Dissertationen zum Thema „Linear and non-linear geometries“

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
We review some relevant examples for String Theory of non-linear sigma models. These are bosonic strings propagating in curved background, the Wess-Zumino-Witten model and superstrings in flat and AdS superspace. The mathematical tools required for the study of these models (e.g. topological quantization, Cartan geometry, Lie superalgebras and geometry on coset spaces) are also described. Throughout the dissertation we have focused on classical aspects of these models such as the construction of the action and its symmetries where conditions for holomorphic symmetry of the bosonic string case were found.
Nesta dissertação estudamos alguns exemplos de modelos sigma não lineares em Teoria de cordas. Estes são a corda bosónica se propagando em espaços curvos, o modelo Wess-Zumino-Witten e supercordas em superespaço plano e AdS. As ferramentas matemáticas que se precisam para o estudo destes modelos (e.g. quantização topológica, geometria de Cartan, super-álgebras de Lie e geometria em espaços coset) também são descritas. Ao longo desta dissertação focamos os aspectos clássicos destes modelos tais como a construção da ação e suas simetrias onde condições para serem estas holomorficas no caso da corda bosónica foram achadas.

Orientador: Andrei Mikhailov
Resumo: We review some relevant examples for String Theory of non-linear sigma models. These are bosonic strings propagating in curved background, the Wess-Zumino-Witten model and superstrings in flat and AdS superspace. The mathematical tools required for the study of these models (e.g. topological quantization, Cartan geometry, Lie superalgebras and geometry on coset spaces) are also described. Throughout the dissertation we have focused on classical aspects of these models such as the construction of the action and its symmetries where conditions for holomorphic symmetry of the bosonic string case were found.
Mestre

Alors que l'image sous toutes ses formes s'est désormais imposée dans la vie quotidienne de chacun d'entre nous, les capteurs d'images sortant du classique modèle perspectif à point de vue unique se banalisent jusqu'à devenir les pièces maîtresses de nombreux produits de hautes technologies, à destination d'industries comme du grand public. Qu'ils soient bio-inspirés, se rapprochant des rétines artificielles ou à large champs de vue, grâce à des lentilles ou à des miroirs, l'utilisation des images acquises pas ces appareils nécessitent des modèles qui, jusqu'à présent, ont été construits comme des généralisations des modèles pré-existants et considèrent qu'un capteur d'images réalise un mapping d'un monde en trois dimensions vers une image plane, reliant chaque point de l'image par un rayon à son antécédent dans l'espace. Tous ces capteurs souffrent pourtant de résolutions variables telles, que l'approximation du champ de vue du pixel comme un rayon de lumière pose de réels problèmes dans leur utilisation. Cette thèse présente une triple approche pour la caractérisation de ces capteurs, la première inspirée de l'architecture biologique de la rétine, la seconde est un modèle générique de caméra utilisant les Algèbres Géométriques et une méthode qui en permet le calibrage, quelque soit le type de caméra employé, et la troisième montre que considérer ces ouvertures angulaires pour chaque pixel d'un point de vue projectif permet de retrouver certaines caractéristiques du capteur, de s'affranchir des distortions optiques, et enfin d'obtenir des images après remapping, correspondant à celles qui auraient été prises si le capteur avait été parfaitement perspectif

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 100-102).
When conveying geospatial information via natural language, people typically combine implicit, commonsense knowledge with explicitly-stated information. Usually, much of this is contextual and relies on establishing locations by relating them to other locations mentioned earlier in the conversation. Because people and objects move through the world, a common and useful kind of geospatial phrase is the path expression, which is formed by designating multiple locations as landmarks on the path and relating those landmarks to one another in sequence. These phrases often include nongeospatial information, and the paths often include linear entities. This thesis builds upon the work done for the GeoCoder spatial reasoning system, by addressing several of its limitations and extending its functionality.
by John Javier Marrero.
M.Eng.

Nos últimos anos, materiais orgânicos tem ganhado grande interesse em áreas que envolvem espectroscopia óptica não linear. Isso se dá devido aos materiais possuirem consideráveis efeitos ópticos não lineares, apresentarem facilidade de síntese e possuirem propriedades fotofísicas e fotoquímicas que os tornam capazes de serem empregados em um vasto número de possíveis aplicações. Entre os materiais orgânicos, é possível destacar as Porfirinas e Ftalocianinas. A síntese desses materiais possibilita um grande número de classes ou grupos distintos, os quais podem ser distinguidos por suas estruturas periféricas e/ou íons metálicos que podem ser inseridos no interior dos macrociclos. Isso resulta em alterações das suas propriedades ópticas, ou seja, através de alterações das estruturas químicas das Porfirinas e Ftalocianinas é possível modelar suas propriedades ópticas, e assim, de acordo com essas propriedades, discriminar em quais aplicações podem ser empregados. Tais materiais, tendo em vista suas propriedades fotofísicas, podem ser empregados como fotossensitizadores na terapia fotodinâmica, células solares, limitadores ópticos ou fotobactericidas entre outras mais. Sendo assim, nesta Dissertação de Mestrado é realizado uma caracterização espectroscópica linear e não linear desses materiais, para assim deterinar propriedades ópticas específicas que podem ser empregadas nas aplicações citadas. Para tal caracterização espectroscópica, foram empregadas técnicas de espectroscopia linear e não linear, dentre elas a técnica de Varredura-Z foi empregada em três configurações distintas (Varredura-Z por Pulso Único, por Trem de Pulsos e por Luz Branca Supercontínua) para determinação de absorções de estados excitados. Tempos de vida de fluorescência, tempos de decaimento radiativo e de conversão interna, seções de choque de absorção de estado singleto e tripleto (fundamental e excitado) e eficiências quânticas (fluorescência, conversão interna e converção para tripleto) foram os parâmetros determinados e, assim, através desses parâmetros, foi possível entender como alterações nas estruturas químicas (periféricas e íons metálicos) influenciam consideravelmente as propriedades de Porfirinas e Ftalocianinas.
In last years, organic materials have won great interest in areas involving non-linear optical spectroscopy. This is due to the fact that the materials have considerable non-linear optical effects, are easy to synthesize, and have photophysical and photochemical properties that make them capable of being used in a wide range of possible applications. Among the organic materials, it is possible to highlight Porphyrins and Phthalocyanines. The synthesis of these materials enables a large number of distinct classes or groups, which can be distinguished by their peripheral structures and / or metal ions that can be inserted into the macrocycles. It results in changes of its optical properties, that is, replacing the chemical structures of such Porphyrins and Phthalocyanines, it is possible to tune its optical properties, and thus, according to these properties, to discriminate in which applications they can be used. Such materials, in view of their photophysical properties, can be used as photosensitizers in photodynamic therapy, solar cells, optical limiters or photobactericides among others. Thus, in this Master\'s Dissertation, a linear and nonlinear spectroscopic characterization of these materials is carried out in order to determine specific optical properties that can be employed in the cited applications. For this spectroscopic characterization, linear and nonlinear spectroscopy techniques were employed, among them the Z-Scan technique was employed in three distinct configurations (Z-Scan by Single Pulse, by Pulse Train and by Supercontinuum White Light) for determination of absorptions of excited states. Fluorescence lifetimes, radiative decay and internal conversion times, single and triple triplet (fundamental and excited) and quantum efficiencies (fluorescence, internal conversion, and triplet formation) were the parameters determined, and with these parameters, it was possible to understand how changes in the chemical structures (peripheral and metallic ions) modify considerable the optical properties of Porphyrins and Phthalocyanines.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
A análise das ressonâncias internas em sistemas estruturais contínuos é uma das principais áreas de pesquisa no campo da dinâmica não linear. A ressonância interna entre dois modos de vibração ocorre quando a proporção de suas frequências naturais é um número inteiro. De particular importância, devido à sua influência na resposta estrutural, é a ressonância interna 1:1, geralmente associada às simetrias do sistema, a ressonância interna 1:2, devida às não linearidades quadráticas e a ressonância 1:3 decorrente de não linearidades cúbicas. A ressonância interna permite a transferência de energia entre os modos de vibração relacionados, levando geralmente a novos fenômenos com profunda influência sobre a estabilidade da resposta dinâmica. As cascas de revolução geralmente exibem ressonâncias internas devido à inerente simetria circunferencial e um denso espectro de frequência em sua faixa de frequências mais baixas. Isso pode levar não apenas a ressonâncias internas do tipo m:n, mas a múltiplas ressonâncias internas. Nesta tese é realizada a análise de múltiplas ressonâncias internas em cascas cilíndricas delgadas, em particular as ressonâncias internas de 1:1:1:1 e 1:1:2:2 são investigadas em detalhes, um tópico pouco explorado na literatura técnica. A investigação de ressonâncias internas em sistemas contínuos geralmente é realizada usando modelos discretos de baixa dimensão. Embora alguns trabalhos anteriores tenham investigado ressonâncias internas do tipo m:n em cascas cilíndricas, muitos resultados não são consistentes, uma vez que os modelos discretos derivados não consideram os acoplamentos modais devido a não linearidades quadráticas e cúbicas. Aqui, usando um procedimento de perturbação, expansões modais consistentes são derivadas para um número arbitrário de modos de interação, levando a modelos de baixa dimensão confiáveis. A precisão desses modelos é corroborada usando o método Karhunen-Loève. Finalmente, é bem sabido que pequenas imperfeições geométricas da ordem da espessura da casca têm uma forte influência na sua resposta não linear. No entanto, sua influência nas ressonâncias internas, instabilidade dinâmica e transferência de energia é desconhecida. Assim, a influência de diferentes tipos de imperfeição modal é devidamente considerada na presente análise. Utilizando os modelos discretos aqui derivados, é apresentada uma análise detalhada das bifurcações, utilizando técnicas de continuação e o critério de estabilidade de Floquet, esclarecendo a importância das ressonâncias internas nas vibrações não lineares e instabilidades de cascas cilíndricas. Os resultados também confirmam que a forma e a magnitude das imperfeições geométricas iniciais têm uma influência profunda nos resultados, permitindo ou impedindo a transferência de energia entre os modos ressonantes considerados.
The analysis of internal resonances in continuous structural systems is one of the main research areas in the field of nonlinear dynamics. Internal resonance between two vibration modes occur when the ratio of their natural frequencies in an integer number. Of particular importance, due to its influence on the structural response, is the 1:1 internal resonance, usually associated with system symmetries, the 1:2 internal resonance, due to quadratic nonlinearities, and the 1:3 resonance arising from cubic nonlinearities. The internal resonance enables the energy transfer between the related vibration modes, leading usually to new phenomena with profound influence on the stability of the dynamic response. Shells of revolution usually exhibit internal resonances due to the inherent circumferential symmetry and a dense frequency spectrum in their lower frequency range. This may lead not only to m:n internal resonances, but also multiple internal resonances. In this thesis, the analysis of multiple internal resonances in slender cylindrical shells is conducted, in particular 1:1:1:1 and 1:1:2:2 internal resonances are investigated in detail, a topic rarely found in the technical literature. The investigation of internal resonances in continuous systems is usually conducted using low dimensional discrete models. Although some previous works have investigated m:n internal resonances in cylindrical shells, many results are not consistent since the derived discrete models do not consider the modal couplings due to quadratic and cubic nonlinearities. Here, using a perturbation procedure, consistent modal expansions are derived for an arbitrary number of interacting modes, leading to reliable low dimensional models. The accuracy of these models is corroborated using the Karhunen-Loève method. Finally, it is well known that small geometric imperfections of the order of the shell thickness has a strong influence on the shell nonlinear response. However, their influence on internal resonances, dynamic instability and energy transfer is largely unknown. Thus, the influence of different types of modal imperfection is properly considered in the present analysis. Using the derived discrete models, a detail bifurcation analysis, using continuation techniques and Floquet stability criterion, is presented, clarifying the importance of internal resonances on the nonlinear vibrations and instabilities of cylindrical shells. The results also confirm that the form and magnitude of initial geometric imperfections has a profound influence on the results enabling or preventing the energy transfer among the considered resonant modes.

