Cette thèse introduit le concept de comportement géométrique d'un assemblage mécanique. Cette notion permet de rendre compte du caractère assemblable ou mobile d'un mécanisme sous la forme d'un système de relations algébriques entre les paramètres géométriques permettant de le décrire. Dans un premier temps, cette thèse montre l'intérêt de ce concept pour traiter des problèmes faisant intervenir plusieurs effets physiques et plusieurs scénarios d'utilisation. Ce chapitre est appliqué à l'étude de l'assemblabilité d'un treillis pyramidal de conception à 4 barres décrit par un modèle géométrique non cartésien issu de la littérature. Dans un second temps, après avoir constaté le manque de modèles adaptés permettant de représenter des mécanismes mobiles, ce travail en propose un non cartésien. Il détaille aussi une méthode de mise en équation afin de traduire la mobilité d'un mécanisme. Une application de ce modèle et de la méthode est également faite. Elle permet de résoudre localement le problème de la mobilité d'un mécanisme de Bennett. Enfin, la dernière partie de ce travail expose une solution pour associer et comparer deux objets décrits par des représentations non cartésiennes. Cette technique est utile pour comparer deux états physiques du même objet utilisé dans différents scénarios pour assurer le suivi d'une exigence géométrique. Elle peut également être utilisée pour associer des objets réels et des objets idéalisés pour traiter des problèmes de tolérancement / This thesis introduces the concept of geometrical behavior of mechanical assembly. The geometrical behavior is constituted by a set of algebraic relations that translate the assemblability or mobility conditions of a product. It is expressed thanks to a specific geometrical model for the early phases of product design. Firstly, this work shows the interest of the geometrical behavior to tackle multi-physics problems at the early stages of product design. This part is illustrated on a ten bar pyramid subjected to mechanical and thermal strains. Secondly, this thesis proposes a coordinate free geometrical model dedicated to the representation of mobile mechanisms. This part also indicates a technique to express the mobility conditions of a loop as mathematical equations. An application of these model and technique is proposed to express the geometrical behavior of the Bennett mechanism. Finally, this work exposes a solution to associate and compare two objects described in the above-mentioned coordinate free model. This technique is useful to compare two states of the same object used under different operating conditions. It can also be used to associate ideal and real objects to tackle tolerancing issues.

Lors de la réalisation des pièces d’un mécanisme, le fabricant se doit de respecter les exigences géométriques exigées par le client. Ces exigences sont issues de besoins fonctionnels du mécanisme à tous les stades de son cycle de vie. Le fabricant lors des opérations successives d’usinage, avec ou sans enlèvement de matière, doit définir les exigences de la géométrie ajoutée au poste. La combinaison de ces exigences affectées de leur tolérance doit être comparée aux exigences géométriques du client. L’objectif du travail présenté est la définition d’une méthode optimisant, rationnellement, les exigences géométriques des surfaces créées. Nous définirons les spécifications géométriques, au sens de l’iso 1101, mais la valeur de ces tolérances ne sera pas abordée dans ce travail, d’autres équipes ayant réalisés des travaux de qualité. L’étude poussée de la méthode 1D utilisée dans l’ensemble du groupe Renault pour définir les fiches schéma nous a montré ses limites lors de la multiplication des posages orientés différemment. Par contre l’optimisation du choix des spécifications influentes a retenu notre intérêt. L’étude des méthodes du bureau d’études pour la recherche de spécifications des pièces composant un mécanisme nous a permis de faire l’analogie avec les phases d’usinages. En effet le passage successif de la pièce sur les différents postes d’usinage s’apparente à des assemblages temporaires qui mettent en œuvre des surfaces actives qu’elles soient de posage ou créées à l’opération. La modélisation du processus d’usinage à l’aide d’une représentation graphique est largement utilisée par la communauté travaillant dans le tolérancement. Nous avons développé dans notre travail un modèle de représentation appelé SPIDER GRAPH. Ce modèle essentiellement pédagogique nous permet de visualiser le déroulement de l’algorithme développé à l’occasion de ce mémoire. Il met en valeur la succession de liens entre les différentes surfaces intervenant pour réaliser une spécification exigée. Deux méthodes utilisant le concept SATT pour la mise en position des ensembles de surfaces de tolérancement de fabrication 3D sont décrites : « Recherche des chemins du process contraignant les degrés de liberté de la spécification fonctionnelle ». Nous avons identifié, en se référant aux résultats développés par DESROCHERS, toutes les combinaisons possibles entre des entités simples et leurs correspondances en termes de type de tolérance. Une validation par un exemple a été établie et un ensemble de spécifications géométriques de fabrication a été généré. Cette