This thesis provides improvements to computational fluid dynamics accuracy and ef- ficiency through two main methods: a new boundary condition verification procedure and preconditioning techniques. First, a new verification approach that addresses boundary conditions was developed. In order to apply the verification approach to a large range of arbitrary boundary condi- tions, it was necessary to develop unifying mathematical formulation. A framework was developed that allows for the application of Dirichlet, Neumann, and extrapolation bound- ary condition, or in some cases the equations of motion directly. Verification of boundary condition techniques was performed using exact solutions from canonical fluid dynamic test cases. Second, to reduce computation time and improve accuracy, preconditioning algorithms were applied via artificial dissipation schemes. A new convective upwind and split pressure (CUSP) scheme was devised and was shown to be more effective than traditional precon- ditioning schemes in certain scenarios. The new scheme was compared with traditional schemes for unsteady flows for which both convective and acoustic effects dominated. Both boundary conditions and preconditioning algorithms were implemented in the context of a "strand grid" solver. While not the focus of this thesis, strand grids provide automatic viscous quality meshing and are suitable for moving mesh overset problems.

We investigate the existences and qualitative properties of periodic solutions of the following two classes of nonlinear differential equations: I) (Special) Relativistic Pendulum Equations (RPEs); II) (2-coupled) Gross-Pitaevskii Equations (GPEs). The pendulum equation describes the motion of a pendulum. According to Special Relativity, which was published by A. Einstein in 1905, causality is more fundamental than constant time-space, thus time will ow slower and space will distort to keep causality if the speed of motion is near the speed of light. In such high speed situations, the pendulum equation needs to be revised due to Special Relativity. The revised equation is called RPE. Our result answers some open questions about the existence of multiple periodic solutions for RPEs. GPEs are sometimes called coupled nonlinear schrodinger equations. the Schrodinger equation is the fundamental equation of Quantum Mechanics which is the \exotic" probabilistic fundamental physics law of the \micro" world { the world of atoms and molecules. A well-known physicist and Nobel laureate, R. Feynman, said \I think I can safely say that nobody understands quantum mechanics." which indicates the physical/ philosophical difficulty of interpretations. It raises paradoxical problems such the well-known Schrodinger's Cat. Setting aside these difficult, if we combine Special Relativity and Quantum Mechanics as a many-body system, then we have Quantum Field Theory (QFT) which is more deterministic, and governs even elementary particle physics. GPEs are also related to QFT. For example, superconductivity and Bose Einstein Condensates (BEC). These phenomena in condensed matter physics can be thought of as the emergence of the mysterious micro world physics at \macro" level. We study these equations from the viewpoint of mathematical interest. It is generally difficult to solve nonlinear differential equations. It is also generally difficult even to prove the existence of solutions. Although we show there exist solutions, we still do not know how to solve the differential equations analytically. Variational Methods (or Calculus of Variations) are useful tools to show there exist solutions of differential equations. The idea is to convert the problem of solving equations into the problem of finding critical points (i.e. minimum/maximum points or saddle points) of a functional, and each critical point can generally correspond to a weak solution. However, it is also generally difficult to find out such critical points because we look for critical points in an infinite-dimensional functions space. Thus many advanced mathematical theories or tools have been developed and used for decades in nonlinear analysis. We use some topological theories. From information of the functional's shape, these theories deduce if there exists a critical point, or how many critical points exist. The key of these theories is to use the symmetry of the equations. We also investigate bifurcation structures for II), i.e. the connection structures between the solutions. By linearizations which look at the equations \locally," we reduce the problem in the infinite dimension to one in a finite dimension. Furthermore, it allows us to apply Morse Theory, which connects between local and global aspects of the functional's information. In several cases, we show that there are infinitely many bifurcation points that give rise to global bifurcation branches.

In this thesis, we will examine the properties of subelliptic jets in the Engel group of step 3. Step-2 groups, such as the Heisenberg group, do not provide insight into the general abstract calculations. This thesis then, is the first explicit non-trivial computation of the abstract results.