The main goal of this thesis is a contribution to the classification of all incidence geometries

of rank two on which some group PSL(2,q), q a prime power, acts flag-transitively.

Actually we require that the action be RWPRI (residually weakly primitive) and (2T)1

(doubly transitive on every residue of rank one). In fact our definition of RWPRI requires

the geometry to be firm (each residue of rank one has at least two elements) and RC

(residually connected).

The main goal is achieved in this thesis.

It is stated in our "Main Theorem". The proof of this theorem requires more than 60pages.

Quite surprisingly, our proof in the direction of the main goal uses essentially the classification

of all subgroups of PSL(2,q), a famous result provided in Dickson’s book "Linear groups: With an exposition of the Galois field theory", section 260, in which the group is called Linear Fractional Group LF(n, pn).

Our proof requires to work with all ordered pairs of subgroups up to conjugacy.

The restrictions such as RWPRI and (2T)1 allow for a complete analysis.

The geometries obtained in our "Main Theorem" are bipartite graphs; and also locally 2-arc-transitive

graphs in the sense of Giudici, Li and Cheryl Praeger. These graphs are interesting in their own right because of

the numerous connections they have with other fields of mathematics.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

Neural Processes (NPs) are a class of regression models that learn a map from a set of input-output pairs to a distribution over functions. NPs are computationally tractable and provide a number of benefits over traditional nonlinear regression models. Despite these benefits, there are two main domains where NPs fail. This thesis is focused on presenting extensions of the Neural Process to these two areas. The first of these is the extension of Neural Processes graph and network data which we call Graph Neural Processes (GNP). A Graph Neural Process is defined as a Neural Process that operates on graph data. It takes spectral information from the graph Laplacian as inputs and then outputs a distribution over values. We demonstrate Graph Neural Processes in edge value imputation and discuss benefits and drawbacks of the method for other application areas. The second extension of Neural Processes comes in the fundamental training mechanism. NPs are traditionally trained using maximum likelihood, a probabilistic technique. We show that there are desirable classes of problems where NPs fail to learn. We also show that this drawback is solved by using approximations of the Wasserstein distance. We give experimental justification for our method and demonstrate its performance. These Wasserstein Neural Processes (WNPs) maintain the benefits of traditional NPs while being able to approximate new classes of function mappings.

Using robots to navigate through un-mapped environments, specially man-made infrastructures, for the purpose of exploration or inspection is a topic that has gathered a lot of interest in the last years. Micro Aerial Vehicles (MAV's) have the mobility and agility to move quickly and access hard-to-reach areas where ground robots would fail, but using MAV's for that purpose comes with its own set of problems since any collision with the environment results in a crash. The control architecture used in a MAV for such a task needs to perform obstacle avoidance and on-line path-planning in an unknown environment with low computation times as to not lose stability. In this thesis a Non-linear Model Predictive Controller (NMPC) for obstacle avoidance and path-planning on an aerial platform will be established. Included are methods for constraining the available state-space, simulations of various obstacle avoidance scenarios for single and multiple MAVs and experimental validation of the proposed control architecture. The validity of the proposed approach is demonstrated through multiple experimental and simulation results. In these approaches, the positioning information of the obstacles and the MAV are provided by a motion-capture system. The thesis will conclude with the demonstration of an experimental validation of a centralized NMPC for collision avoidance of two MAV's.

In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.

Dans la première partie de cette thèse, nous étudions les équations différentielles algébriques (en abrégé EDA) linéaires et les systèmes de contrôles linéaires associés (en abrégé SCEDA). Les problèmes traités et les résultats obtenus sont résumés comme suit : 1. Relations géométriques entre les EDA linéaires et les systèmes de contrôles génériques SCEDO. Nous introduisons une méthode, appelée explicitation, pour associer un SCEDO à n'importe quel EDA linéaire. L'explicitation d'une EDA est une classe des SCEDO, précisément un SCEDO défini, à un changement de coordonnées près, une transformation de bouclage près et une injection de sortie près. Puis nous comparons les « suites de Wong » d'une EDA avec les espaces invariants de son explicitation. Nous prouvons que la forme canonique de Kronecker FCK d'une EDA linéaire et la forme canonique de Morse FCM d'un SCEDO, ont une correspondance une à une et que leurs invariants sont liés. De plus, nous définissons l'équivalence interne de deux EDA et montrons sa particularité par rapport à l'équivalence externe en examinant les relations avec la régularité interne, i.e., l'existence et l'unicité de solutions. 2. Transformation d'un SCEDA linéaire vers sa forme canonique via la méthode d'explicitation avec des variables de driving. Nous étudions les relations entre la forme canonique par bouclage FCFB d'un SCEDA proposée dans la littérature et la forme canonique de Morse pour les SCEDO. Premièrement, dans le but de relier SCEDA avec les SCEDO, nous utilisons une méthode appelée explicitation (avec des variables de driving). Cette méthode attache à une classe de SCEDO avec deux types d'entrées (le contrôle original et le vecteur des variables de driving) à un SCEDA donné. D'autre part, pour un SCEDO linéaire classique (sans variable de driving) nous proposons une forme de Morse triangulaire FMT pour modifier la construction de la FCM. Basé sur la FMT nous proposons une forme étendue FMT et une forme étendue de FCM pour les SCEDO avec deux types d'entrées. Finalement, un algorithme est donné pour transformer un SCEDA dans sa FCFB. Cet algorithme est construit sur la FCM d'un SCEDO donné par la procédure d'explicitation. Un exemple numérique illustre la structure et l'efficacité de l'algorithme. Pour les EDA non linéaires et les SCEDA (quasi linéaires) nous étudions les problèmes suivants : 3. Explicitations, analyse externe et interne et formes normales des EDA non linéaires. Nous généralisons les deux procédures d'explicitation (avec ou sans variables de driving) dans le cas des EDA non linéaires. L'objectif de ces deux méthodes est d'associer un SCEDO non linéaire à une EDA non linéaire telle que nous puissions l'analyser à l'aide de la théorie des EDO non linéaires. Nous comparons les différences de l'équivalence interne et externe des EDA non linéaires en étudiant leurs relations avec l'existence et l'unicité d'une solution (régularité interne). Puis nous montrons que l'analyse interne des EDA non linéaire est liée à la dynamique nulle en théorie classique du contrôle non linéaire. De plus, nous montrons les relations des EDAS de forme purement semi-explicite avec les 2 procédures d'explicitations. Finalement, une généralisation de la forme de Weierstrass non linéaire FW basée sur la dynamique nulle d'un SCEDO non linéaire donné par la méthode d'explicitation est proposée
In the first part of this thesis, we study linear differential-algebraic equations (shortly, DAEs) and linear control systems given by DAEs (shortly, DAECSs). The discussed problems and obtained results are summarized as follows. 1. Geometric connections between linear DAEs and linear ODE control systems ODECSs. We propose a procedure, named explicitation, to associate a linear ODECS to any linear DAE. The explicitation of a DAE is a class of ODECSs, or more precisely, an ODECS defined up to a coordinates change, a feedback transformation and an output injection. Then we compare the Wong sequences of a DAE with invariant subspaces of its explicitation. We prove that the basic canonical forms, the Kronecker canonical form KCF of linear DAEs and the Morse canonical form MCF of ODECSs, have a perfect correspondence and their invariants (indices and subspaces) are related. Furthermore, we define the internal equivalence of two DAEs and show its difference with the external equivalence by discussing their relations with internal regularity, i.e., the existence and uniqueness of solutions. 2. Transform a linear DAECS into its feedback canonical form via the explicitation with driving variables. We study connections between the feedback canonical form FBCF of DAE control systems DAECSs proposed in the literature and the famous Morse canonical form MCF of ODECSs. In order to connect DAECSs with ODECSs, we use a procedure named explicitation (with driving variables). This procedure attaches a class of ODECSs with two kinds of inputs (the original control input and the vector of driving variables) to a given DAECS. On the other hand, for classical linear ODECSs (without driving variables), we propose a Morse triangular form MTF to modify the construction of the classical MCF. Based on the MTF, we propose an extended MTF and an extended MCF for ODECSs with two kinds of inputs. Finally, an algorithm is proposed to transform a given DAECS into its FBCF. This algorithm is based on the extended MCF of an ODECS given by the explication procedure. Finally, a numerical example is given to show the structure and efficiency of the proposed algorithm. For nonlinear DAEs and DAECSs (of quasi-linear form), we study the following problems: 3. Explicitations, external and internal analysis, and normal forms of nonlinear DAEs. We generalize the two explicitation procedures (with or without driving variable) proposed in the linear case for nonlinear DAEs of quasi-linear form. The purpose of these two explicitation procedures is to associate a nonlinear ODECS to any nonlinear DAE such that we can use the classical nonlinear ODE control theory to analyze nonlinear DAEs. We discuss differences of internal and external equivalence of nonlinear DAEs by showing their relations with the existence and uniqueness of solutions (internal regularity). Then we show that the internal analysis of nonlinear DAEs is closely related to the zero dynamics in the classical nonlinear control theory. Moreover, we show relations of DAEs of pure semi-explicit form with the two explicitation procedures. Furthermore, a nonlinear generalization of the Weierstrass form WE is proposed based on the zero dynamics of a nonlinear ODECS given by the explicitation procedure

