The focus of this thesis is to provide an introduction to Lie groups—the study of continuous symmetries—and related concepts. Starting with topology and geometry, progressing through the construction of Cayley-Dickson algebras, the thesis ultimately explores a few of the most common Lie groups. Finally, geometric and visual interpretations of SO(3) and SU(2), as well as the relations between them, are investigated.

No description available.

[pt] Incrustações em trocadores de calor são inevitáveis e provocam a redução da sua efetividade térmica e aumento nos custos de bombeamento. Esta dissertação objetiva validar um dispositivo alternativo de limpeza de trocadores de calor, que automatiza o processo e não requer a interrupção do processo industrial que faz uso de trocadores. A motivação da pesquisa resultou do desafio imposto ao Programa de Metrologia da PUC-Rio para conceber uma solução inovadora para realizar a limpeza on-line de trocadores de calor de hidrogeradores, viabilizada com financiamento do setor elétrico e que motivou esta dissertação. A metodologia de desenvolvimento da pesquisa de mestrado perseguiu duas estratégias de otimização: (i) aprimorar a hidrodinâmica dos circuitos hidráulicos do dispositivo de limpeza concebido, visando reduzir custos de bombeamento e (ii) simular o número de ciclos mínimos de limpeza para assegurar que todos os tubos do trocador de calor sejam visitados por artefatos de limpeza. Dentre os resultados consolidados, destacam-se: (i) melhoria dos fluxos hidrodinâmicos nos distintos tramos hidráulicos do dispositivo servo-hidráulico de limpeza; (ii) confiabilidade metrológica do sistema de medição embarcada no equipamento e (iii) desenvolvimento de modelagem probabilística capaz de prever o número de ciclos de limpeza capaz de assegurar eficácia do procedimento de limpeza do trocador, o que contribui para o seu entendimento. Os ensaios de desempenho realizados em laboratório suportam a conclusão de que a pesquisa de mestrado foi capaz de validar e disponibilizar uma versão hidrodinamicamente mais eficiente e operacionalmente mais eficaz do dispositivo de limpeza originalmente concebido. / [en] Fouling in heat exchangers is inevitable and causes a reduction in their thermal effectiveness and an increase in pumping costs. This dissertation aims to validate an alternative heat exchanger cleaning device, which automates the process and does not require the interruption of the industrial process that uses exchangers. The motivation for the research resulted from the challenge imposed on the Metrology Program at PUC-Rio to devise an innovative solution to perform the online cleaning of hydrogenerator heat exchangers, made possible with financing from the electricity sector and which motivated this dissertation. The master s research development methodology pursued two optimization strategies: (i) improving the hydrodynamics of the hydraulic circuits of the designed cleaning device, aiming to reduce pumping costs and (ii) simulating the number of minimum cleaning cycles to ensure that all the tubes of the heat exchanger are visited by cleaning artefacts. Among the consolidated results, the following stand out: (i) improvement of hydrodynamic flows in the different hydraulic sections of the servo-hydraulic cleaning device; (ii) metrological reliability of the measurement system embarked in the equipment and (iii) development of probabilistic modeling capable of predicting the number of cleaning cycles capable of ensuring the efficiency of the exchanger cleaning procedure, which contributes to its understanding. The performance tests performed in the laboratory support the conclusion that the master s research was able to validate and make available a hydrodynamically more efficient and operationally more effective version of the cleaning device originally designed.

This study focuses on the role and contribution of women in the context of the social and economic development of two towns in Hertfordshire during the nineteenth century. Although the age saw an increase in urbanisation, Hertfordshire remained an agricultural county with long established land owners, a middle class with influence in the towns and its closeness to London attracting the newly wealthy in search of a country estate. The towns selected for this study, Hertford and Hitchin, changed little in their character and, compared with others which experienced industrial expansion, saw a modest population growth. This, however, brought the consequential pressures on housing and poverty. This research is unique in combining the study of the activities of women and the challenges faced by two market towns over a period of time of change and thus making a contribution to the debate on the concept of “separate spheres” by demonstrating that women had a place in the public arena. The daily life of a country town was reliant on a thriving economic environment. As this research demonstrates, many women had trades and businesses, contributed to good causes and were central to the education of children and adults. Their philanthropic efforts supported the building and maintenance of churches, schools, and hospitals. It charts the role of ordinary women, operating in a small town environment, before extension of the suffrage and Equal Opportunities legislation established their position as legitimate influencers of policy and practice. Little work has been done on how the English small town coped with its growth in population and the summons from central government on compliance with an increasing body of legislation on how the town should be run. It was men who undertook the necessary offices associated with this seed of local government but a micro-history of the people who inhabited these two towns demonstrates that women made a significant contribution to social and economic life of these towns.