Over the last 100 Years, the cyanidation process has been the most popular method for recovering gold from its ores. Despite this, there are still efforts to improve the efficiency of the process, particularly as ores become more difficult to treat. Many investigators have studied the cyanidation process, although a large proportion of these studies have obtained contradictory results. This thesis presents a kinetic and electrochemical study of the leaching of gold in cyanide solutions, and emphasis is placed on rationalising the conflicting results which have been published in the past.The leaching rate of gold was measured using a rotating electrochemical quartz crystal microbalance, an instrument which allows the simultaneous measurement of electrochemical data and mass changes at the solid-solution interface in real time. A proportion of this project was devoted to the on-going design of this instrument, and a number of modifications are discussed in detail. Initially, the leaching of gold in cyanide solutions was investigated under conditions of high purity. Under these conditions, it was found that the gold surface is blocked by a passive film, presumably AuCN. The presence of such a film results in the reaction being chemically controlled, and under typical cyanidation conditions (4 mM cyanide, pH 10.0), the rate of dissolution is very low. These kinetic results were supported by complimentary electrochemical studies, which showed that gold is passive in the potential region where cyanidation occurs.The second part of this thesis presents a study of the effect of system purity on the leaching of gold in cyanide solutions. Solution phase purity was investigated by adding controlled amounts of lead or silver to the leach solutions. It was found that in the presence of low concentrations of lead, the dissolution of gold in 20 mM cyanide solutions was oxygen ++ / diffusion controlled (as compared to chemical control for gold in the absence of lead). However, high concentrations of lead were found to be detrimental to the leaching process. It is believed that the role of lead is to modify the surface by cementation, hence reducing the effect of the passive film. Silver was also found to be effective at reducing passivation, and the role of silver believed to be similar to that of lead. It was found that unlike lead, high concentrations of silver are not detrimental to the dissolution of gold in cyanide solutions.Solid phase purity was also found to be important in the leaching of gold, and it was found that the leaching of a gold sample which contains 1 % silver is diffusion controlled. This finding is important from an industrial viewpoint, as most native gold contains some silver. Consequently, attempts were made to rationalise the leaching of gold/silver with current plant practice. Discussion on the effect of cyanide and oxygen concentrations, temperature and lead addition is presented.

Professional treatment, mainly medical and psychological, dominates research and clinical practice concerning women and their recovery from depression. This thesis challenges the assumption that women cannot be 'experts' actively involved in their own recovery. This study explored the narratives of eighteen women in Aotearoa New Zealand whose lives had been seriously disrupted by depression. They had found ways other than, or in addition to, professional solutions that helped them to live undisrupted meaningful lives. The research used a narrative inquiry approach informed by authors from across the social sciences including Arthur Frank, Jerome Bruner and Rivka Tuval-Mashiach. The underpinning social constructionist understanding of depression is informed by the work of Jane Ussher and Janet Stoppard. The women whose individual narratives provide the core data for the study ranged in age from 32 to 70 years at the time they told their stories. Their lives had been disrupted by depression at different times during the last 50 years of the twentieth century. Five of the women met as a group with the researcher as the analysis began, and their ideas informed significant aspects of the conclusions. The women had all experienced major depressive disorder, although this was not always formally diagnosed. Their recovery had involved a range of responses from outside the professional mainstream including physical, mental, social and spiritual aspects. Each woman had sought and found a 'formula' that was 'right' for her. The narratives showed all the women talked of their experience with depression and recovery in an holistic and contextualised way. They all talked about 'chocolate' solutions which provided symptom relief, and 'deeper' and often more complex sets of solutions which enabled them to discover or re-discover meaningful ways to live. Meaning-making often involved growing spiritual or transpersonal awareness in the broadest sense. A surprising finding was that the patterns of recovery were not related to the severity of the depression at the worst time. Rather, it emerged that the ways the women talked about their recovery journeys mirrored their stories of the 'jolly good reasons' why they were depressed; the more complex and lengthy the story leading up to the worst times, the more complex the formulae required for recovery. The implications of the research for clinical practice and for policy makers are that depression and recovery need to be seen as gendered, contextualised, and holistic. Women need opportunities to discover and take advantage of a range of 'things' so that they can find their own 'right formula' for recovery. This formula may involve professional treatment including anti-depressant medication and psychological therapy, but it is likely to involve many other things as well. This study challenges the notion that recovery needs to be guided by a professional expert, and creates hope for women being able to learn from each other's experiences.

The study challenges current literature, which views the notion of problem-finding as the initial identification of a problem to be solved. The concept of problem-finding in this study is that problem-finding continues throughout the problem-solving process and is not distinct from it. This thesis aims to develop a better understanding of problem-finding by examining high school students using problem-finding to solve industrial design problems. The study seeks to find out what types of problem-finding exist and what roles they play in solving design problems. To explore problem-finding, this study uses a Think Aloud methodology to examine the thinking of three high school industrial design students and one high school industrial design teacher solving an authentic industrial design problem. Protocol data was gathered from the subjects and then transcribed, segmented and analysed in three ways, each of which became progressively more specific: Firstly, a macroscopic examination which identified problem-finding episodes occurring throughout the design process; secondly, a microscopic examination which identified four categories of problem-finding; and lastly, a microscopic examination which looked at the role played by the different problem-finding categories in solving design problems. The findings of this study are fourfold. Firstly, problem-finding was found to be used throughout the entire design process. Secondly, there were four categories of problemfinding. Thirdly, each category played an important role predominantly through interaction with other categories. Lastly, the more experienced a person was, the more able they were to use problem-finding effectively to solve design problems. Many current practices use trial and error methods to solve design problems. The importance of this study is that through a better understanding of problem-finding, designers may be able to use metacognitive strategies more efficiently in the process. Similarly, in educational practice, high school design students may be able to learn to think about the methods they use to solve design problems, and this may result in more creative designs.