Neste trabalho foi desenvolvida uma formulação alternativa para o acoplamento entre o método dos elementos de contorno (MEC) e o método dos elementos finitos (MEF) para análise não linear geométrica de estruturas reticuladas ligadas a meios contínuos bidimensionais heterogêneos, aplicado a problemas de interação solo-estrutura. O solo foi considerado com comportamento elástico linear e modelado via MEC por meio de uma formulação alternativa à clássica técnica de sub-região permitindo a consideração de múltiplas inclusões mais ou menos rígidas do que o material padrão e de linhas de carga internas aos domínios. Este código foi então acoplado ao programa AcadFrame, baseado no MEF posicional para análise não linear geométrica de pórticos com consideração de cinemática exata. O acoplamento numérico foi realizado por meio de uma formulação algébrica onde a matriz de rigidez do solo e a força de contato são condensadas e somadas à matriz e ao vetor de forças internas da estrutura a cada iteração no processo de Newton-Raphson. Em ambos os programas foi utilizada uma generalização do grau de aproximação dos elementos através dos polinômios de Lagrange, o que permite a utilização de elementos curvos de alta ordem. Foi utilizada ainda a técnica dos mínimos quadrados para reduzir as oscilações de forças de superfície no contato. Os resultados obtidos de forma geral são bastante satisfatórios e comprovam a eficiência da formulação. O trabalho permite a análise de problemas de edificações apoiadas sobre solos estratificados com múltiplas inclusões e linhas de carga. Permite tanto a análise de elementos apoiados diretamente sobre o solo (sapatas, radies) quanto de elementos internos e em qualquer direção, como no caso de estacas verticais ou inclinadas. Pode-se inclusive considerar as estacas passando por diferentes camadas de solo. A aplicação pode ser estendida ainda a outros problemas elásticos, acoplamento entre peças mecânicas e análise de materiais compostos.
This work presents an alternative coupling of the boundary element method (BEM) and the finite element method (FEM) to create a computer program for non linear geometric analysis of frames coupled to continuous domains, applied to soil-structure interaction. A linear elastic behavior is considered for the soil, modeled by BEM. An alternative formulation is adopted for the classic sub-region technique, allowing the consideration of multiple inclusions and load lines inside the soil domain. The BEM computational code is coupled to the AcadFrame software, based on positional FEM for non linear geometric analysis of frames, considering exact kinematics. The numerical coupling is made by an algebraic formulation where the soil stiffness matrix and contact forces are condensed and added to the structure matrix and internal forces for each iteration on Newton-Raphson process. On both programs it is adopted a generalization of the element degree assuming the Lagrange polynomials, which allows the use of curved high order elements. It was also implemented the least square method in order to obtains better and smoother results of surface forces in the contact interface. The obtained results are satisfactory and prove the formulation efficiency. The program allows the analysis of buildings supported by layered soils with multiples inclusions and load lines. It considers directly supported elements over the soil (footing foundations, radies) and internal elements in any direction, like vertical and diagonal piles. It can also consider piles going through different layers of the soil. This formulation can be applied to other elastic problems like coupling between mechanic pieces and composite material analysis.

O principal objetivo deste trabalho é analisar a interação tridimensional entre núcleos e as estruturas usuais de contraventamento, tais como, treliças, pórticos e pilares isolados, considerando a influência da flexibilidade das suas fundações no equilíbrio final do sistema estrutural, sobretudo quando são introduzidos os efeitos da não linearidade geométrica. A influência dos trechos rígidos e das excentricidades entre os eixos longitudinais dos elementos, incidentes em um mesmo ponto nodal, também é pesquisada na rigidez global do sistema. Para possibilitar estas análises, elaborou-se um programa em linguagem FORTRAN 90 com recursos para processar estruturas complexas. A automação dos cálculos fundamenta-se no método dos deslocamentos e nas técnicas de análise matricial. Na determinação da rigidez do sistema aplicou-se o princípio da energia potencial total mínima. As estruturas dos edifícios usadas na aferição dos resultados, fornecidos pelo referido programa, são reticuladas e suas lajes funcionam corno diafragmas horizontais infinitamente rígidos nos seus planos e sem qualquer resistência à flexão. Os efeitos de segunda ordem são computados através de um processo de cálculo iterativo, onde a matriz de rigidez da estrutura tem seus coeficientes afetados pelo esforço normal e no caso dos sistemas com núcleos, além deste, os momentos fletores e os bimomentos.
The principal aim of this work is to analyse the tridimesional interaction between cores and the usual bracing structure, such as, trusses, frames and isolated column, considering their foundation flexibility in the structural system final equilibrium, even when the geometric non linear effects are introduced. The offsets and the eccentricities among longitudinal axis of the elements, incidents in the same nodal point, is researched in the system global stiffness as well. To make this analysis possible, a program in FORTRAN 90 language was made with resourses to process complex structures. The calculus automation is based on the stifthess method and on the matricial analysis technique. To obtain the system stiffness, the minimum total potential energy principle was applied. The building structures used to check the results, given by the mentioned program, are reticulated and their slabs works as horizontal diaphragm, infinitely stitfened in their planes and without any beding resistance. The second order effects are computed thru a iterative calculus process, where the structrure stiffness matrix has its coefficients affected by the axjal force and in cases of systems with cores, besides it, the bending moments and the bimoments.

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The aim of this work is to present a formulation and corresponding computational implementation for sizing optimization of plane frames and cable-stayed columns considering geometric non liner behavior. The structural analysis is based on the finite element method using the updated lagrangian approach for plane frame and cable elements, which are represented by plane truss elements. The non linear system is solved by the Newton-Raphson method coupled to load increment strategies such as the arch length method and the generalized displacement parameter method, which allow the algorithm to transpose any critical point that happen to appear along the equilibrium path. In the optimization process the design variables are the heights of the crosssection of the frame elements, the objective function represents the volume of the structure and the constraints impose limits to displacements and critical load. Lateral constraints impose limits to the design variables. The finite difference method is used in the sensitivity analysis of the displacement and critical load constraints. The optimization process is carried out using three different optimization strategies: the sequential quadratic programming algorithm; the interior points algorithm; and the branch and bound method. Some numerical experiments are carried out so as to test the analysis and the sensitivity strategies. Numerical experiments are presented to show the validity of the implementation presented in this dissertation.
O objetivo deste trabalho é a otimização de dimensões de pórticos planos e de colunas estaiadas planas pela minimização do volume da estrutura, considerando os efeitos da não-linearidade geométrica em seu comportamento. A formulação utiliza, para análise das estruturas, elementos finitos de pórtico e de treliça planos e referencial lagrangeano atualizado. O método de Newton-Raphson foi utilizado como estratégia para solução do sistema de equações não lineares. Foram acopladas estratégias especiais para ultrapassagem de pontos críticos que possam existir ao longo da trajetória de equilíbrio, tais como o comprimento de arco cilíndrico e o controle dos deslocamentos generalizados. Na otimização, as variáveis de projeto são as alturas das seções transversais dos elementos, a função objetivo é o volume do material e as restrições dizem respeito a limitações impostas a deslocamentos e à carga limite, além de limitações impostas aos valores das variáveis. A sensibilidade da função objetivo foi obtida por diferenciação direta e a sensibilidade das restrições pelo método das diferenças finitas. Foram utilizados o algoritmo de programação quadrática seqüencial, PQS, o algoritmo de pontos interiores, PI, e o algoritmo de Branch and Bound, B&B. São apresentados exemplos de validação das estratégias de análise não linear e da análise de sensibilidade, além dos exemplos de validação da formulação empregada para a otimização resolvidos pelos métodos implementados.

