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Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The availability of laser systems capable of generating ultrashort optical pulses in the visible spectral range have made it possible to study molecular species with a temporal resolution in the order of intra-molecular dynamics which previously were not accessible. Henceforth, in this study a popular pump-probe technique called ultrafast transient absorption spectroscopy (UTAS) is employed to study the initial photochromic reaction of metal complex, dithizonatophenylmercury (II) (DPM) under various conditions. These conditions include the use of different solvents and electronically altering DPM by the addition of substituents with specific electron affinity properties. For this study the photochromic behaviour of DPM dissolved in methanol is used as standard. Using this standard, the initial photochromic reaction after ultrafast excitation within less than 100 fs caused a radiationless photoreaction with a time constant of about 2 ps, which is interpreted as C=N isomerization along the twist coordinate. It is found that during this isomerization reaction an orthogonally twisted intermediate state was formed and observed through its excited-state absorption, which funnels through a conical intersection onto the ground state potential. Once here, bifurcation along pathways towards the ground states of the reactant and product configurations occurs. This was the first observation of photochromism for DPM in a strong polar solvent such as methanol. From the results of the test compound in methanol, comparisons to the photo-behaviour of DPM dissolved in deuterated methanol and dichloromethane are made. What is established is that changing the solvent resulted in slightly different decay times as well as spectral shifts in the absorption profile which suggested that the potential energy surface of the excited state is modified. This is similar to the results found from the electronically altered DPM species. Here the entire photoreaction is found to either be sped up (1 ps) or slowed down (4 ps) depending on the sample investigated. Previous studies on the photochromicity of DPM like systems concluded that apart from the photo-activated forward reaction, a back reaction occurs in the absence of light. Therefore a detailed look at the back reaction of DPM and its derivatives are also studied. This is done by temporally monitoring the absorption change of the photo-product as it converts back to the reactant. In doing so the lifetime of the photo-product is determined and found to differ greatly depending on the solvent and substituent used. Lastly, in assuming that the back reaction follows first order kinetics, an Arrhenius type measurement on the photo-product of DPM is conducted. The result of this measurement is that a potential energy barrier of 64.8 kJ/mol is overcome in the back reaction. The measurements performed and the results obtained from the photochromicity of DPM contribute to the understanding of photo-induced cis-trans isomerization reactions about a C=N double bond. / AFRIKAANSE OPSOMMING: Die beskikbaarheid van laser sisteme in staat om ultrakort optiese pulse te genereer in die sigbare spektrale gebied, het die studie van molekulˆere spesies met ’n tydresolusie in die orde van intra-molekulˆere dinamika wat voorheen nie toeganklik was nie. Voortaan, in hierdie studie word ’n populˆere aktiveer-interogeer tegniek genaamd ultravinnige tydafhanklike absorpsie spektroskopie (UTAS) aangewend om die aanvanklike fotochromiese reaksie van die metaal kompleks, ditisoonfenielkwik (II) (DFK) onder verskillende kondisies te bestudeer. Hierdie kondisies sluit in die gebruik van verskillende oplosmiddels en die elektroniese verstelling van DFK deur die toevoeging van substituente met spesifieke elektron affiniteit eienskappe. Vir hierdie studie word die fotochromiese gedrag van DFK, opgelos in metanol, as standaard gebruik. Met hierdie standaard, word gevind dat die aanvanklike fotochroom reaksie na ultravinnige opwekking binne minder as 100 fs, ’n stralingslose fotoreaksie met ’n tydkonstante van 2 ps veroorsaak. Hierdie fotoreaksie word verklaar as die C=N isomerisasie met betrekking tot die draai ko¨ordinaat. Daar is ook gevind dat gedurende hierdie isomerisasie reaksie, ’n ortogonaal verdraaide oorgangstoestand gevorm word wat waargeneem is deur sy absorpsie in die opgewekte toestand wat tregter deur ’n koniese kruispunt na die potensiaal van die grondtoestand. By hierdie punt vurk die proses na die grondtoestande van die reaktant en die produk vorme. Di´e was die eerste waarneming van fotochromisme van DFK opgelos in ’n sterk polˆere oplosmiddel soos metanol. Vanuit die resultate vir die toets mengsel in metanol word vergelykings getrek tot die fotogedrag van DFK opgelos in gedeureriese metanol en dichlorometaan. Wat hieruit vasgestel is, is dat die verandering in oplosmiddel wel die fotoreaksie be¨ınvloed deurdat verskillende vervaltye en spekrale verskuiwings in die apsorpsie profiel waargeneem word. Hierdie verskille dui aan dat die potensie¨ele energie oppervlakte van die opgewekte toestand wel gemodifiseer word. Dit is ook soortgelyk aan die resultate vir die elektronies verstelde BFK spesies. Hier is gevind dat die tempo van die totale fotoreaksie `of toeneem (1 ps) `of afneem (4 ps) afhanklik van die spesifieke spesie wat bestudeer word. Vorige studies van die fotochromiese gedrag van sisteme soortgelyk aan DFK het gevind dat behalwe vir die fotogeaktiveerde voorwaartse reaksie, daar ook ’n keersy reaksie plaasvind in die afwesigheid van lig. Dus word die keersy reaksie vir DFK en sy derivate ook in detial bestudeer. In hierdie studie word die absorpsie verskille van die fotoproduk tydelik waargeneem soos dit terugkeer na die reaktant. Op hierdie manier word die leeftyd van die fotoproduk bepaal en gevind dat dit grootliks afhang van die tipe oplosmiddel en tipe substituent wat gebruik word. Ten slote, wanneer daar aanvaar word dat di´e keersy reaksie eerste orde kinetika volg, word ’n Arrhenius tipe meting op die fotoproduk uitgevoer. Die resultaat van hierdie meting is dat ’n potensie¨ele enrgie versperring van 64.8 kJ/mol oorkom word in die keersy reaksie. Die metings wat uitgevoer is en die resultate wat verkry is van die fotochromiese gedrag van DFK dra by tot die verstandhouding van lig-ge¨ınduseerde cis-trans isomerisasie reaksies rondom ’n C=N dubbelbinding.