méthode qui s’appuie successivement sur les surfaces du système de référence ne permet pas une écriture se référant à des systèmes de référence. Nous avons donc développé une alternative à ce travail initial. « Méthode rationnelle de tolérancement de fabrication 3D » Cette méthode est représentée par un logigramme qui prend en compte la hiérarchie des surfaces lors des posages. Il prend également en compte les inversions de spécifications entre la référence et la surface spécifiée. Lors de la création de surfaces temporaires qu’elles soient de posage ou d’usinage, la méthode permet de spécifier ces surfaces dans les opérations considérées. Lors du développement de cette méthode originale, nous avons repris la totalité des fiches de cotations SATT, développées par CLEMENT et aussi les modélisations vectorielles de ces cas d’association décrites par GAUNET. A l’aide des lois d’identification des paramètres de mise en position relative entre SATT, nous avons pu générer, l’ensemble des spécifications géométriques capables de mener au respect de la spécification géométrique fonctionnelle. Cette méthode assure la traçabilité des liens successifs entre les surfaces actives lors des différentes opérations. [...] / During the realization of the mechanism pieces, the manufacturer must respect the customer geometrical requirements. These requirements arise from functional needs of the mechanism in all its life cycle stages. During the successive operations of manufacturing, with or without material removing, the manufacturer has to define the added geometry requirements in each phase. The combination of these requirements affected by their tolerance must be compared with the functional geometrical requirements. The objective the actual work is to define a method optimizing, in a rational way, the geometrical requirements of the created surfaces. We shall define the geometrical specifications, according to the standard “ISO on 1101”, but the quantification of the tolerance zones will not be approached on this work, other teams have given good results. The 1D method, used in the whole of the group Renault to define process cards, is limited during the reproduction of positioning surfaces directed differently. On the other hand the optimization of the influential specifications retained our interest. The study of the engineering consulting firm method, used for the search of the each pieces specification composing a mechanism, allowed us to make analogy with the manufacturing phases. Indeed the successive manufacturing operation on various posts is similar to temporary assemblies which implement active surfaces whether they are positioning or machined surfaces, existing in this phase. The modeling of the manufacturing process by means of a graphic representation is widely used on the tolerance filed. We developed in our work a model of representation called SPIDER GRAPH. This essentially educational model allows us to show the progress of the algorithm, developed in this these. It emphasizes the succession of links between the various surfaces with intervene in the generation of needed manufacturing specification. Two methods based on the TTRS concept to select all needed surfaces in 3D manufacturing tolerancing are described: « Search of the process links constraining the functional forbidden displacement ». In this method we identified, by referring to the results developed by DESROCHERS, all the possible combinations between simple entities and their tolerance type correspondences. An example of validation is afterward established and a set of geometrical manufacturing specifications were generated. With this previous method we are constrained to treat the surfaces that constitute the functional reference system independently, one by one, which is not conform to the standard. What urged us to look for another alternative able to remedy to this problem. « Rational method for 3D manufacturing tolerancing synthesis based on TTRS approach » This method is represented by an algorithm which takes into account the hierarchy of positioning surfaces and the specifications inversions between the reference and the specified surface. During the creation of temporary surfaces, whether they are used for positioning or they are machined, the method allows to generate the appropriate tolerance specification in the considered phase. During the development of this method, we took back the totality of the tolerancing process TTRS cards, developed by CLÉMENT and also the vectorial modelling of these associations’ cases, described by GAUNET. With the relatives positioning parameters rules, we were able to generate at the end of the treatment all the geometrical specifications capable to ensure the respect of the functional geometrical specification. This method insures the traceability of the successive links between the active surfaces during the various manufacturing operations. These links which can be represented on the SPIDER GRAPH will allow determining mathematically or in a probability way the consequence of these various pieces transfer between machines.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1981. / Bibliography: leaves 105-107. / by Vincent C. Lin. / Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1981.