Les alliages de titane beta-métastables ont des propriétés mécaniques remarquables à température ambiante, liées à l'évolution sous contrainte de la microstructure. Un mode de déformation spécifique à ces alliages joue un rôle essentiel : le système de maclage {332}<11-3>. On s'intéresse ainsi à une modélisation champ de phase de l'évolution sous contrainte des variants de macle {332}. Une première partie est consacrée à un modèle champ de phase de type Allen-Cahn avec prise en compte d'une élasticité dans un formalisme géométriquement linéaire (GL). On utilise une énergie d'interface isotrope ou anisotrope afin d'étudier l'influence de cette dernière sur la croissance et le degré d'anisotropie des variants de macle. Le rôle d'une élasticité formulée dans le formalisme géométriquement non-linéaire (GNL) est ensuite discuté et donne lieu à la deuxième partie de ces travaux. Un solveur mécanique dans le formalisme GNL par méthode spectrale est alors mis en place et validé. Il est ensuite utilisé dans le développement d'un modèle champ de phase de type Allen-Cahn avec prise en compte d'une élasticité GNL. Nous procédons alors à une étude comparative fine des microstructures obtenues en GL et GNL. Les résultats montrent une différence majeure entre les microstructures obtenues dans les deux cadres élastiques, concluant sur la nécessité d'une élasticité dans le GNL pour reproduire les microstructures de macle observées. Enfin, nous présentons une étude prospective d'un modèle basé sur une méthode de réduction de Lagrange, qui permettrait de prendre en compte le caractère reconstructif du maclage et la nature hiérarchique des microstructures observées expérimentalement
Beta-metastable titanium alloys exhibit remarkable mechanical properties at room temperature, linked to the microstructure evolution under stress. A specific deformation mode plays an essential role: the {332}<11-3> twinning system. This thesis work thus concerns a modeling, by the phase field method, of {332} twin variants evolution under stress. The first part is devoted to an Allen-Cahn type phase field model with an elasticity taken into account in a geometrically linear formalism. This model is used with an isotropic or anisotropic interface energy in order to study the influence of the latter on the growth of twin variants. The role of an elasticity formulated in finite strain is then discussed and gives rise to the second part of this work. A mechanical equilibrium solver formulated in the geometrically non-linear formalism using a spectral method is then set up and validated. It is then used in the development of an Allen-Cahn type phase field model considering a geometrically non-linear elasticity. We then proceed to a fine comparative study of the microstructures obtained in linear and non-linear geometries. The results show a major difference between the microstructures obtained in the two elastic frameworks, concluding on the need for elasticity in finite strain formalism to reproduce the twin microstructures observed experimentally. Finally, we present a prospective study of a more general phase field formalism than the previous ones, based on a Lagrange reduction method, which would allow to fully take into account the reconstructive character of twinning and the hierarchical nature of the microstructures observed experimentally