The late University of Canterbury civil engineering lecturer Peter Giddens developed a range of simple microhydro turbines, with publications from as early as the 1980s. He considered that a range of simple but well-designed turbines which covered the gamut of possible small sites would be more useful than any single turbine. He started with radial inflow turbines, then set about extending their range of applicability by increasing specific speed. That extension was continued by the research in this thesis, which aimed to produce a design with a minimum efficiency of 70 % at a specific speed of at least 600 (rev/min, kW, m). Achieving those targets would differentiate it from existing microhydro designs. In order to reach those performance targets, the volute, runner, and draft tube were examined through experiment and computational fluid dynamics models to characterize past designs and test the validity of their embodied assumptions. A prototype with a design specific speed of 650 was built and fully characterized by dynamometer testing. Measurements of the outlet velocity distribution of two of Peter Giddens’s volutes confirmed that single tangential inlet volutes are not torque-free when certain geometric conditions are met; swirl increased through those volutes by 70 % or more depending on the design. A new overall turbine design was proposed, where axial flow enters the runner and swirling flows leaves it. This required the design of a novel volute. Through computational analysis, the effect of swirling flow entering the conical draft tube was shown to affect its pressure recovery: negatively for draft tubes with small angles, positively for larger angles. It was shown that the peak pressure recovery of an optimum draft tube was not likely to be improved upon by the use of swirl, and since there was uncertainty in the analysis, a conservative draft tube was specified for the prototype. A flat-bladed runner was designed for the prototype and computational modeling indicated its performance would be sensitive to small changes in flow angle. Despite that sensitivity — an intrinsic property of high specific speed runner velocity triangles — the computational model was shown to give good predictions of the runner flow characteristics, although not its effciency. Finally, a 1.2 kW prototype was built and achieved a peak net effciency of 64 % as defined by the American Society of Mechanical Engineers at a net head of 2.07 m, a flowrate of 94 L/s, and a runner shaft speed of 1670 rev/min, corresponding to a specific speed of 740. Maximum measured runner efficiency of 87 % also occurred at those conditions. Compared to existing designs, that performance extended the operational envelope of microhydro turbines considerably. A three-zone computational model of the entire prototype was assembled and trialled, but not validated. It is concluded that for efficient high specific speed turbines, volute swirl characteristics must be known with confidence, as the volute sets the conditions at the leading edge for peak runner efficiency. A simple but efficient runner may be made using flat blades, showing the potential for this geometry even when made by limited workshops. Adding a free-vortex tangential velocity distribution to the inlet flow of a stalled conical draft tube may increase its pressure recovery, although it is not likely to exceed the best performance obtainable with axial inlet flow. Therefore taking measures to reduce the peak fluid velocity entering the draft tube could be more beneficial to overall performance than seeking outright improvements in draft tube pressure recovery.

