When sampling from multivariate distributions whose density contours are banana-shaped due to the non-linear correlation structure, traditional Markov chain Monte Carlo methods such as random walk Metropolis and independent Metropolis-Hastings suffer from severe low convergence. In this thesis, a model for bivariate banana-shaped distributions is constructed which is used to fit general banana-shaped distributions in terms of the probability density function. Transformations which are aimed at converting the variables to orthogonal variables by changing the coordinate system are designed for this distribution model. A new Markov chain Monte Carlo algorithm involving this set of transformations is proposed to sample these complex distributions. The key point of the new algorithm is to approximate the target density function using function using a parametric model which can facilitate the MCMC sampling after changing to another coordinate system. Detailed comparisons of convergence rate and estimation efficiency between the new method and existing methods are performed using both benchmark examples and practical examples, which showed the advantage of the new method. / 在多元概率分佈中，如果變量問存在非線性相關性使其等高線為香蕉形，傳統的馬爾科夫蒙特卡洛方法，如隨機漫步蒙特卡洛及獨立M-H方法都只有非常低的收斂速度和有效樣本數。本論文設計一種二元香蕉形分佈函數模型對一般香蕉形分佈進行擬合及一套能將其變量正交化的變換函數，並以此模型及變換函數為基礎建立一種新的馬爾科夫蒙特卡洛方法，實現對香蕉形分佈的高效率抽樣。該方法的關鍵在於對一般香蕉形分佈進行近似的參數模型能夠在進行坐標轉換後便於採樣。本論文將在不同例子中以收斂速度及估計效率為標準比較新方法與已有方法，模擬實驗和實例都顯示新方法較優。 / Chan, Kwun Cheung. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 50-52). / Abstracts also in Chinese. / Title from PDF title page (viewed on 05, October, 2016). / Detailed summary in vernacular field only.

Choy, Chun Wing = 皺摺界面和柱形微粒群的靜電共振 / 蔡振榮. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 53-56). / Text in English; abstracts in English and Chinese. / Choy, Chun Wing = Zhou zhe jie mian he zhu xing wei li qun de jing dian gong zhen / Cai Zhenrong. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Electric field near corrugated interfaces --- p.1 / Chapter 1.2 --- Electrostatic resonances of cylindrical clusters --- p.2 / Chapter 1.3 --- Objective of the thesis --- p.4 / Chapter 2 --- Review on Green Function Formalism --- p.5 / Chapter 2.1 --- Integral equation formalism --- p.5 / Chapter 2.2 --- Periodic corrugated interfaces --- p.8 / Chapter 2.3 --- Solution by mode expansion --- p.11 / Chapter 2.4 --- Numerical Results --- p.12 / Chapter 3 --- Electric Field at the Interface --- p.15 / Chapter 3.1 --- Formalism --- p.15 / Chapter 3.2 --- Numerical Results --- p.18 / Chapter 3.3 --- Effective medium approximation --- p.22 / Chapter 3.4 --- Discussion --- p.24 / Chapter 4 --- Application of GFF in cylindrical clusters --- p.26 / Chapter 4.1 --- Review of Bergman's spectral representation --- p.26 / Chapter 4.2 --- Extension of Bergman's spectral representation using Green Function Formalism --- p.29 / Chapter 4.3 --- Finding pole spectrum using Green Function Formalism --- p.31 / Chapter 4.4 --- Numerical Results --- p.34 / Chapter 4.4.1 --- Two approaching cylinders --- p.34 / Chapter 4.4.2 --- Three cylinders arranging in a horizontal array --- p.40 / Chapter 4.4.3 --- Three cylinders arranging in an equilateral triangle --- p.42 / Chapter 4.4.4 --- Three cylinders arranging in an isosceles triangle --- p.46 / Chapter 5 --- Summary --- p.51 / Bibliography --- p.53 / Chapter A --- Multiple image method to a pair of cylinders --- p.57 / Chapter A.1 --- Dipole factor of a pair of cylinders --- p.57 / Chapter A.2 --- Spectral representation --- p.58 / Chapter B --- Illustration of Bergman-Milton Spectral Representation --- p.60 / Chapter B.1 --- Series combination --- p.61 / Chapter B.2 --- Parallel combination --- p.62

Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex microstructure effects to develop high-performance materials, but general microstructure quantification is an unsolved problem. Motivated by statistical physics, I envision microstructure as a low-dimensional manifold, and construct this manifold by leveraging multiple machine learning approaches including transfer learning, dimensionality reduction, and computer vision breakthroughs with convolutional neural networks.