Der zunehmende Einsatz regenerativer Energiequellen erfordert die Nutzung von Energiezwischenspeichern, die umweltfreundlich, günstig und skalierbar sein sollten. Die Zink-Luft-Flussbatterie (ZLFB) kann perspektivisch diese Anforderungen erfüllen, wobei zur Bereitstellung der gespeicherten Energie eine Suspension aus Zinkpartikeln in einem gelierten Elektrolyt durch eine elektrochemische Zelle gepumpt wird. Um die Strömungsstruktur der ZLFB auszulegen und Fehlfunktionen zu vermeiden, ist ein grundlegendes Verständnis der Rheologie der Zinksuspension notwendig. Außerdem kann über die Einstellung einer geeigneten Strömung die bei der Entladung erreichte elektrische Leistungsdichte gesteigert werden. Bereits die Flüssigphase der Zinksuspension weist eine komplexe nicht-Newtonsche Rheologie auf, welche durch die Zugabe der Partikel komplexer wird. Für das grundlegende Verständnis der Rheologie werden daher Modellexperimente durchgeführt, wobei in dieser Arbeit ein L-förmiger Kanal mit Strömungsaufweitung untersucht wurde, um die komplexen strömungsmechanischen Eigenschaften der Zinksuspension abzubilden. Zur Erfassung des Strömungsfeldes ist eine Ortsauflösung von 1 … 2 mm in einem Messbereich von 20 × 15 mm2 erforderlich. Ultraschall ist prinzipiell geeignet, um das Strömungsfeld in der opaken Suspension zu erfassen, wobei die wesentliche Herausforderung in den starken Wellenfrontverzerrungen besteht, welche durch die Zinkpartikel eingebracht werden. Es konnte gezeigt werden, dass die Ultrasound Imaging Velocimetry (UIV) robuster gegenüber diesen Störungen ist, als die Ultraschall-Doppler-Velozimetrie (UDV). Die UIV wurde daher mittels Geschwindigkeitsnormal an die messtechnischen Randbedingungen der Zinksuspension angepasst und charakterisiert. Bei einer Ortsauflösung von 1,6 mm wurde eine Gesamtmessunsicherheit von 2,5 % axial und 4,1 % lateral zur Schallausbreitungsrichtung erreicht. Das im Modellexperiment gemessene Strömungsfeld weist eine Totzone an der Strömungsumlenkung auf, deren Auftreten durch eine von der Scherhistorie abhängige Viskosität erklärt werden kann. Dieser Effekt wird als Thixotropie bezeichnet. Durch die In-situ-Messung der Strömung in einer aktiven ZLFB kann eine Korrelation von Strömung und elektrischer Leistung erfolgen und die erzielte Leistungsdichte perspektivisch durch eine Anpassung der Strömung gesteigert werden. Bei der Messung im 2,6 mm hohen Anodenspalt muss aufgrund der komplexen Rheologie der Suspension und der daraus resultierenden hohen Geschwindigkeitsgradienten eine Ortsauflösung von unter 100 µm bei gleichzeitig kleiner Ultraschallfrequenz realisiert werden, da der Ultraschall für hohe Frequenzen nicht in die Zinksuspension eindringt. Um dieses Ziel zu erreichen, wurde die Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) genutzt, welche Ortsauflösungen unterhalb des Beugungslimits ermöglicht. Einzelne nichtlineare Streupartikel werden mittels Harmonic Imaging isoliert abgebildet und verfolgt, wobei die durch die Zinkpartikel eingebrachten Wellenfrontstörungen durch einen kohärenzgewichteten Strahlformer kompensiert werden. Es wurde eine Ortsauflösung von 67 µm axial und 30 µm lateral zur Schallausbreitungsrichtung bei einer Anregungswellenlänge von 330 µm erreicht. Trotz der stark streuenden Zinksuspension, konnte so eine Messung in der aktiven ZLFB mit einer maximalen Messunsicherheit von 12,5 % durchgeführt werden. Dabei wurde eine Wandgleitgeschwindigkeit von 3 mm s−1 bei einer maximalen Geschwindigkeit von etwa 8 mm s−1 festgestellt. Die SRPTV kann darüber hinaus in anderen technischen Prozessen eingesetzt werden, in denen Suspensionsströmungen in kleinen Geometrien auftreten.:Symbolverzeichnis xiii Abkürzungsverzeichnis xv 1 Einleitung 1 1.1 Motivation und Zielstellung 1 1.2 Stand der Technik 4 1.3 Lösungsansatz und Struktur der Arbeit 8 2 Theoretische Grundlagen 11 2.1 Grundlagen der Schallausbreitung 11 2.1.1 Schallausbreitung in homogenen Medien 11 2.1.2 Schallausbreitung in inhomogenen Medien 13 2.2 Ultraschall Bildgebung 14 2.2.1 Phased-Array-Prinzip 15 2.2.2 Plane wave imaging 16 2.2.3 Grenzen der Schallfeldfokussierung 16 2.3 Messung von Strömungsfeldern 17 2.3.1 Ultraschall-Doppler-Velozimetrie 18 2.3.2 Ultrasound Imaging Velocimetry 19 2.3.3 Ultrasound Particle Tracking Velocimetry 19 2.4 Nichtlineare akustische Effekte 20 2.4.1 Beschreibung von Linearität 20 2.4.2 Interaktion von nichtlinearen Streupartikeln und Schallwelle 20 2.4.3 Harmonic Imaging 21 3 Experimentelle Grundlagen 25 3.1 Charakterisierung der Zinksuspension 25 3.1.1 Zusammensetzung der Zinksuspension 25 3.1.2 Bestimmung von Dämpfung und Schallgeschwindigkeit 26 3.1.3 Bestimmung der spezifischen akustischen Impedanz 29 3.2 Messtechnik 30 3.2.1 Ultraschallforschungsplattform: Phased Array Ultrasound Dopp- ler Velocimeter 30 3.2.2 Ultraschallwandler 32 4 Verfahren zur Strömungsmessung im Modellexperiment 37 4.1 Experimenteller Aufbau 37 4.2 Untersuchung geeigneter Verfahren zur Messung von Strömungsfel- dern in der Zinksuspension 38 4.3 Optimierung der Signalverarbeitung und Charakterisierung der Messei- genschaften 44 4.3.1 Geschwindigkeitsnormal 44 4.3.2 Optimierung der Messsystemparameter 45 4.3.3 Charakterisierung der Messeigenschaften 48 4.3.4 Validierung 49 4.4 Messung der Suspensionsströmung im Modellexperiment 55 4.4.1 Messergebnisse 55 4.4.2 Vergleich von Simulation und Messung 58 4.5 Fazit 61 5 Verfahren zur In-situ-Strömungsmessung in einer Zink-Luft-Flussbatterie 63 5.1 Experimenteller Aufbau 63 5.2 Strömungsmessung unterhalb des Beugungslimits - Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) 65 5.2.1 Nutzung nichtlinearer Streupartikel 68 5.2.2 Trennung von linearem und nichtlinearem Signalanteil 72 5.2.3 Strahlformung mit Kompensation der Streuung 76 5.2.4 Particle Tracking 80 5.3 Charakterisierung der Messeigenschaften 81 5.3.1 Vorgehen zur Charakterisierung der Messeigenschaften 82 5.3.2 Untersuchung der Positionsunsicherheit 83 5.3.3 Untersuchung der Geschwindigkeitsunsicherheit 92 5.4 Messung an einer aktiven Zink-Luft-Flussbatterie 95 5.4.1 Aufbau und Durchführung 95 5.4.2 Messergebnisse 97 5.4.3 Vergleich von Simulation und Messung 97 5.5 Fazit 102 6 Zusammenfassung und Ausblick 103 6.1 Erkenntnisse und Fortschritt 103 6.1.1 Ultrasound Imaging Velocimetry 103 6.1.2 Super Resolution Ultrasound Particle Tracking Velocimetry 104 6.1.3 Fazit 106 6.2 Ausblick und weiterführende Arbeiten 106 6.2.1 Messtechnik 106 6.2.2 Anwendung 107 Literaturverzeichnis 109 Publikationsverzeichnis 117 Artikel in Zeitschriften mit peer-review 117 Tagungsbeiträge 117 Patente 119
For the efficient use of renewable energies, energy storage systems are required that are environmentally friendly, low priced and scalable. The zinc-air flow battery (ZAB), which is operated by pumping an opaque suspension of zinc particles in an gelled electrolyte through an electrochemical cell, is a promising candidate as energy storage system for these requirements. To design the fluidic structures and avoid malfunction, a fundamental understanding of the rheology of the zinc suspension is required. Additionally, the electrical performance of the cell can be imporved by optimizing the flow in the electrochemical cell. The liquid phase of the suspension itself has complex non-Newtonian properties, which are even more complex when the particles are considered. For the fundamental understanding of the suspension rheology, model experiments are conducted. In this work an L-shaped channel with a widening is used to represent relevant effects from the complex rheology of the suspension. To measure the flow field, a spatial resolution of 1 … 2 mm and a measurement area of 20 × 15 mm2 are required. Ultrasound can be used to measure the flow in opaque liquids, but wavefront distortions are introduced by the zinc particles. Established measurement methods for homogeneous opaque fluids, the Ultrasound Imaging Velocimetry (UIV) and the Ultrasound Doppler Velocimetry (UDV), were compared for the application at the suspension. The UIV has a 50 % lower random deviation, which makes it more suitable for the flow measurement in the suspension and it was adapted to the measurement conditions in the suspension. At a spatial resolution of 1.66 mm, a velocity uncertainty of 2.5 % axial and 4.1 % lateral to the ultrasound propagation were achieved. The application of the UIV to the suspension flow in the model experiment revealed a thixotropic behavior of the fluid, which resulted in a dead flow zone opposite to the inlet of the channel. The in situ measurement of the flow in an active ZAB, allows to correlate electrical performance and flow and thereby an improvement of the cell performance by adapting the flow. For the measurement in the anodic channel with a width of 2.6 mm, a spatial resolution of 100 µm is required because of the high velocity gradients due to the non-Newtonian rheology of the suspension. The high spatial resolution has to be achieved at low ultrasound frequencies, since the ultrasound does not penetrate into the suspension for high frequencies. To achieve this, the Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) was used, which allows a spatial resolution beyond the diffraction limit. Harmonic Imaging is used to image isolated non-linear tracer particles, which are tracked for velocity estimation. The speckle and image distortion due to the induced wavefront distortions are compensated with a coherence weighting beamformer. A spatial resolution of 67 µm axial and 30 µm lateral to the ultrasound propagation were achieved. Despite the strong scattering of the ultrasound at the zinc particles, a maximum velocity uncertainty of 12.5 % referred to the maximum velocity was achieved for the measurement in the active ZAB. A slip velocity of 3 mm at a maximum velocity of 8 mm was observed. The SRPTV can be applied to other technical processes, where suspension flows in small geometries play an important role.:Symbolverzeichnis xiii Abkürzungsverzeichnis xv 1 Einleitung 1 1.1 Motivation und Zielstellung 1 1.2 Stand der Technik 4 1.3 Lösungsansatz und Struktur der Arbeit 8 2 Theoretische Grundlagen 11 2.1 Grundlagen der Schallausbreitung 11 2.1.1 Schallausbreitung in homogenen Medien 11 2.1.2 Schallausbreitung in inhomogenen Medien 13 2.2 Ultraschall Bildgebung 14 2.2.1 Phased-Array-Prinzip 15 2.2.2 Plane wave imaging 16 2.2.3 Grenzen der Schallfeldfokussierung 16 2.3 Messung von Strömungsfeldern 17 2.3.1 Ultraschall-Doppler-Velozimetrie 18 2.3.2 Ultrasound Imaging Velocimetry 19 2.3.3 Ultrasound Particle Tracking Velocimetry 19 2.4 Nichtlineare akustische Effekte 20 2.4.1 Beschreibung von Linearität 20 2.4.2 Interaktion von nichtlinearen Streupartikeln und Schallwelle 20 2.4.3 Harmonic Imaging 21 3 Experimentelle Grundlagen 25 3.1 Charakterisierung der Zinksuspension 25 3.1.1 Zusammensetzung der Zinksuspension 25 3.1.2 Bestimmung von Dämpfung und Schallgeschwindigkeit 26 3.1.3 Bestimmung der spezifischen akustischen Impedanz 29 3.2 Messtechnik 30 3.2.1 Ultraschallforschungsplattform: Phased Array Ultrasound Dopp- ler Velocimeter 30 3.2.2 Ultraschallwandler 32 4 Verfahren zur Strömungsmessung im Modellexperiment 37 4.1 Experimenteller Aufbau 37 4.2 Untersuchung geeigneter Verfahren zur Messung von Strömungsfel- dern in der Zinksuspension 38 4.3 Optimierung der Signalverarbeitung und Charakterisierung der Messei- genschaften 44 4.3.1 Geschwindigkeitsnormal 44 4.3.2 Optimierung der Messsystemparameter 45 4.3.3 Charakterisierung der Messeigenschaften 48 4.3.4 Validierung 49 4.4 Messung der Suspensionsströmung im Modellexperiment 55 4.4.1 Messergebnisse 55 4.4.2 Vergleich von Simulation und Messung 58 4.5 Fazit 61 5 Verfahren zur In-situ-Strömungsmessung in einer Zink-Luft-Flussbatterie 63 5.1 Experimenteller Aufbau 63 5.2 Strömungsmessung unterhalb des Beugungslimits - Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) 65 5.2.1 Nutzung nichtlinearer Streupartikel 68 5.2.2 Trennung von linearem und nichtlinearem Signalanteil 72 5.2.3 Strahlformung mit Kompensation der Streuung 76 5.2.4 Particle Tracking 80 5.3 Charakterisierung der Messeigenschaften 81 5.3.1 Vorgehen zur Charakterisierung der Messeigenschaften 82 5.3.2 Untersuchung der Positionsunsicherheit 83 5.3.3 Untersuchung der Geschwindigkeitsunsicherheit 92 5.4 Messung an einer aktiven Zink-Luft-Flussbatterie 95 5.4.1 Aufbau und Durchführung 95 5.4.2 Messergebnisse 97 5.4.3 Vergleich von Simulation und Messung 97 5.5 Fazit 102 6 Zusammenfassung und Ausblick 103 6.1 Erkenntnisse und Fortschritt 103 6.1.1 Ultrasound Imaging Velocimetry 103 6.1.2 Super Resolution Ultrasound Particle Tracking Velocimetry 104 6.1.3 Fazit 106 6.2 Ausblick und weiterführende Arbeiten 106 6.2.1 Messtechnik 106 6.2.2 Anwendung 107 Literaturverzeichnis 109 Publikationsverzeichnis 117 Artikel in Zeitschriften mit peer-review 117 Tagungsbeiträge 117 Patente 119