Nanoindentation has become a widely used technique to measure the mechanical properties of materials. Due to its capability to deform materials in micro- and nano-scale, nanoindentation has found more applications in characterizing the deformation behavior and determining the mechanical properties of thin films and coatings. This research deals with the characterization of samples received from Center for Advanced Microstructures and Devices (CAMD) and Integran Technologies Inc., Toronto, Canada and the objective of this investigation was to utilize the experimental data obtained from nanoindentation to determine the deformation behavior, mechanical properties of thin films on substrates and bulk materials, and the effect of geometrically different indenters (Berkovich, cubecorner, and conical). X-ray diffraction (XRD), transmission electron microscope (TEM), scanning electron microscopy (SEM), and atomic force microscopy (AFM) analysis were performed on these materials to determine the crystal orientation, grain size of the material, and also to measure any substrate effects like pile-up or sin-in respectively. The results indicate that indentation size effect (ISE) strongly depends on shape of the indenter and less sensitive to penetration depth where as the hardness measurements depends on shape of indenter and depth of penetration. There is a negligible strain rate dependency of hardness at deeper depths and a significant increase in the hardness due to the decrease in grain size and results also indicate that there is no significant substrate effect on thin films for 10% and 20% of film thicknesses. Nanocrystalline material could not validate a dislocation based mechanisms deformation for indentation made by cubecorner and conical indenters in depths less than 1mm.

In this work we study two problems about parabolic partial differential equations on Riemannian manifolds with conical singularities. The first problem we are concerned with is the existence and regularity of solutions to the Cauchy problem for the inhomogeneous heat equation on compact Riemannian manifolds with conical singularities. By introducing so called weighted Hölder and Sobolev spaces with discrete asymptotics, we provide a complete existence and regularity theory for the inhomogeneous heat equation on compact Riemannian manifolds with conical singularities. The second problem we study is the short time existence problem for the generalized Lagrangian mean curvature flow in almost Calabi-Yau manifolds, when the initial Lagrangian submanifold has isolated conical singularities that are modelled on stable special Lagrangian cones. First we use Lagrangian neighbourhood theorems for Lagrangian submanifolds with conical singularities to integrate the generalized Lagrangian mean curvature flow to a nonlinear parabolic equation of functions, and then, using the existence and regularity theory for the heat equation, we prove short time existence of the generalized Lagrangian mean curvature flow with isolated conical singularities by letting the conical singularities move around in the ambient space and the model cones to rotate by unitary transformations.

Este trabalho é um estudo realizado em torno das principais curvas cônicas estudadas por alunos do ensino básico: parábola, elipse e hipérbole. A ideia central do trabalho é a autosuficiência, pois apresentamos todas as ferramentas matemáticas necessárias para o entedimento desses entes e suas aplicações, desde os axiomas iniciais da geometria plana até as definições formais das cônicas e demonstrações de suas propriedades. Espera-se que uma pessoa não especializada em matemática, ao ler o trabalho, entenda toda a matemática no entorno das aplicações dessas cônicas. / This work is a study carried out around the main conic curves studied by elementary school students: parabola, ellipse and hyperbola. The main idea of this work is to be self-contained, starting from the basic axioms from the geometry and after we present formal definitions, properties and applications of conics in the everyday life. It is expected that a person that is not a specialist in mathematics, are able to read and understand all the mathematics in the surroundings of the applications of these conics.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-02-16T12:25:44Z No. of bitstreams: 1 Carlos Alberto Fernandes de Siqueira.pdf: 3351578 bytes, checksum: f97afcc5c4cc8147eb94e446d14eee69 (MD5) / Made available in DSpace on 2017-02-16T12:25:44Z (GMT). No. of bitstreams: 1 Carlos Alberto Fernandes de Siqueira.pdf: 3351578 bytes, checksum: f97afcc5c4cc8147eb94e446d14eee69 (MD5) Previous issue date: 2016-12-01 / Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP / This research aims to construct a mathematical and didactic study of the conics in the scope of Geometry and Analytical Geometry from the outline of the methodology of the bibliographic research, in which we analyze documents that have already received an analytical treatment such as official documents of basic education, books, Dissertations, theses and articles related to the research topic. This analysis allowed the development of the research problem and the guiding question: How can the Frames, Viewpoints and Semiotic Representation Registers be articulated for the teaching of Conics in the basic cycle? In order to answer it we are based on the notions of Frames and Frames game, the Theory of Semiotic Representation Records and the notions of Viewpoints. In this sense, we verified that the articulation sought in the research question should consider the Tables of Geometry and Analytical Geometry, the View of the intersection between cone and straight circular plane, the View of the Geometric Place, the Point of View of Eccentricity And the Analytical Point of View, in addition to the Records of Semiotic Representation material, figural, figural dynamic, graphic and algebraic, as well as to seek treatments and conversions associated with these points of view. We point out for future investigations, that can carry out a study like this with a focus on higher education, considering the notions of Envolvente, Descriptive Geometry and Linear Algebra and studies that develop a didactic engineering with third year high school students and the organization of A teacher training, using this study as a basis to explore other relevant aspects that may complement this research / Esta pesquisa tem por objetivo construir um estudo matemático e didático das cônicas no âmbito da Geometria e da Geometria Analítica a partir do delineamento da metodologia da pesquisa bibliográfica, na qual analisamos documentos que já receberam um tratamento analítico tais como documentos oficiais da educação básica, livros, dissertações, teses e artigos relacionados ao tema de investigação. Esta análise permitiu o desenvolvimento da problemática da pesquisa e da questão norteadora: Como os Quadros, os Pontos de Vista e os Registros de Representação Semiótica podem ser articulados para o ensino de Cônicas no ciclo básico? Para respondê-la nos baseamos nas noções de Quadros e Jogo de Quadros, na Teoria dos Registros de Representação Semiótica e nas noções de Pontos de Vista. Neste sentido, verificamos que a articulação buscada na questão de pesquisa deve considerar os Quadros da Geometria e da Geometria Analítica, o Ponto de Vista da interseção entre cone e plano circular reto, o Ponto de Vista do Lugar Geométrico, o Ponto de Vista da Excentricidade e o Ponto de Vista Analítico, além dos Registros de Representação Semiótica material, figural, dinâmico figural, gráfico e algébrico, bem como buscar tratamentos e conversões associados a estes pontos de vista. Pontuamos para futuras investigações, que possam realizar um estudo como esse com foco no ensino superior, considerando as noções de Envolvente, de Geometria Descritiva e de Álgebra Linear e estudos que desenvolvam uma engenharia didática com alunos da terceira série do ensino médio e a organização de uma formação de professor, utilizando como base este nosso estudo de modo a explorar outros aspectos relevantes que possam complementar esta pesquisa