Neste trabalho estudamos a continuidade da dinâmica assintótica relativamente a perturbações e, em particular, exploramos a obtenção de melhorias para as taxas de convergência de atratores globais através da introdução de fatores de correção, inspirados pelos resultados da teoria de homogeneização e nos trabalhos de (BABIN; VISHIK, 1992) e (CARVALHO; CHOLEWA, 2011), e através da introdução de mecanismos que melhoram a transferência da taxa de convergência de semigrupos para a taxa de convergência de atratores, inspirados pelos trabalhos (SANTAMARÍA, 2013) e (BABIN; VISHIK, 1992; CARVALHO; CHOLEWA, 2011). A proposta inicial está centrada na obtenção de melhores taxas de convergência de atratores globais através da obtenção de equiatração e da melhoria da taxa de convergência dos semigrupos. Para isto, buscamos melhorar a taxa de convergência do resolvente dos operadores setoriais envolvidos, por meio de uma perturbação singular do resolvente limite que ainda gere uma família de operadores setoriais com resolventes que aproximam o resolvente do problema limite e aproximam melhor os resolventes das perturbações iniciais. Feito isto, obtemos uma melhora imediata de convergência dos semigrupos lineares, depois dos não lineares (através da fórmula da variação das constantes). Motivados pelos resultados de (SANTAMARÍA, 2013), que oferecem uma menor perda na transferência das taxas de convergência dos semigrupos para as taxas de convergência dos atratores, buscamos melhor compreender a propriedade Lipschitz Shadowing, que é responsável direta pela obtenção da taxa de convergência dos atratores diretamente da taxa de convergência dos semigrupos. Isto nos levou a descobrir que podemos obter as propriedade Lipschitz Shadowing e estabilidade estrutural para perturbações Lipschitz de semigrupos Morse-Smale. / Here we compare the continuity of the asymptotic dynamics with respect to perturbations and, in particular, we explored to obtain improvement of rates of convergence of the global attractor through the introduction of correction factors, inspired by the results of homogenization theory and work of (BABIN; VISHIK, 1992) and (CARVALHO; CHOLEWA, 2011), and the introduction of mechanisms that improve the transference of the convergence rate of semigroups to the convergence rate of attractors, inspired by the work of (SANTAMARÍA, 2013) and (BABIN; VISHIK, 1992; CARVALHO; CHOLEWA, 2011). The initial proposal is focused on achieving best rates of convergence of the global attractors by obtaining equi-atraction and improving the convergence rate of semigroups. For this, we seek to improve the rate of convergence of the resolvents of sectorial operators, through a singular perturbation of the resolvent associated with the limit problem and generate a new family of sectorial operators whose resolvents both approximate the resolvent of the limit problem as they were closer to the resolvents the initial perturbation. Having done this, we obtain an immediate improvement of convergence of linear semigroups, after the non-linear (using the variation of constants formula). Motivated by the results of (SANTAMARÍA, 2013), which offer an improvement in obtaining convergence rates, we seek to study property better Lipschitz Shadowing, which is basically responsible for obtaining the distance of the attractors directly from the convergence rate of the semigroups. This has led us to discover that we can both preserve the Lipschitz Shadowing property under Lipschitz perturbations of Morse-Smale semigroups, and The geometric stability of the attractors.

Este trabalho aborda a formulação geométrica das teorias clássicas de calibre, ou Yang-Mills, considerando-as como uma importante classe de modelos que deve ser incluída em qualquer tentativa de estabelecer um formalismo matemático geral para a teoria clássica dos campos. Tal formulação deve vir em (pelo menos) duas variantes: a versão hamiltoniana, que passou por uma fase de desenvolvimento rápido durante os últimos 10-15 anos, levando ao que hoje é conhecido como o ``formalismo multissimplético\'\', e a mais tradicional versão lagrangiana utilizada nesta tese. O motivo principal justificando tal investigação é que teorias de calibre constituem os mais importantes exemplos de sistemas dinâmicos que são altamente relevantes na Física e onde a equivalência entre a versão lagrangiana e a versão hamiltoniana, que no caso de sistemas não-singulares é estabelecida pela transformação de Legendre, deixa de ser óbvia, pois teorias de calibre são sistemas degenerados do ponto de vista lagrangiano e são sistemas vinculados do ponto de vista hamiltoniano. Esta propriedade característica das teorias de calibre é uma consequência direta do seu alto grau de simetria, isto é, da sua invariância de calibre. No entanto, numa formulação plenamente geométrica da teoria clássica dos campos, capaz de incorporar situações topologicamente não-triviais, a invariância sob transformações de calibre locais (transformações de calibre de segunda espécie) e, surpreendentemente, até mesmo a invariância sob as transformações de simetria globais correspondentes (transformações de calibre de primeira espécie) não podem ser adequadamente descritas em termos de grupos de Lie e suas ações em variedades, mas requerem a