Shan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 74-76). / Abstracts in English and Chinese. / Chapter 0 --- Introduction --- p.1 / Chapter 1 --- Preliminary --- p.9 / Chapter 1.1 --- Harmonic maps between Riemann Surfaces --- p.9 / Chapter 1.2 --- "Minkowski 3-spaces, M21" --- p.17 / Chapter 1.3 --- Preliminaries from analysis --- p.21 / Chapter 2 --- Holomorphic quadratic differentials --- p.27 / Chapter 2.1 --- Solution on the Poincare disk D --- p.28 / Chapter 2.2 --- Solution on the complex plane C --- p.37 / Chapter 3 --- Harmonic Diffeomorphisms into H2 --- p.46 / Chapter 3.1 --- The case from D onto D --- p.46 / Chapter 3.2 --- Open harmonic embeddings from C into H --- p.53 / Chapter 4 --- Open harmonic embeddings with polynomial Hopf differentials --- p.57 / Chapter 4.1 --- Proof of the theorem --- p.58 / Chapter 4.2 --- Open harmonic embeddings on C with fixed ideal polygonal images in H2 --- p.65 / Bibliography --- p.74

by Lam Kwan Hang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 75-76). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Maps into locally compact Riemannian complex --- p.8 / Chapter 2.1 --- Exitsence of energy minimizing maps --- p.8 / Chapter 2.2 --- Length minimizing curves --- p.10 / Chapter 3 --- Harmonic maps into nonpositively curved spaces --- p.13 / Chapter 3.1 --- Nonpositively curved spaces --- p.13 / Chapter 3.2 --- Properties of the distance function --- p.16 / Chapter 4 --- Basic properties of harmonic maps into NPC spaces --- p.21 / Chapter 4.1 --- Monotonicity formula --- p.21 / Chapter 4.2 --- Approximately differentiable maps --- p.24 / Chapter 4.3 --- Local properties of harmonic maps --- p.28 / Chapter 5 --- Existence and uniqueness of harmonic maps in a ho- motopy class --- p.33 / Chapter 5.1 --- Convexity properties of the energy functional --- p.33 / Chapter 5.2 --- Existence and Uniqueness Theorem --- p.37 / Chapter 6 --- Homogeneous approximating maps --- p.40 / Chapter 6.1 --- Regular homogeneous map --- p.40 / Chapter 6.2 --- Homogeneous approximating map --- p.46 / Chapter 7 --- More results on regularity --- p.52 / Chapter 7.1 --- Intrinsically differentiable maps --- p.52 / Chapter 7.2 --- Good homogeneous approximating map --- p.62 / Chapter 8 --- Harmonic maps into building-like complexes --- p.65 / Chapter 8.1 --- F-connected complex --- p.65 / Chapter 8.2 --- Regularity and the Bochner technique --- p.66 / Bibliography --- p.75

by Wu Man Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 60-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Harmonic functions with linear growth --- p.3 / Chapter 2.1 --- A sharp estimate for dim H1 (M) --- p.3 / Chapter 2.2 --- Linear growth harmonic functions on Kahler manifolds --- p.8 / Chapter 3 --- Harmonic functions of polynomial growth --- p.21 / Chapter 3.1 --- Harmonic sections of polynomial growth --- p.21 / Chapter 3.2 --- Harmonic functions on manifolds with Sobolev in- equality --- p.34 / Chapter 4 --- Harmonic functions on manifolds with nonnegat --- p.ive / sectional curvature --- p.43 / Bibliography --- p.60