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This master thesis describes an intelligent classifier system applied to multiclass non-linearly separable problems called Slicer. The system adopts a low computacional cost supervised learning strategy (evaluated as ) based on linear separability. During the learning period the system determines a set of hyperplanes associated to oneclass regions (sub-spaces). In classification tasks the classifier system uses the hyperplanes as a set of if-then-else rules to infer the class of the input attribute vector (non classified object). Among other characteristics, the intelligent classifier system is able to: deal with missing attribute values examples; reject noise examples during learning; adjust hyperplane parameters to improve the definition of the one-class regions; and eliminate redundant rules. The fuzzy theory is considered to design a hybrid version with features such as approximate reasoning and parallel inference computation. Different classification methods and benchmarks are considered for evaluation. The classifier system Slicer reaches acceptable results in terms of accuracy, justifying future investigation effort.
Este trabalho de mestrado descreve um sistema classificador inteligente aplicado a problemas multiclasse não-linearmente separáveis chamado Slicer. O sistema adota uma estratégia de aprendizado supervisionado de baixo custo computacional (avaliado em ) baseado em separabilidade linear. Durante o período de aprendizagem o sistema determina um conjunto de hiperplanos associados a regiões de classe única (subespaços). Nas tarefas de classificação o sistema classificador usa os hiperplanos como um conjunto de regras se-entao-senao para inferir a classe do vetor de atributos dado como entrada (objeto a ser classificado). Entre outras caracteristicas, o sistema classificador é capaz de: tratar atributos faltantes; eliminar ruídos durante o aprendizado; ajustar os parâmetros dos hiperplanos para obter melhores regiões de classe única; e eliminar regras redundantes. A teoria nebulosa é considerada para desenvolver uma versão híbrida com características como raciocínio aproximado e simultaneidade no mecanismo de inferência. Diferentes métodos de classificação e domínios são considerados para avaliação. O sistema classificador Slicer alcança resultados aceitáveis em termos de acurácia, justificando investir em futuras investigações.

This study investigates seismic response of the Moment-Resisting-Steel Frames (MRSF) with the architectural setbacks. The main objective of the study is to understand the variation of the elastic and inelastic, static and dynamic behavior with changes in the geometric dimensions of the tower portion. A second objective of the study is to determine the adequacy of the analysis procedures of various rigors, specified in current seismic design provision, in predicting those behaviors for MRSF with various size of setback. The analytical study is conducted using a regular and 16 irregular models to capture all possible combinations of configuration of setback in five-story, five-bay MRSFs. An irregular model is developed by gradually changing the horizontal and vertical dimensions of the tower portion of the regular base 2D frame-model. All models were designed for (a) equal global displacement and uniform distribution of inter-story drift under First-Mode (FM) lateral force distribution pattern at first significant yield, and (b) equal period of vibration at the first mode, using Nonlinear Static Seismic analysis procedure. Among the conclusions derived from the research is that the variation of (a) the elastic and inelastic inter-story drift, the ductility demand for the top three stories, and (b) the elastic and inelastic global displacement exhibited a pattern similar to the variation of the FM participation factor at the roof, PF1Φr,1. The square-root-of-sum-of-square (SRSS) distribution provided accurate estimates of elastic story shear and inter-story drift demand as well as the story yield strength and drift.

This research studies a particular curvature-driven geometric flow rule in the plane using techniques from differential geometry, computational mathematics, and formal asymptotics. The flow rule is a combination of the well-studied curve shortening flow, which is governed by a parabolic system of partial differential equations, and the Eikonal equation, which is governed by a hyperbolic system. The physical motivations for considering our model include propagating fire fronts and phase separation. The focus is on a variety of mathematical problems related to the flow rule, such as the explicit form of travelling wave solutions, linear stability, self-intersection, singularity formation, and the extinction problem for convex curves.

Alle optischen Systeme haben den gleichen Zweck: Sie manipulieren Eigenschaften des Lichts, durch Interaktion mit Materie. In dieser Arbeit werden zwei wichtige Teilaspekte aus diesem Kontext untersucht, im linearen und im nicht-linearen Bereich. In Teil I werden die bekannten Bragg-Reflexionen in neuem Licht betrachtet. Bragg Reflexion findet statt, wenn Licht mit einem periodischen Medium interagiert. Die Bragg-Bedingung verknüpft den Gitterabstand in einem Kristall mit der Wellenlänge, die von ihm reflektiert wird. In dieser Arbeit werden die Bragg Reflexionen in gewellten Wellenleitern untersucht. Es wird gezeigt, dass die Bragg-Bedingung nicht ausreicht, um die Streuung in diesen Wellenleitern zu verstehen. Es wird numerisch und analytisch demonstriert, dass unebene Ränder eine neue Reflexionsbedingung schaffen, die über das einfache Bragg-Bild hinausgeht. Dieser Streueffekt, der Square Gradient Bragg-Mechanismus ist aus statistischen Streuansätzen bekannt. Er hängt mit der Krüummung des Randes zusammen und hat einen starken Einfluss auf die Wellenleitung in diesen Systemen. In dieser Arbeit wird die erste allgemeine Theorie für den Square Gradient Bragg Streumechanismus vorgestellt, die es ermöglicht, Voraussagen für einzelne Wellenleiter mit beliebig deformierten Rändern zu treffen. Eine weitere wichtige Eigenschaft des Lichts wird in Teil II dieser Arbeit untersucht: Die Verschränkung zwischen zwei Photonen. Verschränkung ist ein intuitiv nicht verständliches Phänomen, weil es in der uns umgebenden klassischen Welt kein Analogon hat. Insbesondere verletzt es unsere implizite Annahme eines lokalen Realismus, weil voneinander entfernte Teilchen scheinbar instantan miteinander wechselwirken können. In dieser Arbeit wird eine neue und verstimmbare Quelle für verschränkte Photonen entworfen. Die Photonenpaare werden in nicht-linearen Kristallen erzeugt, aber ihre Verschränkung wird rein geometrisch erzwungen. Dieser geometrische Ansatz erlaubt es, die Frequenz der Photonen einzustellen. Hier übertrifft diese neue Quelle ihre Vorgänger, die ausführlich besprochen werden. Die Verschränkung der erzeugten Photonen wird experimentell nachgewiesen.
Any optical experiment, any optical technology is only about one thing: Manipulating the properties of light through interaction with matter. This thesis will address two important issues in this broad context, in the linear and in the non-linear regime. In Part I, the well-known Bragg reflection is revised. Bragg reflection takes place whenever light interacts with a periodic structure. The famous Bragg condition relates the lattice spacing in a crystal to the wavelength which is effectively reflected by that lattice. In this thesis the Bragg reflection in dielectric waveguides is investigated. It is shown that the Bragg condition is not sufficient to describe the scattering situation in waveguides with corrugated boundaries. It is demonstrated, analytically and numerically, that corrugated boundaries cause a new type of reflection condition, which goes beyond the Bragg picture. This scattering mechanism, the Square Gradient Bragg Scattering, is known from statistical scattering approaches. It is connected to the curvature of the boundary and has a strong influence on the wave propagation in these systems. Here the first general theory for Square Gradient Bragg Scattering is presented, which allows for making predictions for single corrugated waveguides with arbitrary boundaries. Another important property of light is investigated in Part II of this thesis: The entanglement of two photons. Entanglement is a counter-intuitive phenomenon, because it has no classical analogy. It especially violates our assumption of local realism, because distant particles seemingly act on each other instantaneously. In this thesis a new tunable and portable source of photon pairs is designed. The photon pairs are created in non-linear crystals, but their entanglement is enforced in a purely geometrical manner. This geometrical approach makes the setup tunable. This is where the new design supersedes its predecessor, which will be discussed in detail. The entanglement of the generated photons is demonstrated experimentally.

The subject matter of this thesis is the formation of large-scale structure in the universe. Most of the study has dealt with the non-linear evolution of cosmological uctuations, focusing on the scalar sector of perturbation theory. The period of transition between the radiation era and the matter era has been largely examined, extending the already known linear results to a nonstandard matter model and to a non-linear analysis. The obtained second order solutions for the matter uctuations variables have been used to find the skewness of the density and velocity distributions, an important statistical estimator measuring the level of non-Gaussianity of a distribution. In the context of cosmological perturbations, a complete Post-Newtonian (1PN) treatment is presented with the aim of obtaining a set of equations suitable in particular for the intermediate scales. The final result agrees with both the non linear Newtonian theory of small scales and the linear general relativistic theory of large scales. Analyzing the limiting cases of our approach to 1PN cosmology, we have clarified the link between the Newtonian theory of gravity and General Relativity. This work is the result of the agreement signed by the Department of Physics, University of Roma Tor Vergata and the Institute of Cosmology and Gravitation, University of Portsmouth, United Kingdom in the formal context of the co-tutela project. The chapters 5, 6 and 7 are the themes of two articles in preparation, that will be shortly submitted: "How the universe got its skewness" - M. Bruni, I.Milillo, K.Koyama; "Post-Newtonian Cosmology" - I. Milillo, D.Bertacca, M. Bruni

