In this dissertation, we first introduce an equal-area spherical map, HEALPix, which is borrowed from astrophysics. Its associated sample pattern is uniformly distributed over the sphere surface. Then we discuss its application in environment mapping. Although the HEALPix representation is more balanced than the traditional cubemap, it cannot utilize the built-in hardware operations like cubemap, and the mipmapping construction is more complicated. Therefore, its rendering speed is not comparable to that of the cubemap. This motivates us to invent a new six-face spherical map, called isocube. Unlike cubemap, isocube is an equal-area mapping, i.e., each texel spans the same area and is equally important. Due to the six-face representation, isocube can fit nicely into the cubemap hardware and hence can fully exploit the hardware operations tailored for cubemap. In addition, its mapping computation only involves a small overhead. Therefore the look-up speed for isocube is very fast. / Next we discuss another application of HEALPix map, the dynamic environment sequence sampling. Previous work only considers the static case where the environment map is approximated by finite directional light sources. In the dynamic case, the individual regeneration of samples for each frame may introduce abrupt, changes in the rendering animation. To handle this temporal inconsistency problem, we propose spherical q2-tree based on IIEALPix map. The adaptiveness of the quadtree can suppress the abrupt changes between consecutive frames, and hence a rather smooth rendering can be produced. This method, however, generates sample pattern independently for each environment frame, and therefore it may still cause unexpected, lumps in some situations. To fully utilize the temporal coherence in the sequence, we present a global sampling approach which treats the dynamic environment sequence as a all volume and performs sampling in the volume. The volumetric sampling adapts the sample number according to each frame and restricts the temporal/spatial changes within small subdivided volumes, and hence ensures a smooth sampling sequence. Within the framework, we present a volumetric importance metric and develop a binary-quad tree to perform stratification. Experimental results show that our volumetric sampling method can generate light samples with a better temporal consistency. / Spherical map is the foundation for many applications in computer graphics, such as environment mapping, precomputed radiance transfer, radiosity and image-based rendering. For these applications that involve intensive computation on spherical domain, it is generally desirable to employ equal-area and uniform spherical maps as the underlying parameterization. However, equal-area spherical maps are less exploited in graphics. / Wan, Liang. / "August 2007." / Adviser: Tien-Tsin Wong. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1121. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 118-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Cálculos dos espectros (E,J ) e das propriedades eletromagnéticas (U,Q,BE2,BM1) são realizados para isótopos ímpares do Ni, e isótopos ímpares com N=82, empregando o modelo de camadas (MC), a aproximação BCS usual (uma e três quasipartículas), BCS com blocking (BBCS) e BCS projetada (PBCS). São examinadas, em detalhe, a importância das correlações de cinco quasipartículas e das correções introduzidas em BCS. Os graus de liberdade coletivos do caroço são introduzidos através do acoplamento quasipartículas cluster vibrador (ACQPV), de modo que nosso formalismo possibilita tanto a inclusão de blocking como a projeção em número de partículas no cluster de uma e três quasipartículas. São realizados cálculos comparativos entre a versão com blocking (BQPCV) e com projeção (PQPCV) para os espectros e as propriedades eletromagnéticas de isótopos ímpares do Zn. A versão projetada é aplicada a isótopos do Césio, na descrição dos estados 5/2+ gerados pelo acoplamento anômalo. / We calculate nuclear spectra (E,J ) and electromagnetic properties (U,,BE2,BM1) for odd Ni isotopes and N=82 odd nuclei, using the shell model (MC), the usual BCS approximation (one and three quasiparticles ), blocking (BBCS) and projected (PBCS) BCS. The effects of five quasiparticles correlations and BCS corrections are carefully investigated. We introduce the core collective degrees of freedom by the quasiparticle- cluster- vibration coupling (ACQPV) , in such a way that our treatment makes possible to introduce both blocking and particle- number- projection in one and three quasiparticle cluster. Blocking (BQPCV) and projected (PQPCV) versions are compared for spectra and electromagnetic properties of odd Zn isotopes . Projected version is applied to Cs isotopes, in order to describe the 5/2+ states generated by anomalous coupling.

