The main subject of this thesis is solitons due to degenerate parametric four-wave mixing. Derivation of the governing equations is carried out for both spatial solitons (slab waveguide) and temporal solitons (optical fibre). Higher-order effects that are ignored in the standard paraxial approximation are discussed and estimated. Detailed analysis of conventional solitons is carried out. This includes discovery of various solitons families, linear stability analysis of fundamental and higher-order solitons, development of theory describing nonlinear dynamics of higher-order solitons. The major findings related to the stationary problem are bifurcation of a two-frequency soliton family from an asymptotic family of infinitely separated one-frequency solitons, jump bifurcation and violation of the bound state principle. Linear stability analysis shows a rich variety of internal modes of the fundamental solitons and existence of a stability window for higher-order solitons. Theory for nonlinear dynamics of higher-order solitons successfully predicts the position and size of the stability window, and various instability scenarios. Equivalence between direct asymptotic approach and invariant based approach is demonstrated. A general analytic approach for description of localised solutions that are in resonance with linear waves (quasi-solitons and embedded solitons) is given. This includes normal form theory and approximation of interacting particles. The main results are an expression for the amplitude of the radiating tail of a quasi-soliton, and a two-fold criterion for existence of embedded solitons. Influence of nonparaxiality on soliton stability is investigated. Stationary instability threshold is derived. The major results are shift and decreasing of the size of the stability window for higher-order solitons. The latter is the first demonstration of the destabilizing influence of nonparaxiality on higher-order solitons. Analysis of different aspects of solitons is based on universal approaches and methods. This includes Hamiltonian formalism, consideration of symmetry properties of the model, development of asymptotic models, construction of perturbation theory, application of general theorems etc. Thus, the results obtained can be extended beyond the particular model of degenerate four-wave mixing. All theoretical predictions are in good agreement with the results of direct numerical modeling.

Cubic boron nitride (c-BN) has been in focus for several years due to its interesting properties. The possibility for large area chemical vapor deposition (CVD) is a requirement for the realization of these different properties in various applications. Unfortunately, there are at present severe problems in the CVD growth of c-BN. The purpose with this research project has been to theoretically investigate, using density functional theory (DFT) calculations, the possibility for a layer-by-layer CVD growth of c-BN.  The results, in addition with experimental work by Zhang et al.57,  indicate that plasma-enhanced atomic layer deposition (PEALD), using a BF3-H2-NH3-F2 pulse cycle and a diamond substrate, is a promising method for deposition of c-BN films. The gaseous species will decompose in the plasma and form BFx, H, NHx, and F species (x = 0, 1, 2, 3). The H and F radicals will uphold the cubic structure by completely hydrogenate, or fluorinate, the growing surface. Surface radical sites will appear during the growth process as a result of atomic H, or F, abstraction reactions. However, introduction of energy (e.g., ionic bombardment) is probably necessary to promote removal of H from the surface. The addition of NHx growth species (x = 0, 1, 2) to the B radical sites, and BFx growth species (x = 0, 1, 2) to N radical sites, will then result in a continuous growth of c-BN.

No description available.

Transmissivity (T) and Hydraulic apertures are often calculated from hydraulic test data obtained in fractured rock using analytical solutions such as the Thiem and cubic law equations developed for flow through unconsolidated porous media. These analytical solutions use a variety of simplifying assumptions, which are often violated due to the complex nature of flow through fractured rock systems which introduces error into the calculated hydraulic apertures. A 3-D discrete fracture network numerical model (SMOKER) for flow in dual-permeability media was used to simulate constant-head straddle packer tests to assess the errors in fracture characterization that result from deviations from the Thiem and cubic law assumptions caused by permeable rock matrix, variable aperture fractures, and complex flow patterns. The simulations indicate that SMOKER offers potential as a useful tool for representing non-ideal scenarios of rock and fracture network characteristics to assist in estimates and error analysis in T values and resultant errors in hydraulic aperture. / NSERC: Natural Sciences and Engineering Research Council of Canada