As commercially manufactured nanomaterials become more commonplace, they have the potential to enter ecological and biological environments sometime during their lifecycle of production, distribution, use or disposal. Despite rapid advances in the production and application of nanomaterials, little is known about how nanomaterials may interact with the environment or affect human health. This research investigates an environmental application of nanomaterials and characterizes the physicochemical properties of commonly manufactured nanomaterials in environmental health and safety studies. Characterization of nanomaterials for applications and environmental health and safety studies is essential in order to understand how physicochemical properties correlate with chemical, ecological, or biological response or lack of response. Full characterization includes determining the bulk and surface properties of nanomaterials. Bulk characterization methods examine the shape, size, phase, electronic structure and crystallinity, and surface characterization methods include surface area, arrangement of surface atoms, surface electronic structure, surface composition and functionality. This work investigates the selective catalytic reduction (SCR) of NO2 to N2 and O2 with ammonia on nanocrystalline NaY, Aldrich NaY and nanocrystalline CuY using in situ Fourier transform infrared (FTIR) spectroscopy. It was determined that the kinetics of SCR were 30% faster on nanocrystalline NaY compared to commercial NaY due to an increase in external surface area and external surface reactivity. Copper-cation exchanged nanocrystalline Y resulted in an additional increase in the rate of SCR as well as distinct NO2 and NH3 adsorption sites associated with the copper cation. These superior materials for reducing NOx could contribute to a cleaner environment. This work consists of characterization of commonly manufactured or synthesized nanomaterials and studies of nanomaterials in specific environmental conditions. Bulk and surface characterization techniques were used to examine carbon nanotubes, titanium dioxide nanoparticles, bare silver nanoparticles and polymer-coated silver nanoparticles, and copper nanoparticles. Lithium titanate nanomaterial was collected from a manufacturing facility was also characterized to identify occupational health risks. Particle size distribution measurements and chemical composition data showed the lithium titanate nanomaterial forms larger micrometer agglomerates, while the nanoparticles present were due to incidental processes. A unique approach was applied to study particle size during dissolution of nanoparticles in aqueous and acidic conditions. An electrospray coupled to a scanning mobility particle sizer (ES-SMPS) was used to determine the particle size distribution (PSD) of bare silver nanoparticles in nitric acid and copper nanoparticles in hydrochloric acid. The results show unique, size-dependent dissolution behavior for the nanoparticles relative to their micrometer sized counterparts. This research shows size-dependent properties of nanomaterials can influence how they will be transported and transformed in specific environments, and the behavior of larger sized materials cannot be used to predict nanomaterial behavior. The type of nanomaterial and the media it enters are important factors for determining the fate of the nanomaterial. These studies will be important when considering measures for exposure control and environmental remediation of nanomaterials.

Identified as one of the 7 Millennium Problems, the Riemann zeta hypothesis has successfully evaded mathematicians for over 100 years. Simply stated, Riemann conjectured that all of the nontrivial zeroes of his zeta function have real part equal to 1/2. This thesis attempts to explore the theory behind Riemann’s zeta function by first starting with Euler’s zeta series and building up to Riemann’s function. Along the way we will develop the math required to handle this theory in hopes that by the end the reader will have immersed themselves enough to pursue their own exploration and research into this fascinating subject.

