The study aims to generate a simulated, ultra high-resolution climatology over the southwestern Cape of South Africa, and in particular the Stellenbosch wine producing region, by the dynamical downscaling of observed synoptic-scale circulation. A variable-resolution global model, the conformal-cubic atmospheric model (CCAM), and a multiple-nudging strategy are applied in order to reach this goal. CCAM is employed in stretched-grid mode as a regional climate model (RCM) to simulate climate for the period 1976-2005 at four different spatial resolutions. Nudging from coarse-resoltion (2.5° in latitude and longitude), the model was first applied at a 60 km resolution over southern Africa in order to obtain a simulation of the synoptic-scale circulation over the region. Two higher resolution simulations, at 8 km and 1 km resolution, were obtained consecutively over the western and southwestern Cape, nudging from the 60 km and 8 km simulations, respectively. Finally, a 200 m simulation was performed over the Stellenbosch region. Because of the high computational requirements of high-resolution runs, each progressively higher resolution simulation is performed over a progressively smaller area of interest over which the spatial resolution is high. The simulations verify well against observed datasets, and generally capture the important climatic features over the area of interest. The 60 km CCAM simulation gives a good representation of the synoptic scale weather over southern Africa, with realistic seasonal circulation patterns and rainfall percentages as well as intra-annual rainfall totals over various regions. The mesoscale climate over the Western Cape of South Africa is captured by the 8 km simulation, especially with respect to seasonal variations in temperature and rainfall percentages - although the actual rainfall over the southwestern tip of the Western Cape is severely underestimated. The ultra high-resolution simulated diurnal cycle of temperature, relative humidity and screen level wind speed compared well against observations for the month of February. The CCAM climate simulations might not be accurate enough for some of the very sensitive studies of the wine industry, but it can have great value for the demarcation of areas which are climatically suited for viticulture and some more general viticultural studies. Ultra high-resolution climate parameter maps are presented for 1976-2005. / Dissertation (MSc)--University of Pretoria, 2009. / Geography, Geoinformatics and Meteorology / Unrestricted

Knowledge regarding carbon dioxide (CO2)-brine interfacial tension (IFT) is important for petroleum industry and Carbon Capture and Storage (CCS) strategies. In petroleum industry, CO2-brine IFT is especially importance for CO2 – based enhanced oil recovery strategy as it affects phase behavior and fluid transport in porous media. CCS which involves storing CO2 in geological storage sites also requires understanding regarding CO2-brine IFT as this parameter affects CO2 quantity that could be securely stored in the storage site. Several methods have been used to compute CO2-brine interfacial tension. One of the methods employed is by using Density Gradient Theory (DGT) approach. In DGT model, IFT is computed based on the component density distribution across the interface. However, current model is only applicable for modelling low to medium ionic strength solution. This limitation is due to the model only considers the increase of IFT due to the changes of bulk phases properties and does not account for ion distribution at interface. In this study, a new modelling strategy to compute CO2-brine IFT based on DGT was proposed. In the proposed model, ion distribution across interface was accounted for by separating the interface to two sections. The saddle point of tangent plane distance where ( ) was defined as the boundary separating the two sections of the interface. Electrolyte is assumed to be present only in the second section which is connected to the bulk liquid phase side. Numerical simulations were performed using the proposed approach for single and mixed salt solutions for three salts (NaCl, KCl, and CaCl2), for temperature (298 K to 443 K), pressure (2 MPa to 70 MPa), and ionic strength (0.085 mol·kg-1 to 15 mol·kg-1). The simulation result shows that the tuned model was able to predict with good accuracy CO2-brine IFT for all studied cases. Comparison with current DGT model showed that the proposed approach yields better match with the experiment data. In this study, the thermodynamic properties were computed using Cubic Plus Association (CPA) equation of state, and the electrolyte contribution was accounted for by adding Debye-Huckel activity coefficient in the thermodynamic properties computation.

Philosophiae Doctor - PhD / The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problems regarding the uncolourability of cubic graphs, centering around these parameters. We introduce new ideas regarding the structural complexity of these graphs in question. In particular, we consider their 3-critical subgraphs, speci cally in relation to resistance. We further introduce new parameters which measure the uncolourability of cubic graphs, speci cally relating to their 3-critical subgraphs and various types of cubic graph reductions. This is also done with a view to identifying further problems of interest. This thesis also presents solutions and partial solutions to long-standing open conjectures relating in particular to oddness, weak oddness and resistance.

The (BMN) bulk materials were sintered at 1050°C, 1100°C, 1150°C, 1200°C by the conventional ceramic process, and their microstructure and dielectric properties were investigated by Scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectroscopy, Transmission electron microscopy (TEM) (including the X-ray energy dispersive spectrometry EDS and high resolution transmission electron microscopy HRTEM) and dielectric impedance analyzer. We systematically investigated the structure, dielectric properties and voltage tunable property of the ceramics prepared at different sintering temperatures. The XRD patterns demonstrated that the synthesized BMN solid solutions had cubic phase pyrochlore-type structure when sintered at 1050°C or higher, and the lattice parameter (a) of the unit cell in BMN solid solution was calculated to be about 10.56Å. The vibrational peaks observed in the Raman spectra of BMN solid solutions also confirmed the cubic phase pyrochlore-type structure of the synthesized BMN. According to the Scanning Electron Microscope (SEM) images, the grain size increased with increasing sintering temperature. Additionally, it was shown that the densities of the BMN ceramic tablets vary with sintering temperature. The calculated theoretical density for the BMN ceramic tablets sintered at different temperatures is about 6.7521 . The density of the respective measured tablets is usually amounting more than 91% and 5 approaching a maximum value of 96.5% for sintering temperature of 1150°C. The microstructure was investigated by using Scanning Transmission Electron Microscope (STEM), X-ray diffraction (XRD). Combined with the results obtained from the STEM and XRD, the impact of sintering temperature on the macroscopic and microscopic structure was discussed. The relative dielectric constant ( ) and dielectric loss ( ) of the BMN solid solutions were measured to be 161-200 and (at room temperature and 100Hz-1MHz), respectively. The BMN solid solutions have relative high dielectric constant and low dielectric loss. With increasing sintering temperature, the dielectric constant showed the maximum at 1150°C. The leakage current of BMN ceramic material is extraordinary small. When the voltage and thickness of the BMN capacitor are 4000V and 300um, the leakage current amounts only about 0.13-0.65 . The excellent physical and electrical properties make BMN thin films promising for potential tunable capacitor applications.