introdução e o uso sistemático de um novo conceito, a saber, fibrados de grupos de Lie e suas ações em fibrados (sobre a mesma variedade base). A meta principal da presente tese é tomar os primeiros passos no desenvolvimento de ferramentas matemáticas adequadas para lidar com este novo conceito de simetria e, como uma primeira aplicação, dar uma definição clara e simples do procedimento de ``acoplamento mínimo\'\' e uma demonstração simples do teorema de Utiyama, segundo o qual lagrangianas para potenciais de calibre (conexões) de primeira ordem (i.e., que dependem apenas dos próprios potenciais de calibre e de suas derivadas parciais até primeira ordem) que são invariantes sob transformações de calibre são necessariamente funções dos campos de calibre (i.e., do tensor de curvatura) invariantes sob as transformações de simetria globais correspondentes. / This thesis deals with the geometric formulation of classical gauge theories, or Yang-Mills theories, regarded as an important class of models that must be included in any attempt to establish a general mathematical framework for classical field theory. Such a formulation must come in (at least) two variants: the hamiltonian version which has gone through a phase of rapid development during the last 10-15 years, leading to what is now known as the ``multisymplectic formalism\'\', and the more traditional lagrangian version studied in this thesis. The main motivation justifying this kind of investigation is that gauge theories constitute the most important examples of dynamical systems that are highly relevant in physics and where the equivalence between the lagrangian and the hamiltonian version, which for non-singular systems is established through the Legendre trans% formation, is far from obvious, since gauge theories are degenerate systems from the lagrangian point of view and are constrained systems from the hamiltonian point of view. This characteristic property of gauge theories is a direct consequence of their high degree of symmetry, that is, of gauge invariance. However, in a fully geometric formulation of classical field theory, capable of incorporating topologically non-trivial situations, invariance under local gauge transformations (gauge transformations of the second kind) and, surprisingly, even invariance under the corresponding global symmetry transformations (gauge transformations of the first kind) cannot be described adequately in terms of Lie groups and their actions on manifolds but requires the introduction and systematic use of a new concept, namely Lie group bundles and their actions on fiber bundles (over the same base manifold). The main goal of the present thesis is to take the first steps in developing adequate mathematical tools for handling this new concept of symmetry and, as a first application, give a simple clear-cut definition for the prescription of ``minimal coupling\'\' and a simple proof of Utiyama´s theorem, according to which lagrangians for gauge potentials (connections) that are gauge invariant and of first order, i.e., dependent only on the gauge potentials themselves and on their partial derivatives up to first order, are necessarily functions of the gauge field strengths (i.e., the curvature tensor) invariant under the corresponding global symmetry transformations.

Neste trabalho, construímos novas soluções com simetria esférica ou axial para as equações do campo gravitacional induzido num cenário brana do tipo Randall-Sundrum, onde uma 3-brana com constante cosmológica está imersa num espaço-tempo 5-dimensional conhecido como bulk. Para o caso esfericamente simétrico, com constante cosmológica negativa, obtivemos uma família de soluções numa brana assintoticamente anti-de Sitter, sendo que cada membro desta é diferenciado de outro por uma constante integração C, que fixada proveu-nos soluções de buracos negros ou buracos de minhocas. Com a mesma simetria, geometrias que descrevem buracos de minhoca foram encontradas numa brana assintoticamente de Sitter. Para o caso axialmente simétrico, métricas assintoticamente anti-de Sitter e de Sitter foram construídas no contexto citado. Propriedades óticas, como a rotação do vetor de polarização, foram estudadas, mostrando-nos algumas diferenças entre os mundos brana, tratados como uma teoria de gravitação modificada, e a relatividade geral. / In this work we have constructed new solutions, with axial or spherical symmetry, to the induced gravitational field equations within a Randall-Sundrum type brane world scenario, where a 3-brane with cosmological constant is embedded in a 5-dimensional space-time called bulk. For the spherical case with negative cosmological constant, we have found a family of solutions in an anti-de Sitter brane, where each member of the family is different from another when C is fixed. With a fixed C we have black holes or wormholes. In this same case, with spherical symmetry, we have obtained wormhole solutions in a de Sitter brane. In the same context, for the axially symmetric case, metrics asymptotically anti-de Sitter and de Sitter were built. Optics features, like rotation of polarization vector, have been studied. These features showed some differences between brane worlds, a theory of modified gravity, and the General Relativity.