Purpose: To develop an approach to formulating an injectable solution containing both hydrophilic and lipophilic drugs for subcutaneous administration. Based on the literature survey, isotropic medium chain mono-and diglyceride (MCMDG) systems were chosen for study. For this purpose, analytical methods were developed and validated. In vitro assessments of the MCMDG systems, and in vitro release and in vivo studies were conducted. Methods: The phase diagrams of the isotropic MCMDG systems were constructed with systems comprising two and three components. The isotropic region was examined by visual inspection and confirmed using polarized light microscopy. Viscosities of formulations were measured. The validated HPLC assay methods were developed for determination of levamisole and abamectin in liquid formulations and in sheep plasma. The HPLC assay was capable of evaluating stability of abamectin and levamisole in liquid formulations. Solubilities of levamisole hydrochloride or levamisole phosphate and abamectin were determined in the isotropic MCMDG formulations using a HPLC assay method. Stabilities of levamisole phosphate and abamectin were conducted in the isotropic MCMDG formulations at 60�C for 10 days. In vitro release studies for levamisole phosphate were carried out for selected formulations using modified Franz diffusion cells. Based on stability and in vitro release studies, one formulation (MCMDG/propylene glycol (PG):glycerol formal (GF), 20/20:60 % w/w) was selected for a preliminary in vivo study. The selected MCMDG/PG:GF (20/20:60) formulation containing both levamisole phosphate and abamectin was injected subcutaneously into sheep, and the injection site was examined after subcutaneous injection. Pharmacokinetic profiles were determined. A correlation between in vitro fraction released (FR) and in vivo fraction absorbed (FA) for levamisole phosphate from the MCMDG/PG:GF (20/20:60) formulation was assessed. Results: The isotropic systems of the MCMDG systems containing two or three components were characterized through phase diagrams and viscosity. The solubility of the levamisole hydrochloride in the isotropic MCMDG/sesame oil/water formulations was higher in the absence of abamectin than in combination with abamectin. Solubility of levamisole phosphate was higher in the MCMDG system containing GF or PG compared to the MCMDG/SO/water system. The isotropic MCMDG/PG:GF systems allowed preparations of levamisole phosphate/abamectin solution dose forms containing more than the usual dosage of levamisole. Stability of both levamisole phosphate and abamectin in MCMDG/PG:GF formulations was higher compared with MCMDG/PG:GF/water formulations. Levamisole phosphate degraded in the presence or absence of abamectin in the MCMDG/PG:GF (20/20:60) formulation at 60�C for 10 days. Abamectin alone was found to be stable in the formulation at 60�C for 10 days. In vitro release of levamisole phosphate from water and the MCMDG formulations tested displayed first-order kinetics. Water from the receptor compartment was observed to pass through the membrane into the donor compartment. Therefore, an advancing layer of turbidity occurred in the donor phase. A highly significant decrease in release rate of levamisole phosphate was obtained in MCMDG/GP:GF (20/20:60) formulation compared to water and the other formulations. Pharmacokinetic studies of subcutaneous injection of MCMDG/PG:GF 20/20:60) formulation showed the tmax values of 2.2 h and 4.2 days for levamisole phosphate and abamectin, respectively. The Cmax was 0.94 [mu]g/ml for levamisole phosphate and 6.24 ng/ml for abamectin while the formulation displayed the AUC value was 5.2 [mu]g�h�ml⁻1 for levamisole phosphate and 84.7 ng�day�ml⁻1 for abamectin. No inflammatory reaction was observed at the injection site. Linear regression analysis showed that a significant relationship between the FR (in vitro) and FA for the subcutaneously injected formulation. Conclusion: The study carried out in this thesis introduces a new approach to formulating an injectable solution of the isotropic MCMDG/PG:GF systems containing both levamisole (hydrophilic drug) and abamectin (lipophilic drug) for subcutaneous administration, and presents the development of the HPLC assay methods for determination of levamisole and abamectin in liquid MCMDG formulations and plasma, in order to investigate in vitro and in vivo release from the isotropic MCMDG/PG:GF formulations. The MCMDG/PG:GF formulations may represent an alternative to the more traditional formulations for both lipophilic and hydrophilic drugs.