A family of oxygen-deficient perovskite phases with compositions, Ca₂Mn_2-xNb_xO_γ has been synthesised and characterised using X-ray Powder Diffraction and Thermogravimetry. Property characterisation has included the study of electrical properties by Impedance Spectroscopy and the investigation of magnetic properties for one composition, x = 1.0. Some compositions were tested for possible application as electrode materials in gas sensors. The Ca₂Mn_2-xNb_xO_γ system 0 ≤ x ≤ 1.2, with variable oxygen content, γ, can accommodate up to 20% vacancies at oxygen sites and Mn occurs in valence states ranging from +2 to +4. Depending on the B-cation ratio and oxygen content, two solid solution form: an extensive GdFeO₃-type solid solution over the entire range of cation content, 0 ≤ x ≤ 1.2, with zero or small oxygen deficiencies and a closely-related, grossly oxygen-deficient solid solution over the range 0.3 ≤ x ≤ 0.8 with a simple cubic perovskite structure. Unit cell volume and orthorhombic GdFeO₃-type distortion vary greatly with Mn valency, oxygen content and B-cation content. The orthorhombic GdFeO₃-type structure of composition x = 1.0 was refined by the Rietveld method. Mn and Nb are disordered over the B-sites. Jahn-Teller activity of Mn³⁺ does not result in cooperative distortions of (Mn,Nb)O₆ octahedra, but it was observed to effect the oxygen stoichiometry. The Nb-rich composition, x = 1.0, can accommodate large amounts of Ca-vacancies (up to 10%). Electrical conductivity varies greatly with the composition. Results suggest that t_2g electrons are responsible for a variation of conductivity and activation energy rather than e_g electrons. Conductivities are believed to depend mainly on the degree of π-orbital overlap between Mn and oxygen and hence, on interatomic distances. At low temperatures, the material exhibits spin glass-like behaviour.

In this diploma work, two versions of the discrete nonlinear Schrödinger (DNLS) equation are used to model a nonlinear layered photonic crystal system; the cubic DNLS (cDNLS) equation and the saturable DNLS (sDNLS) equation. They both have site-dependent coefficients to break mirror symmetry with respect to propagation direction, as well as to describe the linear and nonlinear properties of the system. Analytical solutions taking on plane wave form are, via the backward transfer map, used to derive a transmission coefficient as well as a rectifying factor to quantify the diode effect. The effect of varying site-dependent coefficients is studied in detail. Numerical simulations of Gaussian wave packets impinging on the system, using open boundary conditions, show the breaking of parity symmetry. Evidence of a change in the wave packet dynamics occurring in the transition between the cubic and the saturable DNLS model is presented. A saturated system prevents the wave packet from getting stuck in the nonlinear lattice layers. The transmission properties were found to be very sensitive to slight changes of the system parameters.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 41-42). Also available via the Internet.

Thesis (Ph. D.)--University of Alberta, 2010. / Title from pdf file main screen (viewed on July 13, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta. Includes bibliographical references.

This research has been conducted in order to develop a short-range ensemble numerical weather prediction system over southern Africa using the Conformal-Cubic Atmospheric Model (CCAM). An ensemble prediction system (EPS) combines several individual weather model setups into an average forecast system where each member contributes to the final weather forecast. Four different EPSs were configured and rainfall forecasts simulated for seven days ahead for the summer months of January and February, 2009 and 2010, for high (15 km) and low (50 km) resolution over the southern African domain. Statistical analysis was performed on the forecasts so as to determine which EPS was the most skilful at simulating rainfall. Measurements that were used to determine the skill of the EPSs were: reliability diagrams, relative operating characteristics, the Brier skill score and the root mean square error. The results show that the largest ensemble is consistently the most skilful for all forecasts for both the high and the low resolution cases. The higher resolution forecasts were also seen to be more skilful than the forecasts made at the low resolution. These findings conclude that the largest ensemble at high resolution is the best system to predict rainfall over southern Africa using the CCAM. / Dissertation (MSc)--University of Pretoria, 2014. / gm2014 / Geography, Geoinformatics and Meteorology / unrestricted

Open file dissertation.pdf to read abstract / Dissertation (MSc)--University of Pretoria, 2007. / Geography, Geoinformatics and Meteorology / Unrestricted