Chan, Pui Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 72-75). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

This paper is a study of T-sets of normed linear spaces. Geometrical properties of normed linear spaces are developed in terms of intersection properties shared by a subcollection of T-sets of the space and in terms of special spanning properties shared by each T-set of a subcollection of T-sets of the space. A characterization of the extreme points of the unit ball of the dual of a normed linear space is given in terms of the T-sets of the space. Conditions on the collection of T-sets of a normed linear space are determined so that the normed linear space has the property that extreme points of the unit ball of the dual space map canonically to extreme points of the unit ball of the third dual space.

Made available in DSpace on 2017-07-21T20:56:32Z (GMT). No. of bitstreams: 1 Gilmar KLoster.pdf: 2898946 bytes, checksum: a6884d601b79157da063128a79a81ae6 (MD5) Previous issue date: 2014-08-04 / Complex numbers have applications both in mathematics and in other areas of knowledge. But in high school, at which time the student begins the study of this set of numbers, they are taught with emphasis on algebraic manipulations, leaving only the geometric applications reduced the representation of points in the complex plane. In many cases, even this geometric application is addressed. This work aims to address the set of complex numbers using the geometry, enhancing the visualization of some results in GeoGebra, to provide more meaningful to the student learning. / Os números complexos possuem aplicações tanto na matemática como em outras áreas do conhecimento. Porém no ensino médio, momento em que o aluno inicia o estudo deste conjunto numérico, eles são ensinados dando ênfase as manipulações algébricas, deixando as aplicações geométricas reduzidas apenas a representação de pontos no plano complexo. Em muitos casos, nem mesmo esta aplicação geométrica é abordada. Este trabalho tem por objetivo abordar o Conjunto dos Números complexos utilizando a geometria, valorizando a visualização de alguns resultados no GeoGebra, para proporcionar à aprendizagem mais significativa ao aluno.

En vision par ordinateur, les points saillants sont des caractéristiques essentielles aux algorithmes. Les performances dépendent de paramètres extérieurs (ex. illumination). Les mesures de similarité sont centrales à la reconnaissance. Pour assurer l'efficacité de traitement, les caractéristiques extraites d'une image doivent être stables, et la mesure de similarité doit les distinguer parfaitement.Dans cette thèse, des caractéristiques conjointes géométrie/couleur sont étudiées : lignes de couleur et régions. Elles fondent la détection d'une troisième, la profondeur, qui sert en retour à évaluer leurs performanceLes lignes sont des extensions des classiques lignes de niveau: l'espace couleur 3-D est projeté sur un espace 1-D adapté pour résumer l'information chromatique là où elle est adéquate,Les régions exploitent classiquement la connexité image mais jointe à une compacité dans l'histogramme bidimensionnel issu du modèle dichromatique. L'homogénéité ainsi définie garantit une robustesse a priori aux variations d'éclairage en séparant la couleur de l'intensité et les couleurs entre elles.Cette homogénéité est exploitée selon 2 méthodes d'extraction d'ensembles compacts autour des modes de l'histogramme: extraction analytique des extrema locaux de couleur, extraction de ces mêmes extrema contrôlée par les régions correspondantes de l'image.Pour la profondeur, trois calculs de disparité stéréoscopique sont proposés et les performances comparées avec la réalité terrain:1. Appariement de lignes couleur avec une distance de Hausdorff revisitée.2. Exploitation de la forme des histogrammes de disparité par régions3.Coopération entre appariement de points et de régions. / In computer vision, salient points are essential features to algorithms. Performances depend on external parameters (e.g. illuminant). Similarity measures are central to recognition.To secure the processing efficiency, extracted features have to be stable enough, and the similarity measure needs to perfectly distinguish between them.In the thesis, joint geometrical and color features are studied: color lines and regions. They found the detection of a third one, range, that helps in turn to assess their goodness.Color lines are extensions of classical level lines: the 3 D color space is mapped onto a 1 D scale especially designed to retain the chromatic information where it is suitable.Regions require the usual image connectivity but in association with compactness in the bi-dimensional histogram stemming from the dichromatic model. The so-designed homogeneity is granting an a priori good robustness against illumination variations in separating the body colors and splitting color from intensity.The latter homogeneity gives raise to 2 methods for extracting compact sets around histogram modes: color first analysis (an analytic extraction of color local extrema) , and joint color/space analysis (same but controlled by the region growing).As for depth, 3 methods to compute the stereo disparity are proposed for their results to be confronted with the ground-truth:1. Color line matching based on a modified Hausdorff distance,2. Studying the shape of the disparity histogram between regions,3. Cooperation between pixel correlation and region matching.The robustness of the designed features is proved on several stereo pairs. Future work deals with improving efficacy and accuracy.