"May 2003" / Includes bibliographical references (leaves 261-270) / xvi, 271, [16] leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, School of Chemistry and Physics, 2003

Nous présentons dans ce travail un modèle numérique performant pour le calcul de la température, du flux thermique, des déplacements et des contraintes dans un multicouche épais. Ce modèle est basé sur une approche "couche discrète " et utilise des fonctions polynomiales de degré 2 dans l'épaisseur de chaque couche. La spécificité du modèle proposé est qu'il assure la continuité, tant pour tant pour la composante normale du flux thermique que pour le vecteur contrainte suivant la normale aux interfaces. Ce modèle autorise la présence de résistance de contact aux interfaces ; il permet de diminuer le nombre de paramètres du modèle tout en assurant une meilleure approximation. Pour valider ce modèle, nous avons été amené à expliciter les solutions analytiques exactes, pour certaines géométries. Nous avons également comparé ce modèle à des modèles couramment utilisés par les codes éléments finis spécifiques aux multicouches et nous avons montré qu'il apportait une amélioration certaine sur la précision des résultats, pour des problèmes de conduction thermique, d'élasticité et de thermoélasticité.

Cette thèse est divisée en deux parties. La première partie introduit une méthode probabiliste numérique pour les EDPs parabolique et complètement non-linéaire, puis on considère ses propriétés asymptotiques (convergence et taux de convergence) et aussi l'analyse de l'erreur due à l'approximation de l'espérance conditionnelle par une méthode de type Monte Carlo. Les EDPs complètement non- linaires apparaissent dans plusieurs applications en ingénierie, économie et finance. Citons par exemple le problème de propagation de front par courbure moyenne, ou le problème de sélection de portefeuille. Une classe importante d'EDP complètement non-linéaire est constituée par les équations de HJB découlant du contrôle optimal stochastique. Dans la plupart des cas, il n'existe pas de solution dans le sens classique. Par conséquent, la notion de solution de viscosité est utilisé pour les EDP complètement non-linéaires. En raison de manque de de solution explicite dans de nombreuses applications, les schémas d'approximation sont devenus très importants. Pour montrer la convergence, la méthode utilisée dans cette thèse a été introduite par Barles et Souganidis. Leurs travaux fournissent le résultat de convergence vers des solutions de viscosité pour une solution approchée obtenue à partir cohérente, monotone et stable régime. An d'obtenir le taux de convergence, nous avons supposé que le EDP a non-linéarité concave de type HJB. En d'autres termes, la non-linéarité est une borne inférieure des opérateurs linéaires. La thèse a utilisé la méthode de Krylov des coefficients secoué et d'approximation par un système d'équations HJB couplées pour obtenir des bornes sur les taux de convergence. La mise en œuvre du schéma requiert d'introduire une approximation des espérances conditionnelles. Pour une classe d'estimateurs, nous avons obtenu une borne inférieure sur le nombre de chemins échantillon qui préserve la vitesse de convergence obtenue avant. La généralisation de la méthode à des équations intégro-diférentielles est simple et on peut utiliser les mÃa mes arguments que dans le cas local pour obtenir la convergence et le taux de convergence. Notons cependant que le cas non local introduit la difficulté supplémentaire d'approximation des termes non locaux. La première partie sera terminée est illustrée par quelques expériences numériques. La méthode est utilisée pour résoudre le problème géométrique des taux de courbure moyenne, le problème de la sélection sur un portefeuille d'actifs avec volatilité stochastique dans le modèle de Heston, et le problème de sélection de portefeuille de deux actifs à la fois avec une volatilité stochastique, on satisfait modèle de Heston et l'autre CEV modèle. La deuxième partie de la thèse traite de la politique de production optimale dans le marché des allocations des permis d'émission de carbone. Le marché des permis d'émissions de carbone est une approche de marché pour mettre en œuvre le protocole de Kyoto. Nous avons calculé la production optimale dans 4 cas: quand il n'y a pas un tel marché, quand il y a un tel marché, mais sans grand producteur de carbone, quand il y a un gros producteur qui n'est pas teneur de marché, et quand il existe un marché avec un grande producteur. Nous avons montré que dans les premiers, la production optimale est toujours diminuée. Cependant, dans le dernier cas, nous avons montré que le gros producteur peut bénéficier du marché en changeant la prime de risque de l'allocation de carbone en raison de sa production d'appoint. Cette partie est illustrée par quelques expériences numériques qui montre des cas que le grand producteur peut bénéficier d'une production d'appoint.