Descritores moleculares são essenciais em muitas aplicações de física e química computacional, como na análise de similaridade entre ligantes baseada em sua estrutura. Harmônicos esféricos têm sido utilizados como descritores da superfície molecular por serem uma forma compacta de descrição geométrica e por possuírem um descritor invariante por rotação. Assim, este trabalho propõe um método de análise de similaridade estrutural entre ligantes no qual se modela a superfície de uma molécula através de uma expansão em harmônicos esféricos realizada pelo programa LIRA. Os coeficientes encontrados são utilizados para percorrer o banco de dados DUD-E, com descritores previamente calculados, utilizando Distância Euclidiana e diversos valores de corte para selecionar compostos mais semelhantes. O potencial do método é avaliado usando o Ultrafast Shape Recognition (USR) como método padrão, pelo fato de ser uma excelente e rápida métrica para análise da similaridade de ligantes. Foram selecionadas 50 moléculas de diferentes tamanhos e composição de forma a representar todos os grupos moleculares presentes na DUD-E. Em seguida, cada molécula foi submetida à busca de similares variando-se valores de corte para o LIRA em que o conjunto de moléculas selecionadas foi comparado com as selecionadas pelo USR através de um processo de classificação binária e criação e interpretação de curvas ROC. Além do benchmarking, foi realizada a análise das componentes principais para determinar quais descritores são os mais importantes e carregam as melhores informações utilizadas na descrição da superfície da molécula. A partir das componentes principais, foi realizado um estudo do uso de funções peso, associando mais importância aos descritores adequados, e a redução da dimensionalidade do banco de dados, seleção de um novo conjunto de autovetores que formam as bases do espaço vetorial e uma nova descrição das moléculas para o novo espaço, no qual cada variação foi avaliada através de um novo benchmarking. O LIRA se mostrou tão rápido quanto o USR e apresentou grande potencial de seleção de moléculas similares, para a maioria das moléculas testadas, pois as curvas ROC apresentaram pontos acima da linha do aleatório. Tanto a redução da dimensionalidade quanto o uso de funções de ponderação agregaram valor à métrica deixando-a mais veloz, no caso da redução da quantidade de descritores, e seletiva, em ambos os casos. Dessa forma, o método proposto se mostrou eficiente em mensurar a similaridade entre ligantes de forma seletiva e rápida utilizando somente informações a respeito da superfície molecular. / Molecular descriptors are essential for many applications in computational chemistry and physics, such as ligand-based similarity searching. Spherical harmonics have previously been suggested as comprehensive descriptors of molecular structure due to their properties, orthonormality and rotationally invariant. Here we proposed a ligand similarity analysis method where molecule\'s surface is modeled by an expansion in Spherical Harmonics, called LIRA, whose coefficient are used to perform a search in DUD-E database, with all descriptors previously calculated, measured by Euclidian Distance and different cutoff\'s values to select similar compounds. Method\'s potential is evaluated against Ultrafast Shape Recognition (USR), due to it is an excellent a fast metric to ligand similarity analysis, in a benchmarking. Fifty molecules are selected varying chemical composition and size to represent all molecular groups of DUD-E. After that, which one was submitted in a search with different values of cutoff for LIRA and the subset selected was compared with the ones selected by USR through binary classification and ROC curves analysis. Beyond benchmarking, it was performed a principal component analysis to identify which are the most valuable coefficient for shape description. Using principal components two other studies are made, weight functions are applied to descriptors, providing more value for those carry more information, and dimensionality reduction, where a subset of eigenvectors are select to form the new basis of the vector space and the new molecule\'s description was made in the new space, which variation was tested in a new benchmarking. Lira showed to be as fast as USR and a big potential to select similar molecules, for the majority of the molecules tested, because ROC curves had points over the random line. Dimensionality reduction and weight functions improved LIRA results raising velocity, due to the use of less descriptors to model molecule\'s surface, and the selection power, for both cases. In summary, the proposed method showed to be an efficient and fast tool for measure similarity between ligands based in molecular shape.

Over the past couple of decades interest in particle-stabilised emulsions or Pickering emulsions has greatly increased. When using particles as stabilisers, as opposed to surfactants, the interface becomes more rigid and this can lead to interesting physical properties. In addition, the resulting emulsions are found to be longer-lived garnering commercial interest. This thesis aims to explore the mechanical properties of some specific systems containing particle-stabilised interfaces. The main system investigated was the bicontinuous interfacially jammed emulsion gel or bijel. The bijel has two continuous interpenetrating liquid phases separated by a particle-stabilised interface. Therefore, the structure has a very large interface in a fairly small volume and the pore size is under the experimentalist's control giving it promise in a variety of applications, particularly those based on catalysis. The response of bijels stabilised by either spherical particles or anisotropic rod-shaped particles to centrifugal compression has been investigated in this thesis. It was found that, in both cases, the structure was distorted to create anisotropic particle-stabilised sheets orientated perpendicular to the force. The original method for fabricating bijels involves the arrested spinodal decomposition of partially miscible liquids. This method requires partially miscible liquid pairs and particles that are equally wetted by each phase. Due to these requirements, a new method for making bijels using mixing was developed by others and the bijel made by mixing has been tested with oscillatory rheology combined with imaging and squeeze flow experiments. It was found that at low strain the bijel displayed solid-like behaviour and the structure remained intact until well past the yielding point. In addition, two further systems were investigated. The first system was rod-shaped particle-stabilised emulsion droplets that stick together by particle bridging. Bridging is where one particle can stabilise two droplet interfaces, preventing coalescence and leading to droplet clusters. Particle bridging was found to occur regardless of shear rate, particle volume fraction and to some extent aspect ratio with these anisotropic rod-shaped particles. This behaviour is hypothesised to be a consequence of the charged nature of the silica surface above pH 2. The second system was large particle-stabilised water droplets that can sprout tubes by the partitioning of solute from a bath into the droplet. By using different solutes and mixtures of different alcohols, the key requirements for sprouting behaviour have been ascertained. The most important requirement was found to be achieving the correct balance between the interfacial tension and the amount of solute partitioning into the droplet.