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-04-19T13:56:14Z No. of bitstreams: 1 PDF - Edison Fernando da Silva Lima.pdf: 9125981 bytes, checksum: 332497337ebe6b4a6871009d22dde972 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T20:24:27Z (GMT) No. of bitstreams: 1 PDF - Edison Fernando da Silva Lima.pdf: 9125981 bytes, checksum: 332497337ebe6b4a6871009d22dde972 (MD5) / Made available in DSpace on 2016-07-22T20:24:34Z (GMT). No. of bitstreams: 1 PDF - Edison Fernando da Silva Lima.pdf: 9125981 bytes, checksum: 332497337ebe6b4a6871009d22dde972 (MD5) Previous issue date: 2015-05-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this course conclusion work we will of conic approach in the study of analytic geometry and treat procedures in order to recognize the nature of the general equation of a curve of the second degree two variables, performing the analysis of the coefficients of your equation by an algebraic process. Simplification of calculations involved as well as the graphics sketch, the mathematical application Maple 18 will be used. Our aim is to develop students’ ability to relate and better secure the maths contents, since such an approach is not worked in textbooks the high school level. / Neste trabalho de conclusão de curso faremos uma abordagem das cônicas no estudo da Geometria Analítica e trataremos de procedimentos com a finalidade de se reconhecer a natureza da equação geral de uma curva do segundo grau a duas variáveis, realizando a análise dos coeficientes de sua equação por um processo algébrico. Na simplificação dos cálculos envolvidos, bem como no esboço de gráficos, será usado o aplicativo matemático Maple 18. Nosso intuito é desenvolver a habilidade dos alunos em relacionar e melhor fixar os conteúdos matemáticos abordados, visto que, tal abordagem não é trabalhada nos livros didáticos a nível de ensino médio.

Antennas play a crucial role in communication systems since they are the transmitting/receiving elements that transition information from guided transmission to open-space propagation. Antennas are used in many different applications such as aerospace communications, mobile phones, TVs and radios. Since the dimensions of antennas are usually physically proportional to the wavelength at their operating frequencies, it is important to develop large antennas and arrays that can be stowed compactly and easily deployed. Also, it is important to minimize the number of antennas on a platform by developing multifunctional antennas. The first aim of this research is to develop new deployable, collapsible, light-weight and robust reconfigurable antennas based on origami principles. All designs will be validated through simulations and measurements. Paper as well as other substrates, such as, Kapton and fabric, will be used to develop our origami antennas. The second aim of this research is to derive integrated analytical and simulation models for designing optimal origami antennas for various applications, such as, satellite or ground communications. This dissertation presents research on origami antennas for novel reconfigurable communication systems. New designs of reconfigurable monofilar, bifilar and quadrifilar antennas based on origami cylinders are developed and validated. Novel fabrication methods of origami antennas are presented with detailed geometrical analysis. Furthermore, multi-radii origami antennas are proposed, analyzed, fabricated and validated and they exhibit improved circular polarization performance and wide bandwidths. An actuation mechanism is designed for these antennas. For the first time, a low-cost and lightweight reconfigurable origami antenna with a reflector is developed here. In addition, an array is developed using this antenna as its element. Finally, a kresling conical spiral antenna and a spherical helical antenna are designed with mode reconfigurabilities.

The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.