Cette thèse a été dirigée par le Professeur Kauffmann de l’Université de Franche-Comté. Le co-directeur de l’Ecole Royale Militaire était le Docteur Johan Gallant et les essais à l’Institut franco-allemande de recherches de Saint-Louis (ISL) étaient encadrés par le Docteur Markus Schneider.Un lanceur à rails conventionnel est composé de deux rails conducteur connecté par un projectile. L’interaction entre le champ magnétique induit par le courant dans les rails et le courant dans le projectile résulte en une force électromagnétique accélérant. Dans cette thèse on utilise un projectile avec deux ponts de courant. Pour un lanceur à rails conventionnel la méthode la plus efficace pour augmenter la force sur le projectile est d’augmenter le courant dans les rails. Mais la densité de courant est limitée. L’échauffement des contacts entre les rails et les ponts de courant par l’effet Joule et la force de frottement, peut résulter dans la transformation d’un contact solide dans un contact plasma, ce qui est à éviter. Une possibilité d’adresser ce problème est d’ajouter des ponts de courant pour améliorer la distribution de courant. Une autre possibilité est d’appliquer un champ magnétique extérieur généré par un circuit extérieur qui nous permet d’augmenter la force électromagnétique sans augmenter le courant dans le circuit intérieur. Dans cette thèse l’objectif est d’étudier la distribution de courant et de température dans un projectile à deux ponts de courant pour un lanceur augmenté. Comme les deux ponts de courants et les rails du circuit intérieur forment un circuit fermé, le champ augmenté va induire un courant de circulation qui influence la distribution de courant entre les brosses. Le premier modèle de simulation est un modèle global du lanceur en PSpice qui nous permet de déterminer les courants globaux, la force électromagnétique, la position et la vitesse du projectile et la température moyenne des brosses. Le modèle global prend en compte l’effet de peau dû à la vitesse et est validé par des résultats expérimentaux. Le deuxième modèle est un modèle local en ANSYS, un code à éléments finis, pour un projectile fixe. Ce modèle permet une étude locale de la distribution de courant et de température. Un modèle pour la zone de contact entre les rails et la brosse est introduit. Le modèle local est utilisé pour calculer les coefficients de l’équation de force dans le modèle global. Les résultats des deux modèles de simulation sont cohérents.Le lanceur LARA, utilisé pour les essais, a une longueur de 1.5 m et un calibre de 15 mm. On disposait de trois bancs de condensateurs pour l’alimentation du lanceur en configuration non-augmenté et augmenté. Les vitesses à la bouche obtenues varient entre 48 et 214 m/s. Pour la détermination de la distribution de courant nous avons utilisé une méthode proposée par [SCH05a]. Cette méthode est une combinaison d’une mesure de tension entre deux pins dans les rails et dans une boucle. Nous avons constaté que les signaux obtenus avec cette méthode, appliquée dans ce régime de vitesse, sont perturbés par les courants de Foucault induits avant le projectile et les résultats ne répondent pas à nos attentes. Une méthode analytique basée sur la mesure de tension dans la boucle a été développée. Les résultats expérimentaux sont comparés avec les simulations. Nous avons constaté une bonne correspondance entre les valeurs des courants maximaux dans les rails calculés avec PSpice et les valeurs expérimentales, mais le courant calculé avec PSpice est plus faible dans la phase décroissante du courant. Les erreurs sur la vitesse sont inférieures à 10 %. Les deux modèles de simulation et les essais montrent que la brosse avant porte la plus grande partie du courant. La dernière partie de cette thèse est une étude paramétrique avec ANSYS pour