This project explores systematic strategies for establishing a definitive mode of representation in drawing. These strategies are considered in the context of the subjectivities and contingencies of perceptual experience, the mediation of that experience and inherent limitations in representational language. The aim is to explore the possibilities of constructing two-dimensional artworks which serve to define or investigate perceptual processes, perspective devices and spatial relationships.

The thesis focuses on the development of an experimental set up for a recently developed failure recovery technique of spatial robot manipulators. Assuming a general configuration of the spatial robot arm, a task is specified. This task contains constraints on position, velocity and acceleration to be satisfied. These constraints are derived from contact and curvature specifications. The technique synthesizes the serial chain and tests if the task can be satisfied in case of a joint failure. An experimental set up was developed in order to validate the failure recovery technique. It includes a robot arm mounted on a movable platform. The arm and platform are controlled by NI sbRIO board and are programmed in LabVIEW. The experimental results of the failure recovery technique were obtained for the case of Elbow failure in robot manipulators. The thesis considers two applications of the synthesis of spherical five –degree-of-freedom serial chains: Power assist for human therapeutic movement and Synthesis of Parallel Mechanical Linkages. A spherical TS chain has been synthesized for these two applications using the Mathematica software.

A computational fluid dynamics model has been developed to study an oil-coated particle immersed in a uniform aqueous flow, to determine the conditions that favour oil separation. The governing flow equations are discretized using a finite volume approach, and the oil/water interface is captured using the Volume-of-Fluid (VOF) method in a 2D spherical coordinate system. The model predicts different mechanisms for oil separation. At a Reynolds number, Re, equal to 1, and at a low capillary number, Ca << 1, the high interfacial tension can induce rapid contact line motion, to the extent that the oil film can advance past its equilibrium position and separate from the particle. This mechanism requires that the contact angle measured through the oil phase is large. On the other hand, as Ca approaches 1, the shear exerted by the external flow stretches the oil into a thread that will eventually rupture and separate.

A computational fluid dynamics model has been developed to study an oil-coated particle immersed in a uniform aqueous flow, to determine the conditions that favour oil separation. The governing flow equations are discretized using a finite volume approach, and the oil/water interface is captured using the Volume-of-Fluid (VOF) method in a 2D spherical coordinate system. The model predicts different mechanisms for oil separation. At a Reynolds number, Re, equal to 1, and at a low capillary number, Ca << 1, the high interfacial tension can induce rapid contact line motion, to the extent that the oil film can advance past its equilibrium position and separate from the particle. This mechanism requires that the contact angle measured through the oil phase is large. On the other hand, as Ca approaches 1, the shear exerted by the external flow stretches the oil into a thread that will eventually rupture and separate.

Single crystalline silicon spheres have been used as alternative material for solar cell fabrication. This innovative technology has several advantages over traditional wafer technology. However, the material, process flow and characterization techniques are very different from the planar technology due to the spherical geometry. In material characterization, microwave photoconductivity decay is used to measure carrier lifetime. This technique is analyzed theoretically by mathematical treatment in this thesis. Furthermore, the carrier lifetime is measured in order to investigate rapid thermal grown oxide quality in the role of surface passivation of silicon sphere. A traditional way of making spherical cells is to create a p-n junction by high temperature diffusion of phosphorous dopants into p-type silicon spheres. To further reduce the fabrication cost, a low temperature epitaxial film highly doped with phosphorous is deposited on the sphere surface to form an emitter layer using Plasma Enhanced Chemical Vapour Deposition (PECVD). The process flow of device fabrication is very different from silicon wafer thus a new set of process steps are derived for silicon spheres. Two main device structures, omission of insulating layer and silicon nitride as insulating layer between emitter film and substrate, are proposed. The deposition parameters, pressure, power, and deposition time are optimized for spherical geometry. The quality of the junction is evaluated by its current-voltage characteristic and capacitance-voltage characteristic. The results are also compared to similar device structures in planar technology. To examine the photovoltaic performance, illuminated current-voltage measurement is taken to provide information on short circuit current, open circuit voltage and fill factor. Furthermore, spectral response of quantum efficiency is investigated to assess the ability of carrier collection for a spectrum of wavelength. Limitations on spherical diode performance are concluded from the measurement results.

A semiflexible polymer confined to a spherical surface is used as a basic model for understanding DNA conformation in restricted space. By means of Monte Carlo simulation for a bead-rod chain generated on a spherical surface, we find an ordered helicoidal phase at sufficiently high surface density and determine the critical density of the isotropic-helicoidal phase transition for various persistence lengths. We verify that the excluded volume effect is the key factor to cause the helicoidal state. In addition to Monte Carlo simulations, we utilize the model of wormlike chain with Onsager's excluded volume interaction and examine the Landau expansion of the free energy involving both the orientational and spatial order parameters. We also analytically figure out the critical density and transition gap for various ratios of persistence lengths of the polymer chain and the radius of spherical surface. The results from both simulation and analysis are consistent with each other.