Dans cette thèse nous avons étudié de nombreux aspects de la théorie des systèmes désordonnés. En particulier, nous avons étudié les systèmes vitreux. La description détaillée des systèmes désordonnés et vitreux est un problème ouvert en physique de la matière condensée. Dans le cadre de la théorie de champ moyen pour les verres structuraux nous avons étudié la théorie des fluctuations proche de la transition vitreuse dynamique. L’étude des fluctuations peut etre fait avec le formalisme statique de la théorie de répliques. Nous avons fait cela en introduisant une théorie des champs pour la transition vitreuse à partir du potentiel microscopique entre les particules. Nous avons étudié dans ce cadre les fluctuations au niveau gaussien et nous avons évalués les exposants critiques dans ces approximations. Nous avons aussi étudié la région de validité de la prédiction gaussienne avec l’introduction d’un critère de Ginzburg pour la transition vitreuse. Les résultats que nous avons obtenues ne sont valides que dans la région β. Pour obtenir des resultats dans la région α nous avons étudié la pseudodynamique de Boltzmann que a été introduit par Franz and Parisi. Nous sommes parti des équations de Ornstein-Zernike et nous avons obtenu un ensemble d’équations dynamiques. En utilisant l’approximation Hypernetted Chain nous avons obtenu un ensemble complet d’équations qui sont très similaires aux équations de la théorie de mode-coupling. La troisième partie de la thèse porte sur l’étude des états amorphes des sphères dures en hautes dimensions. Pour obtenir les exposants dynamique dans ce cas, nous avons étudié la stabilité du diagramme de phase 1RSB (one-step-replica-symmetry-breaking). Nous avons découvert que ce diagramme de phase possède une région où la solution 1RSB est instable. La région où la solution 1RSB est instable est connectée avec la description théorique de la physique de jamming des sphères dures et nous avons montré que l’instabilité 1RSB est responsable d’une transition de phase en haute densité. Cette transition s’appelle la transition de Gardner. Nous avons cherché une solution 2RSB et nous avons vu qu’il existait un point en densité après lequel on peut avoir une solution 2RSB (et aussi fullRSB). Nous avons étudié le diagramme de phase 2RSB dans la limite de jamming où la pression devient infini. Après la solution 2RSB nous avons cherché à décrire la solution fullRSB. Nous avons écrit les équations fullRSB et nous avons découvert qu’elles sont identiques aux equations que l’on a dans le cas de un modèle de verres de spins qui s’appelle modèle de Sherrington et Kirkpatrick. Nous avons aussi étudié la solution numerique des équations fullRSB dans la limite de jamming. Cette solution montre beaucoup des choses intéressantes. La plus importante est le comportement du mean square displacement dans la limite de jamming. Si l’on regard les résultats numériques et éxperimentaux, il semble que le plateau de le mean square displacement s’approche a zero comme la pression à un exposant proche de −3/2. Nous avons vu que la solution numérique des équations fullRSB est en mesure de reproduire ce comportement. La quatrième partie de la thése a porté sur la dynamique de mode-coupling dans le régime où la transition vitreuse devient continue. / In this thesis we have studied many aspects of the physics of disordered and glassy systems. The first part of the work is about the theory of dynamical fluctuations in the beta regime. When a system undergoes a dynamical arrest, it can be studied by introducing an appropriate dynamical correlation function that plays the role of the order parameter of the transition. To understand the collective effects underlying the glass transition we have studied the fluctuations of the order parameter on a time scale where the system is relaxed in a typical metastable glassy state. To do this we have seen that coming from the glass phase the system develops critical fluctuations with a diverging correlation length at the mean field level. We have thus derived an effective field theory by focusing only on them. This field theory can be used firstly to derive the mode-coupling exponent parameter that controls the relaxation of the dynamical correlation function when the system relaxes in a metastable glassy state. Moreover we can give a Ginzburg Criterion that can be used to determine the region of validity of the Gaussian approximation. These considerations are valid in the beta regime. To clarify what happens in the alpha regime we have studied a quasi-equilibrium construction, called Boltzmann-Pseudodynamics, recently introduced in order to describe with static techniques the long time regime of glassy dynamics. We have extended this formalism to structural glasses by producing a new set of dynamical equations. We have done this in the simplest approximation scheme that is called Hypernetted Chain. Two results have been obtained : firstly, we have computed the mode-coupling exponent parameter and we have shown that it coincides with the one obtained with the formalism of the first part of the thesis ; secondly we have studied the aging regime and we have derived that the condition that determines the fluctuation-dissipation ratio is a marginal stability one. In the third part of the thesis we have studied the theory of amorphous states of hard spheres in high dimensions. Hard spheres provide simple models of glasses and they are extensively studied for the jamming transition. In our framework jammed states can be thought as infinite pressure limit of metastable glassy states. During the last years it has been derived a mean field theory of hard spheres based on the 1RSB assumption on the structure of the free energy landscape. However it has been realized that this construction is inconsistent for what concerns the property of the packings at jamming. In the present work we have firstly investigated the possibility of an instability of the 1RSB solution and we have actually found that the 1RSB solution is unstable in the jamming part of the phase diagram. At the same time we have been able to compute the mode-coupling exponent parameter for this system. In order to go beyond the 1RSB solution we have first tried a 2RSB ansatz and then a fullRSB solution. We have derived a set of variational equations that are very close to the ones that have been derived in the Sherrington-Kirkpatrick model. We have solved numerically the equations and we have shown that the fullRSB solution seems to predict that the plateau value of the mean square displacement scale as the pressure to a power close to 3/2 as it seems to be predicted by scaling arguments and in contrast with the 1RSB predictions that show a scaling with the inverse of the pressure. The last chapter of the thesis is on the mode-coupling theory when the glass transition is becoming continuous. We have been able to show that in such a situation a detailed characterization of the solution of the equations can be obtained in the long time regime.