l’avant-projet du circuit intérieur d’un lanceur à rail existant. / This thesis was supervised by Professor Jean-Marie Kauffmann of the University of Franche-Comté. The co-director at the Royal Military Academy was Dr. Johan Gallant and the experiments at Franch-German Research Institute ISL were directed by Dr. Markus Schneider. A conventional electromagnetic railgun is composed of two conducting rails connected by a projectile. The magnetic field generated by the current in the rails interacts in the projectile resulting in an electromagnetic force accelerating the projectile. The projectile used in this thesis is two brush projectile. For a conventional railgun the most efficient way to increase the force on the projectile is to increase the current in the rails. But the current density is limited. The heating of the sliding contacts between the brushes and the rails due to the Joule losses and the friction can cause the contacts and can result in contact transition which we want to avoid. One way to reduce the heating is to add more current brushes to obtain a better current distribution between the brushes. Another way is to add an extra pair of rails and create an additional magnetic field. This augmenting field allows us to increase the electromagnetic force without increasing the current through the projectile. In this thesis the current and heat distribution in a two brush projectile in a parallel augmented railgun is studied through simulations and experiments. Because the current brushes and the inner rails form a closed loop, the augmenting field will induce a loop current and influence the current distribution between the brushes. The first simulation model is a global model of the railgun in PSice which allows us to predict the global currents as well as the average temperature in the brushes, the force on the projectile and the position and the velocity of the projectile. The model takes into account the velocity skin effect and was validated based on experiments. The second model is a finite element model in ANSYS for a fixed projectile. This model allows a local study of the current and temperature distribution in the projectile. A model for the contact between the rails and the projectile is introduced. The local model is used to calculate the time-dependent coefficients for the force equation used in the global model. Both simulation models are compared and a good correspondence is found. The LARA railgun of ISL with a length of 1.5 m and a square caliber of 15 mm has been used for the experiments. A maximum of three capacitor banks was used for the non-augmented and the augmented configuration. The muzzle velocities obtained in the experiments vary between 48 and 214 m/s. To determine the current distribution between the brushes a technique proposed by [SCH05a] has been used. It is based on the measurement of the voltage between two pins in the rails in combination with the voltage in a loop. When applied to this velocity range, the eddy currents in front of the projectile hamper the interpretation of the signals and the results are not what we expected. An analytical method for the determination of the current distribution based on the voltage in the loop was introduced. The results are then compared with the results of the simulations. The maximum current in the rails found with PSpice shows a good correspondence with the experiments, the calculated decrease of the current is slightly overestimated. The errors on the velocities are less than 10%. Both simulation models and experiments show that the brush towards the breech carries the greater part of the current for the non-augmented as well as the augmented railgun. In the last part a parametric study is carried out with ANSYS for the preliminary design of an augmenting circuit for an existing railgun.