La tesi riguarda la formazione di strutture a larga scala nell'universo, cioè l'origine degli addensamenti di materia che hanno portato alla formazione dei cluster di galassie. La maggior parte del lavoro ha riguardato aspetti non lineari della Teoria delle Perturbazioni Cosmologiche, trattando in particolare il periodo di transizione tra epoca della radiazione e epoca della materia. In questo contesto si è considerato un modello non-standard di materia, analizzando il ruolo dell'indice barotropico nell'evoluzione del contrasto di densità . La nota approssimazione Meszaros è stata generalizzata ad una analisi non lineare che ha permesso di trovare la skewness della distribzione di materia, un importante indice di non-Gaussianità rilevabile dai dati osservativi. Nel contesto delle perturbazioni cosmologiche è stata formulata la teoria Post-Newtoniana (1PN) con lo scopo di ottenere un set di equazioni valido per ogni range di distanze, in particolare per le scale intermedie. I risultati finali coincidono sia con la teoria lineare relativistica per grandi scale sia con la teoria non lineare Newtoniana per piccole scale; quest'ultima connessione fornisce una chiara visione della relazione fra Relatività Generale e teoria Newtoniana.
The subject matter of this thesis is the formation of large-scale structure in the universe, describing the clustering of matter in galaxies and clusters of galax- ies. Most of the study has dealt with the non-linear evolution of cosmological fluctuations, focusing on the scalar sector of perturbation theory. The period of transition between the radiation era and the matter era has been largely examined, extending the already known linear results to a non-standard matter model and to a non-linear analysis. The obtained second order solutions for the matter fluctuations variables have been used to find the skewness of the density and velocity distributions, an important statistic estimator measuring the level of non-Gaussianity of a statistic ensamble. In the contest of cosmological perturbations a complete Post-Newtonian (1PN) treatment is presented with the aim of obtain a set of equations suitable in particular for the intermediate scales. The final result agrees with both the non linear Newtonian theory of small scales and the linear general relativistic theory of large scales. Analyzing the limit cases of our approach to 1PN cosmology, we have clarified the link between the Newtonian theory of gravity and General Relativity.

Este trabalho consiste no desenvolvimento de ferramentas computacionais para análise não linear geométrica de interação fluido-casca utilizando o Método dos Elementos Finitos (MEF). O algoritmo para dinâmica dos fluidos é explícito e a integração temporal é baseada em linhas características. O código computacional é capaz de simular as equações de Navier-Stokes para escoamentos compressíveis tanto na descrição Euleriana como na descrição Lagrangeana-Euleriana arbitrária (ALE), na qual é possível prescrever movimentos para a malha do fluido. A estrutura é modelada em descrição Lagrangeana total através de uma formulação de MEF para análise dinâmica não linear geométrica de cascas baseada no teorema da mínima energia potencial total escrito em função das posições nodais e vetores generalizados e não em deslocamentos e rotações. Essa característica evita o uso de aproximações de grandes rotações. Dois modelos de acoplamentos são desenvolvidos. O primeiro modelo, ideal para problemas onde a escala de deslocamentos não é muito grande comparada com as dimensões do domínio do fluido, é baseado na descrição ALE e o acoplamento entre as duas diferentes malhas é feito através do mapeamento das posições locais dos nós do contorno do fluido sobre os elementos de casca e vice-versa, evitando a necessidade de coincidência entre os nós da casca e do fluido. A malha do fluido é adaptada dinamicamente usando um procedimento simples baseado nas posições e velocidades nodais da casca. O segundo modelo de acoplamento, ideal para problemas com grande escala de deslocamentos tais como estruturas infláveis, considera a casca imersa na malha do fluido e consiste em um procedimento robusto baseado em curvas de nível da função distância assinalada do contorno, o qual integra o algoritmo Lagrangeano de casca com o Fluido em descrição Euleriana, sem necessidade de movimentação da malha do fluido, onde a representação computacional do fluido se resume a uma malha não estruturada maior ou igual ao domínio inicial do fluido e a interface fluido-casca dentro da malha do fluido é identificada por meio de curvas de nível da função distância assinalada do contorno. Ambos os modelos são testados através de exemplos numéricos mostrando robustez e eficiência. Finalmente, como uma sugestão para o futuro desenvolvimento desta pesquisa, iniciaram-se estudos relativos a funções B-splines. O uso desse tipo de funções deverá resolver problemas de estabilidade relativos a oscilações espúrias devidas ao uso de polinômios de Lagrange para a representação de descontinuidades.
This work consists of the development of computational tools for nonlinear geometric fluid-shell interaction analysis using the Finite Element Method (FEM). The fluid solver is explicit and its time integration based on characteristics. The computational code is able to simulate the Navier-Stokes equations for compressible flows written in the Eulerian description as well as in the arbitrary Lagrangian-Eulerian (ALE) description, enabling movements prescription for the fluid mesh. The structure is modeled in a total Lagrangian description, using a FEM formulation to deal with geometrical nonlinear dynamics of shells based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors, not displacements and rotations, avoiding the use of large rotation approximations. Two partitioned coupling models are developed. The first model, ideal for simulations where the displacements scale is not very large compared to the fluid domain, is based on the ALE description and the coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and vice-versa, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell nodal positions and velocities. The second model, ideal for problems with large scales of displacements such as inflatable structures, is based on immersed boundary and consists of a robust level-set based approach that integrates the Lagrangian shell finite and the Eulerian finite element high speed fluid flow solver, with no need for mesh adaptation, where the fluid representation relies on a fixed unstructured mesh larger or equal to the initial fluid domain and the fluid-shell interface inside the fluid mesh is tracked with level sets of a boundary signed distance function. Both models are tested with numerical examples, showing efficiency and robustness. Finally, as a suggestion for future development of this research, we started studies relatives to B-Spline functions. The use of this kind of functions should solve stability problems related to spurious oscillations due to the use of Lagrange polynomials for representing discontinuities.

The multi-armed bandit framework can be motivated by any problem where there is an abundance of choice and the utility of trying something new must be balanced with that of going with the status quo. This is a trade-off that is present in the everyday problem of where and what to eat: should I try a new restaurant or go to that Chinese place on the corner? In this work, a multi-armed bandit algorithm is presented which uses a non-parametric non-linear data model (a Gaussian process) to solve problems of this sort. The advantages of this method over existing work is highlighted through experiments. The method is also capable of modelling correlations between separate instances of problems, e.g., between similar dishes at similar restaurants. To demonstrate this, a few experiments are performed. The first, a synthetic example where the reward function is actually sampled from a Gaussian process, begs the question but helps pin down the properties of the algorithm in a controlled environment. The second, a problem where the objective is to aim a cannon at a distant target, shows how a well-defined objective, i.e., hit the target, can be used to speed up convergence. Finally, the third, an experiment with photographic post-processing, shows how the algorithm can learn from experience. The experiments demonstrate both the flexibility and the computational complexity of the model. This complexity means that problems such as the aforementioned restaurant problem, among others, are still future work.