A cubic lattice with random parameters is reduced to a linear chain by the means of the projection technique. The continued fraction expansion (c.f.e.) approach is herein applied to the density of states. Coefficients of the c.f.e. are obtained numerically by the recursion procedure. Properties of the non-stationary second moments (correlations and dispersions) of their distribution are studied in a connection with the other evidences of transport in a one-dimensional Mori chain. The second moments and the spectral density are computed for the various degrees of disorder in the prototype lattice. The possible directions of the further development are outlined. The physical problem that is addressed in the dissertation is the possibility of the existence of a non-Anderson disorder of a specific type. More precisely, this type of a disorder in the one-dimensional case would result in a positive localization threshold. A specific type of such non-Anderson disorder was obtained by adopting a transformation procedure which assigns to the matrix expressing the physics of the multidimensional crystal a tridiagonal Hamiltonian. This Hamiltonian is then assigned to an equivalent one-dimensional tight-binding model. One of the benefits of this approach is that we are guaranteed to obtain a linear crystal with a positive localization threshold. The reason for this is the existence of a threshold in a prototype sample. The resulting linear model is found to be characterized by a correlated and a nonstationary disorder. The existence of such special disorder is associated with the absence of Anderson localization in specially constructed one-dimensional lattices, when the noise intensity is below the non-zero critical value. This work is an important step towards isolating the general properties of a non-Anderson noise. This gives a basis for understanding of the insulator to metal transition in a linear crystal with a subcritical noise.

Cubic carbides (titanium, tantalum, niobium, and zirconium carbides) can constitute a significant proportion of so-called cubic and cermet grades, where it is added to substitute a portion of tungsten carbide. It is thus critical to understand and be able to thermodynamically model the cubic carbide systems. In order to do this, the thermodynamic descriptions of lower order systems, such as the Ti-Cr-C system, need to be well studied. To approach this goal, an extensive literature survey of thermodynamic data and phase diagram information on the Ti-Cr-C system, the Ta-Cr-C system, the Nb-Cr-C system and the Zr-Cr-C is presented in this work. Experiments are performed in the Ti-Cr-C system using powder metallurgy and heat treatments. The solubility of Cr in FCC_TiC phase was experimentally measured at 1773K and compared with previous studies showing that the solubility reported earlier is too large. Thereafter, a re-optimization of FCC_TiC and liquid interaction parameters of the Ti-Cr-C system was performed taking into account the experimental data obtained both from previous studies and this work. The Gibbs energy descriptions of the Cr-carbide end members were compared between the one from the in-house database [SandvikTDB] and from other studies. With the new description, the solubility of Cr in FCC_TiC is better described.

Equations of the form 𝑎𝑥³ + 𝑏𝑦³ = 1, where the constants 𝑎 and 𝑏 are integers of some number field such that 𝑎𝑥³ + 𝑏𝑦³ is irreducible, are a particularly significant class of cubic Thue equations that notably includes the cubic Pell equation. For a positive cubefree rational integer 𝑑, we consider the family of equations of the form 𝑚𝑥³ − 𝑑𝑛𝑦³ = 1 where 𝑚 and 𝑛 are squarefree. We define an 𝐿-function associated to 𝑑 whose nonvanishing coefficients correspond to the nontrivial solutions of those equations. That definition uses expressions related to the cubic theta function Q (􏰇√ 􏰈-), and we study that 𝐿-function’s analytic properties by using a method generalizing the approach used by Takhtajan and Vinogradov to derive a trace formula using the quadratic theta function for Q. We construct its meromorphic continuation and determine the locations and orders of its poles. Specifically, the poles occur at the eigenvalues of the Laplacian for the Maass forms 𝑢_𝑗 , 𝑗 = 1, 2, 3, · · · in the discrete spectrum, with a double pole at 𝑠 = ½ and possible simple poles at 𝑠=𝑠_𝑗,1−𝑠_𝑗,where𝜆𝑗 =2𝑠_𝑗(2−2𝑠_𝑗)istheLaplaceeigenvalueof𝑢𝑗 and𝜆𝑗 ≠1.

Let S31(?) be the bivariate C1-cubic spline space over a triangulated quadrangulation ?. In this paper, an explicit representation of a locally supported basis of S31(?) is given using the interpolation conditions at vertices.

This thesis provides a survey study on applications of spline functions to statistics. We start with a brief history of splines. Then, we discuss the application of splines to statistics as they are applied today. Several topics included in the discussion are splines, spline regression, spline smoothing, and estimating the smoothing parameter for spline regression. Also, we give a very brief discussion of multivariate splines in statistics and wavelets in statistics. Both of these topics are currently subjects for continuing research by many mathematicians.

We establish consistent definitions for divisors, principal divisors, and Jacobians of a tropical elliptic curve and show that for a tropical elliptic cubic C , the associated Jacobian (or zero divisor class group) is the group S^1(Q).