Let M be a Riemannian manifold with metric g, and let P be a principal G-bundle over M having connection one-form a. One can define a modified version of the Ricci flow on P by fixing the size of the fiber. These equations are called the Ricci Yang-Mills flow, due to their coupling of the Ricci flow and the Yang-Mills heat flow. In this thesis, we derive the Ricci Yang-Mills flow and show that solutions exist for a short time and are unique. We study obstructions to the long-time existence of the flow and prove a compactness theorem for pointed solutions. We represent the Ricci Yang-Mills flow as a gradient flow and derive monotonicity formulas that can be used to study breather and soliton solutions. Finally, we use maximal regularity theory and ideas of Simonett concerning the asymptotic behavior of abstract quasilinear parabolic partial differential equations to study the stability of the Ricci Yang-Mills flow in dimension 2 at Einstein Yang-Mills metrics. / text

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Modeling gravity recovery of platinum group minerals (PGMs) in the grinding circuit is based on three components: Ore characterization of gravity recoverable platinum group minerals (GRPGM), their behavior in grinding mills and hydrocyclones, and the performance of the gravity recovery units. This thesis focuses on the first two components. / A laboratory methodology to characterize gravity-recoverable platinum group minerals (GRPGMs) in an ore with four incremental liberation and recovery stages was developed. It was applied to quantify GRPGM content of four ore samples from Canada. To measure the behavior of GRPGMs in the grinding circuit, a methodology to characterize the already liberated (or available) GRPGMs in the circuit streams was developed. The availability of GRPGM in streams, such as ball mill discharge, was used to model the behavior of the GRPGMs in the ball mills and hydrocyclones. Combining with the potential GRPGM in an ore, they can be used for design and/or optimization of platinum group mineral recovery circuit. / The GRPGM content measured by this methodology varied from 5 to 81% depending on the ore. The GRPGM size distribution varied from fine (most GRPGM below 37mum) to coarse (significant content above 212 mum). The stage size-by-size recovery and the total GRPGM content indicate that the methodology can quantify the GRPGM content of ores. / Based on the measurement of the availability of GRPGM in process streams, the behavior of PGMs in ball mills and hydrocyclones is characterized in terms of the less common cumulative selection functions and conventional classification efficiency curves. Mineralogical analysis indicates that sperrylite (PtAs 2) is the dominant platinum mineral at the Clarabelle mill. Its classification efficiency is similar to that of gold, despite its lower density, while grinding rate is significantly higher than gold. The cumulative selection function of platinum and palladium is 1.3 times higher than the ore for size classes above 212 mum and 50 to 70% of the ore below 212 mum. / As a result, sperrylite accumulates in finer sizes than native gold in the grinding circuit. The cumulative selection function of the platinum group minerals was calculated for the Clarabelle grinding circuit based on the survey data and the GRPGM contents in the ball mill discharge, cyclone underflow, and overflow. / The methodology of characterizing the content of GRPGMs in an ore also offers a way to concentrate the minerals for mineralogical study. The use of secondary electron microscopy (SEM), variable pressure SEM and QEM*SEM for qualitative analysis of platinum group mineral mineralogy is presented and discussed. Most of the GRPGMs recovered are well liberated. Qualitative mineralogical analysis of the GRPGM and its associations in ore samples are also discussed.

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Quantum Field Theory (QFT) provides the essential background for formulating the standard model of elementary particles and, moreover, practically all other theories attempting to explore the physical laws of nature at the sub-atomic level. One of the main observables in QFT are the scattering amplitudes, physical quantities which encode the information of the scattering process of particles. Accordingly, having authentic, well-defined and feasible prescriptions for the calculations of amplitudes is of huge importance to theoretical physicists. Actual calculations show that the text-book prescription, the Feynman method, besides in general being very cumbersome also hides some of the beautiful mathematical features of amplitudes. The last decade has seen tremendous efforts and achievements to improve such calculations, particularly in supersymmetric gauge theories, which have also led to better understanding of QFT itself. Among the known physically and mathematically interesting quantum field theories is perturbative gravity and its supersymmetric version, N=8 supergravity- much less understood than gauge theory. Following the developments in gauge theory, this dissertation mainly aims at exploring scattering amplitudes in gravity as a quantum field theory, using the modern approaches to QFT. The goal is not only to improve our understanding of gravity amplitudes by applying part of the known modern methods of calculations to it but also to introduce and develop new ones.