This thesis is prepared in three parts; the first part is a study of the ant species of the southern Carnarvon Basin, which was undertaken in order to determine the patterns of ant species distribution in this arid zone area. The distribution patterns were looked at in terms of biogeographical regions and they demonstrated the transitional nature of this particular area. Recommendations to alter the border between the South-west Province and the Eremaean Province were supported. The next chapter of this thesis analysed ant species from long unburnt and burnt areas of three main vegetation types (two Triodia species grasslands and Acacia aneura woodlands) in the Gibson Desert Nature Reserve. This study was carried out to observe the recovery of ant populations after fire. The results provided further evidence that invertebrates are measurably impacted by fire in the arid zone. The final chapter is a comparison of these two arid zone studies with six other ant community studies from throughout Western Australia. It demonstrated the uniqueness of some arid zone sites as well as related each study to each other according to their ant communities.

This study explores the concept and practical implementation of continuous innovation in logistics services, particularly Distribution Centres. Continuous innovation is a concept that requires a methodical, programmed, incremental and/or radical approach to business improvement involving employees at all levels in the organisational structure. Theories and models of innovation were analysed in the literature, at the outset of this research. As found by previous authors, specific characteristics of service forms did not allow direct application of traditional models of innovation. Most of these traditional models were constructed from the manufacturing perspective. As a result, a new innovation model was designed for this study. It can be used as a guide for understanding the components necessary in service forms to embark on continuous innovation. This model describes the process of service innovation and incorporates theories from literature, and some variables from the CIMA model. The study is exploratory in nature, using empirical data. The study identified, evaluated, compared and contrasted the factors in ten Distribution Centres in Australia and in Singapore that affected the use of continuous innovation in their operations and processes. The focus of the study investigated the drivers, capabilities, behaviours, contingencies, individual competencies and performance measures of innovation in Distribution Centres with logistics services. Overall, this study has made significant contributions in terms of the theoretical investigation adding to the body of literature. This study was exploratory, using case studies as a first hand approach in gaining an understanding of Distribution Centres. There are areas that would merit further investigation and future research. It suggested that additional work should be carried out to expand on this research and refine the model to meet the needs of a wider range of organisations in various service industries. In addition, there are recommendations flowing from this study concerning the practical management of logistics operations. They are addressed mainly to senior management who typically take lead in the implementation of innovative programmes within the organisation. Firms should address continuous innovation as a planned and integrated approach, taking into account many interacting factors that are essential for successful innovation. The challenge facing Distribution Centres is to develop efficient and flexible processes and systems, by continuously innovating to sustain a leading edge in the logistics industry / Doctor of Philosophy (PhD)

There has been widespread concern expressed by members of the statistics education community in the past few years about the lack of any real understanding demonstrated by many students completing courses in introductory statistics. This deficiency in understanding has been particularly noted in the area of inferential statistics, where students, particularly those studying statistics as a service course, have been inclined to view statistical inference as a set of unrelated recipes. As such, these students have developed skills that have little practical application and are easily forgotten. This thesis is concerned with the development of understanding in statistical inference for beginning students of statistics at the post-secondary level. This involves consideration of the nature of understanding in introductory statistical inference, and how understanding can be measured in the context of statistical inference. In particular, the study has examined the role of the sampling distribution in the students? schemas for statistical inference, and its relationship to both conceptual and procedural understanding. The results of the study have shown that, as anticipated, students will construct highly individual schemas for statistical inference but that the degree of integration of the concept of sampling distribution within this schema is indicative of the level of development of conceptual understanding in that student. The results of the study have practical implications for the teaching of courses in introductory statistics, in terms of content, delivery and assessment.

This work investigates the tensile behaviour of non-uniform fibres and fibrous composites. Wool fibres are used as an example of non-uniform fibres because they're physical, morphological and geometrical properties vary greatly not only between fibres but also within a fibre. The focus of this work is on the effect of both between-fibre and within-fibre diameter variations on fibre tensile behaviour. In addition, fit to the Weibull distribution by the non-brittle and non-uniform visco-elastic wool fibres is examined, and the Weibull model is developed further for non-uniform fibres with diameter variation along the fibre length. A novel model fibre composite is introduced to facilitate the investigation into the tensile behaviour of fibre-reinforced composites. This work first confirms that for processed wool, its coefficient of variation in break force can be predicted from that of minimum fibre diameters, and the prediction is better for longer fibres. This implies that even for processed wool, fibre breakage is closely associated with the occurrence of thin sections along a fibre, and damage to fibres during processing is not the main cause of fibre breakage. The effect of along-fibre diameter variation on fibre tensile behaviour of scoured wool and mohair is examined next. Only wet wool samples were examined in the past. The extensions of individual segments of single non-uniform fibres are measured at different strain levels. An important finding is the maximum extension (%) (Normally at the thinnest section) equals the average fibre extension (%) plus the diameter variation (CV %) among the fibre segments. This relationship has not been reported before. During a tensile test, it is only the average fibre extension that is measured. The third part of this work is on the applicability of Weibull distribution to the strength of non-uniform visco-elastic wool fibres. Little work has been done for wool fibres in this area, even though the Weibull model has been widely applied to many brittle fibres. An improved Weibull model incorporating within-fibre diameter variations has been developed for non-uniform fibres. This model predicts the gauge length effect more accurately than the conventional Weibull model. In studies of fibre-reinforced composites, ideal composite specimens are usually prepared and used in the experiments. Sample preparation has been a tedious process. A novel fibre reinforced composite is developed and used in this work to investigate the tensile behaviour of fibre-reinforced composites. The results obtained from the novel composite specimen are consistent with that obtained from the normal specimens.