Esta pesquisa tem por objetivo investigar as aplicações das cônicas no processo de ensino e aprendizagem, dando uma ampla visão histórica e aplicada do conteúdo em questão. Serão dadas as definições, propriedades, equações e conceitos das cônicas. Classificaremos cônicas a partir de sua equação geral. Apresentaremos as esferas de Dandelin e daremos algumas aplicações das cônicas. / This research aims to investigate conic sections in the process of teaching and learning, providing a broad historic and applied view of the subject. It will be discussed definitions, properties, equations and concepts of the conic sections. We classify them from their general equation. We present the Dandelin spheres and provide applications of the conics.

Nenhuma / O processo sol-gel foi usado para nanoestruturar partículas de oxihidróxido de ferro e aprisiona-las na estrutura de micro-, meso- e macroporos + macroburacos (poros de dimensões micrométricas) da rede polimérica do PVA (álcool polivinílico). Esferas hidrogel de oxihidróxido de Fe-PVA com (3433 63 μm) e sem (2833 69 μm) macroburacos foram obtidas. Espectroscopia Mössbauer mostra que as esferas obtidas têm nanopartículas (majoritariamente ≤20 nm) de α-Fe2O3, -Fe2O3, α-FeOOH e fases ainda superparamagnéticas a 20 K. As esferas hidrogel obtidas possuem elevada estabilidade química e boa rigidez mecânica. Capacidade adsortiva: 77,9 e 204,9 mgF/g, respectivamente para as esferas hidrogel sem (bom ajuste aos modelos de Langmuir e Freundlich) e com (bom ajuste ao modelo de Freundlich) macroburacos. Nos dois tipos de esferas, o mecanismo de quimissorção é predominante, mas o modelo de difusão intrapartícula sugere que o mecanismo de adsorção é mais complexo. Quatro ciclos de adsorção no modo coluna mostram uma pequena queda da eficiência de captura do F de 61,8 para 56,2%; neles, dessorção com solução NH3 min. 25% em peso mostra uma eficiência variando entre 95,8 e 98,8%. A estratégia de nanoestruturar as partículas de oxihidróxido de ferro e introduzir macroburacos na rede polimérica do PVA foi eficaz e realmente reforçou a captura do F. / The sol-gel process was used to nanostructure iron oxyhydroxide particles and to trap them into the structure of micro-, meso-, and macropores + macroholes (micrometer size pore) of the PVA (polyvinyl alcohol) polymeric network. Iron oxyhydroxide-PVA hydrogel spheres with (3433 63 microns) and without (2833 69 microns) macroholes were obtained. Mössbauer spectroscopy shows that the obtained spheres have nanoparticles (mainly ≤20 nm) of α-Fe2O3, -Fe2O3, α-FeOOH, and phases still superparamagnetic at 20 K. The obtained hydrogel spheres have high chemical stability and good mechanical rigidity. Adsorptive capacity: 77.9 and 204.9 mgF/g, respectively for the hydrogel spheres without (fit well by the Langmuir and Freundlich models) and with (fit well by the Freundlich model) macroholes. In both types of spheres, the chemisorption mechanism is predominant, but the intraparticle diffusion model suggests that the adsorption mechanism is more complex. Four cycles of adsorption in the column mode show a small decrease of F capture efficiency from 61.8 to 56.2%; therein, desorption with NH3 solution min. 25 wt% shows an efficiency ranging between 95.8 and 98.8%. The strategy to nanostructure particles of iron oxyhydroxide and to introduce macroholes into the PVA polymer network was effective and really reinforced the F capture. Keywords: fluorine;