Massive gravity is a particular theoretical model that modifies gravity on cosmological scales and therefore could provide a dynamical explanation for the observed accelerated expansion of our Universe. In this thesis we investigate various theoretical problems of massive gravity, important for its consistency and phenomenological viability. It is known that the predictions from the linearized massive gravity contradict the predictions of General Relativity. It is, however, an artifact due to the breakdown of the perturbative expansion in the massless limit. In our work we investigate this problem in the diffeomorphism invariant formulation of massive gravity in which the graviton mass term is written in terms of four scalar fields. We determine the so-called Vainshtein scale below which the scalar modes of the massive graviton enter the non-perturbative regime for a wide class of non-linear mass terms. We find the asymptotic solutions of the spherically symmetric gravitational field below and above the Vainshtein radius, and show that massive gravity goes smoothly to the General Relativity below this scale. We also determine the corresponding corrections to the Newton potential. In general, any non-linear extension of the quadratic graviton mass term propagates the Boulware-Deser ghost. The only theory in which the ghost is not propagating in the high energy decoupling limit, is the de Rham-Gabadadze-Tolley theory. Here we show that the ghost arises in the fourth order of perturbations in this theory away from the decoupling limit. However, we further argue that the ghost can be avoided in the full non-linear theory if not all four scalar fields propagate independent degrees of freedom. In particular, we investigate the simple example of (1+1)-dimensional massive gravity and find that the theory exhibits a gauge symmetry, which reduces the number of degrees of freedom. We also generalize the diffeomorphism invariant formalism of massive gravity to arbitrary curved backgrounds. We find that, given a specific background metric, the resulting generally covariant massive gravity exhibits an internal symmetry in the configuration space of the scalar fields. The symmetry transformations of the scalar fields are given by the isometries of the reference metric. In particular, we investigate massive gravity on de Sitter space in this formalism. We confirm the known result that, in the case when the graviton mass is related to the cosmological constant as m^2=2\Lambda/3, the theory is partially massless and propagates only four degrees of freedom.
Massive Gravitation ist ein theoretisches Modell, welches Gravitation auf kosmologischen Längenskalen modifiziert, und das so eine dynamische Erklärung für die beobachtete Beschleunigung der Expansion des Universums liefern könnte. In dieser Arbeit untersuchen wir verschiedene theoretische Probleme der massiven Gravitation, die wichtig bezüglich der Konsistenz und phänomenologischen Viabilität der Theorie sind. Es ist bekannt, dass die Vorhersagen der massiven Gravitation auf linearer Ordnung den Vorhersagen der allgemeinen Relativitätstheorie widersprechen. Dies ist jedoch ein Artefakt, das vom Zusammenbruch der perturbativen Entwicklung im masselosen Limes verursacht wird. In unserer Arbeit untersuchen wir dieses Problem in der Diffeomorphismen-invarianten Formulierung der massiven Gravitation, in der der Graviton-Massenterm mit vier skalare Feldern ausgedrückt wird. Wir bestimmen die sogenannte Vainshtein-Skala, unterhalb derer sich die skalaren Moden des massiven Gravitons nichtperturbativ verhalten, für eine große Klasse möglicher Massenterme. Wir finden die asymptotischen Lösungen des sphärisch symmetrischen Gravitationsfeldes inner- und außerhalb des Vainshtein-Radiuses und zeigen, dass massive Gravitation sich unterhalb dieser Skala kontinuierlich der Allgemeinen Relativitätstheorie annähert. Außerdem bestimmen wir die resultierenden Korrekturen zum Newton-Potential. Im Allgemeinen propagiert in jeder Theorie mit einer nichtlinearen Erweiterung des quadratischen Graviton-Massenterms ein Boulware-Deser Geist. Die einzige solche Theorie, in der der Geist im Hochenergie-Entkopplungslimes nicht propagiert, ist das de Rham-Gabadadze-Tolley Modell. Hier zeigen wir, dass der Geist selbst in dieser Theorie außerhalb des Entkopplungslimes in vierter Ordnung Störungstheorie erscheint. Wir argumentieren dann jedoch, dass der Geist in der voll nichtlinearen Theorie vermeiden werden kann, wenn nicht alle Skalarfelder unabhängige Freiheitsgrade darstellen. In dieser Hinsicht untersuchen wir das einfache Beispiel (1+1)-dimensionaler massiver Gravitation und finden, dass diese Theorie eine Eichsymmetrie enthält, die die Anzahl der Freiheitsgrade reduziert. Schließlich verallgemeinern wir den Diffeomorphismen-invarianten Formalismus massiver Gravitation auf allgemeine gekrümmte Hintergründe. Wir finden, dass auf bestimmten Hintergründen die resultierende allgemein kovariante massive Gravitation eine Symmetrie im Konfigurationsraum der skalaren Felder aufweist. Die Symmetrietransformationen der skalaren Felder sind durch die Isometrien der Referenzmetrik gegeben. Insbesondere untersuchen wir massive Gravitation auf de Sitter-Raum in diesem Formalismus. Wir bestätigen das bekannte Ergebnis, dass, im Falle einer Gravitonmasse im Verhältnis zur kosmologischen Konstante von m^2=2\Lambda/3, die Theorie teilweise masselos ist. Dadurch propagieren in diesem Fall nur vier Freiheitsgrade.

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1987.
Vita.
Includes bibliographical references (p. 183-184).
by Richard H. Lamb, Jr.
Sc.D.

This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine that distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of the hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E - and M - step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model.

The work done in this thesis is to examine various methods for curve fitting. Linear least squares and non-linear least squares will be described and compared, and the Newton method, Gauss--Newton method and Levenberg--Marquardt method will be applied to example problems.
Syftet med denna uppsats är att beskriva och använda olika metoder för kurvanpassning, det vill säga att passa matematiska funktioner till data. De metoder som undersöks är Newtons metod, Gauss--Newton metoden och Levenberg--Marquardt metoden. Även skillnaden mellan linjär minsta kvadrat anpassning och olinjär minsta kvadrat anpassning. Till sist tillämpas Newton, Gauss Newton och Levenberg--Marquardt metoderna på olika exempel.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Analytic Geometry has been, over the time, reason of much anxiety among students, because it is an area of mathematics that deals with relationsbetween equations and the Cartesian plane. From that anguish emerges the desire of make such subject accessible to any student and, then, the search for examples experienced by them becomesrelevant. This work aims to facilitate the relationship of students with some of the topics inanalytic geometry, namely: the Cartesian plane, and the representation of equations and inequalities with two and three variables. To develop this work, use the linear programming and a mathematical software become an important methodology, since arise some possibilities contributing to the achievement of the following objectives: to deal with modeling, solve real life problems, and interpret results in practical scenarios.
A Geometria Analítica tem sido, ao longo de tempo, motivo de muita angústia entre os alunos, pois é um assunto da Matemática que aborda relaçõesentre equações e o plano Cartesiano. Dessa angústia nasce a vontade de tornar o assunto mais acessível aos alunos e, para isso, a busca de exemplos reais vividos no dia a dia destesse torna relevante. Este trabalho tem como objetivo facilitar a relação dos alunos com alguns dos tópicos da Geometria Analítica, sendo eles: o plano Cartesiano e a representação de equações e inequações com duas e três variáveis. Para desenvolver este trabalho, o uso da programação linear e de um softwarematemático se tornam uma metodologia importante, pois, apoiando-se neles surgem possibilidades que contribuem para o alcance dos seguintes objetivos: lidar com a modelagem, resolver problemas do cotidiano dos alunos e interpretar resultados obtidos em cenários práticos.

New generations of brilliant synchrotron radiation sources and intense X-ray and optical lasers have opened unprecedent opportunities in linear and non-linear spectroscopies of molecules. This together with new instrumentation calls for further development of theory to explain observations and suggest new experiments. These two goals are the main objectives of the present thesis. In the first part of the thesis we study resonant inelastic X-ray scattering of the oxygen molecule. Recent experimental data of O2 show the dependence of the vibrational profile on the polarization of the X-rays. This vibrational scattering anisotropy is explained by the interference of the resonant and nonresonant inelastic scattering channels in O2. The second part of the thesis explores X-ray lasing caused by ultrafast dissociation of the HCl molecule in a repulsive core-excited state pumped by an X-ray free-electron laser. We show that the lasing efficiency is drastically enhanced due to the self-trapping of the amplified pulse into the ridge of the gain. The third part of the thesis is devoted to another non-linear phenomenon - optical limiting. Our time-dependent simulations are in agreement with the experimental data and show that phthalocyanines with heavy central metals exhibit good optical limiting properties for nanosecond pulses. Symmetry and the symmetry breaking are important fundamental concepts in physics, chemistry and biology. In the next part of the thesis we study theoretically the novel symmetry breaking mechanism in resonant Auger scattering. Both theory and electron-ion coincidence measurements for the oxygen molecule evidence the symmetry breaking of the oxygen cation caused by momentum exchange between the fast Auger electron and counter propagating dissociating oxygen atoms. The last part of the thesis is devoted to the role of the rotational degrees of freedom in X- ray ionization of molecules. We present here new results related to the rotational Doppler and angular recoil effects in X-ray ionization using the N2 and HCl molecules as illustrating examples. The dependence of the ionization cross section on the direction of ejection of fast electrons explains the sensitivity of the rotational broadening to the final state and to the polarization of X-rays observed recently for the N2 molecule. The theory reveals the novel effect of site-selectivity of X-ray valence ionization caused by the excitation of the rotational degrees of freedom which is different for different ionization sites. Large recoil angular momentum related to the ejection of an electron from the light hydrogen atom results in a red shifted broad pedestal in the X-ray photoelectron spectrum of HCl.

QC 20131108

The two most advanced applications of contactless magnetic levitation are high-speed magnetic bearings and magnetically levitated vehicles (Maglev) for ground transportation using superconducting magnets and controlled d.c. electromagnets. The repulsion force from superconducting magnets provide stable levitation with low damping, while the suspension force generated by electromagnets is inherently unstable. This instability, due to the in verse force-distance relationship, requires the addition of feedback controllers to sustain stable suspension. The problem of controlling magnetically levitated systems using d.c. electromagnets under different operating conditions has been studied in this thesis with a design process primarily driven by experimental results from a representative single-magnet test rig and a multi-magnet vehicle. The controller-design stages are presented in detail and close relationships have been constructed between selection of performance criteria for the derivation process and desired suspension characteristics. Both linear and nonlinear stabilising compensators have been developed. Simulation and experimental results have been studied in parallel to assess operational stability and the main emphasis has been given to assessing performance under different operational conditions. For the experimental work, a new digital signal processor-based hardware platform has been designed, built with interface to Matlab/Simulink. The controller design methods and algorithmic work presented in this thesis can be divided into: non-adaptive, adaptive, optimal linear and nonlinear. Adaptive algorithms based on model reference control have been developed to improve the performance of the suspension system in the presence of considerable variations in external payload and force disturbances. New design methods for Maglev suspension have been developed using robust control theory (%oo and fi synthesis). Single- and multi-magnet control problems have been treated using the same framework. A solution to the Hoo controller-optimisation problem has been derived and applied to Maglev control. The sensitivity to robustness has been discussed and tools for assessing the robustness of the closed-loop system in terms of sustaining stability and performance in the presence of uncertainties in the suspension model have been presented. Multivariable controllers based on %00 and /i synthesis have been developed for a laboratory scale experimental vehicle weighing 88 kg with four suspension magnets, and experimental results have been derived to show superiority of the proposed design methods in terms of ability to deal with external disturbances. The concept of Hoo control has been extended to the nonlinear setting using the concepts of energy and dissipativity, and nonlinear state-feedback and out put-feed back controllers for Maglev have been developed and reported. Simulation and experimental results have been presented to show the improved performance of these controllers to attenuate guideway-induced disturbances while maintaining acceptable suspension qualities and larger operational bandwidth.