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Polymorphism and crystallinity are now recognised as important issues in drug development. This is shown by the increased amount of research in this area over recent years. In pharmaceutical development milling is an important unit operation for size reduction to improve powder handling, processing and dissolution rate. The aim of this thesis was to investigate the effect of ball milling (and cryo-milling) on the solid state properties, including amorphous drug formation, of pharmaceutical solids. Milling was carried out using an oscillatory ball mill (Mixer Mill MM301, Retsch GmbH & Co., Germany). In cryo-milling the milling jars were immersed in liquid nitrogen for three min before milling. XRPD was used as the main technique to evaluate the milled samples. Ranitidine hydrochloride (RAN) and indomethacin (INDO) were the model drugs used in this study. It was found that upon milling, RAN form 1 converts to RAN form 2 via an amorphous phase. A faster amorphization rate was observed when the crystalline samples were cryo-milled. Amorphous ranitidine hydrochloride was characterized to have a glass transition (T[g]) range of 13 to 30 �C and a crystallization exotherm (T[c]) between 30 and 65 �C. Conversion was found to occur faster when the temperature of the solid powder was greater than the T[c]. Under various storage conditions, similarly, crystallization of the amorphous phase mainly led to RAN form 2. However, some form 1 and amorphous phase was also detected on the XRPD diffractograms. Using partial least squares regression, the amount of solid form components in the ternary RAN mixtures were successfully quantified. RAN form 2 did not convert to form 1 under any milling (including cryo-milling) or storage conditions used in this study. Overall, RAN form 2 was found to be the thermodynamically stable form and the two (RAN) polymorphs are likely to be a monotropic pair. In a co-milling study of INDO and RAN, the two crystalline drugs were successfully converted into a single amorphous phase after 60 min of co-milling in a cold room (4 �C). The T[g] range (26-44 �C) was also characterized for these mixtures. DRIFTS spectra of the co-milled amorphous samples indicated an interaction had occurred between the carboxylic acid carbonyl (HO-C=O) and benzonyl amide (NC=O) of the INDO molecule with the aci-nitro (C=NO₂) of RAN. Depending on the ratio of INDO to RAN, in general, the amorphous mixtures were stable at 4 �C after 30 days of storage. Crystallization was faster when the binary mixtures were stored at higher temperature or contained higher amounts of RAN in the mixture. Although XRPD and DRIFTS suggested an interaction between the two drugs, co-crystal formation was not observed between INDO and RAN. Ball milling can be used to produce amorphous drug. The rate and extent of amorphization is dependent on the milling conditions. A faster rate of amorphization was observed when the crystalline drugs were cryo-milled. Amorphous drug formation can be made either alone or in combination with another crystalline drug. Amorphization could offer a significant improvement on the dissolution profile and the bioavailability of the poorly water soluble drug - indomethacin. Furthermore, ball milling can also be used to produce a homogenous mix between solids. The �goodmix� effect can be used for seed-induced crystallization or, when the XRPD or Raman data were combined with partial least squares regression, to create a reliable calibration model for quantitative analysis.

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The one-loop effective action for N = 2 and N = 4 supersymmetric Yang-Mills theories are computed to order F5; and F6 respectively by the use of heat kernel techniques in N = 1 superspace. The computations are carried out via the introduction of a new method for computing DeWitt-Seeley coefficients in the coincidence limit. To order F5, the bosonic components of both N = 2 and N = 4 supersymmetric Yang-Mills theories are extracted and compared with the existing literature. For N = 4 super Yang-Mills theories the F5 terms are found to be consistent with the non-Abelian Born-Infeld action computed to this order by superstring methods and various other means of computing deformations of supersymmetric Yang-Mills theory. The result proved to be the final piece of a puzzle, leaving little doubt that there exists a unique deformation of maximally symmetric super Yang-Mills theories at this order. The F6 terms will be of importance for comparison with superstring calculations, including direct tests of the AdS/CFT conjecture. The bosonic components of N = 2 supersymmetric Yang-Mills are also shown to be consistent with existing literature, and will be of importance for testing of generalizations of the AdS/CFT conjecture.