Estudamos inicialmente resultados de classificação de difeomorfismos de produtos de esferas de mesma dimensão. Tratado isto, estudamos os mergulhos suaves de produtos de três esferas, sendo a primeira de dimensão um e as demais de dimensão maior ou igual a um, com a dimensão da última maior ou igual a da segunda, em uma esfera em codimensão um, e buscamos a total caracterização do fecho das duas componentes conexas do complementar de tais mergulhos. Tratamos com enfoque especial os mergulhos do produto de três esferas de dimensão um na esfera de dimensão quatro, e, finalmente, estudamos problemas de classificação de mergulhos PL localmente não-enodados de somas conexas de toros em codimensão um. / We study initially results of classification of difeomorfisms of Cartesian products of spheres of same dimension. Treated this, we study the smooth embeddings of cartesian products of three spheres, being the first one of dimension one and excessively of bigger or equal dimension to one, with the dimension of the last equal greater or of second, in a sphere in codimension one, and search the total characterization of the latch of the two connected components of complementing of such embeddings. We deal with special approach the embeddings of the product to three spheres to dimension one in the sphere dimension four, and, finally, we study problems of classification of PL locally unknotted embeddings of connected sums of torus on codimension one.

Neste trabalho,apresentamos um breve compêndio sobre o estudo topológico das fibras de Milnor. Abordamoso caso clássico, estudado por J. Milnor, e a generalização apresentada por Lê D. T. para o caso de germes de funções analíticas definidas em variedades singulares. Nestas duas situações, os resultados principais tratam de germes de funções com singularidades isoladas / In this work, we present a brief compendium about the topological study of J. Milnor fibers. We address the classic case, studied by Milnor, and the generalization presented by Lê D. T. for the case of germs of analytic functions defined on singular varieties. In both situations, the main results deal with germs of functions with isolated singularities

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-09-18T15:23:14Z No. of bitstreams: 2 Tese Karoline V Fernandes.pdf: 2432359 bytes, checksum: a5e472f248ce707b5697190ca4b6d33e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-18T15:39:54Z (GMT) No. of bitstreams: 2 Tese Karoline V Fernandes.pdf: 2432359 bytes, checksum: a5e472f248ce707b5697190ca4b6d33e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-18T15:39:54Z (GMT). No. of bitstreams: 2 Tese Karoline V Fernandes.pdf: 2432359 bytes, checksum: a5e472f248ce707b5697190ca4b6d33e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-09-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study surfaces M in hyperbolic space whose mean curvature H and Gaussian curvature KI satisfy the relation 2(H 􀀀1)e2μ +KI(1􀀀e2μ) = 0; where μ is a harmonic function with respect to the quadratic form s = 􀀀KII + 2(H 􀀀 1)II; and I, II denote, respectively, the first and second quadratic form of M. These surfaces are called Generalized Weingarten surfaces of harmonic type (HGW-surfaces). We obtain a representation type Weierstrass for these surfaces that depend on three holomorphic functions. As an application we obtain a representation type Weierstrass for Bryant surfaces and classify all HGW-surfaces of rotation. / Neste trabalho estudamos superfícies M no espaço hiperbólico cuja curvatura média H e a curvatura Gaussiana KI satisfazem a relação 2(H􀀀1)e2μ+KI(1􀀀e2μ) = 0; onde μ é uma função harmônica com respeito a forma quadrática s = 􀀀KII +2(H 􀀀1)II; onde I e II são respectivamente a primeira e segunda forma quadrática de M. Estas superfícies serão chamadas de Superfícies Weingarten generalizada tipo harmônico (Superfícies-WGH). Obtemos uma representação tipo Weierstrass para estas superfícies que dependem de três funções holomorfas. Como aplicação obtemos uma representação tipo Weierstrass para superfícies de Bryant e classificamos as superfícies-WGH de rotação.