Dans un article publié en 2003, M.Gromov propose une reformulation de la théorie des petites simplifications en géométrie des groupes. Dans cette version, un graphe fini définit une présentation finie de groupe; les générateurs du groupe sont les étiquettes du graphe; les relateurs sont les mots associés aux cycles; les morceaux, mots "courts " qui permettent les petites simplifications dans un groupe, sont des mots qui étiquettent deux chemins distincts du graphe. Cette thèse prend pour point de départ une brève description de cette théorie publiée par Y. Ollivier en 2006. Le concept de groupe de présentation finie à "petites simplifications", développé par R. Lyndon, M. Greendlinger et autres dans les années 60 et 70, est précurseur des groupes hyperboliques de M.Gromov à la fin des années 80, pour lesquels les propriétés combinatoires de la présentation entraînent des propriétés algébriques du groupe. Dans notre travail, nous fondons de manière rigoureuse la théorie des petites simplifications du point de vue des graphes, et développons le concept de base de "mégatuiles", utilisé implicitement par Y. Ollivier dans son article. Nous étendons ses résultats aux cas non-hyperboliques et non-métriques (par exemple$C(4)-T(4)$). Ce point de vue permet une nouvelle preuve, plus naturelle, de la résolubilité des problèmes du mot et de conjugaison pour les présentations des groupes des entrelacs alternés premiers. Nous prolongeons également les résultats d'un théorème de M. Greendlinger au cas non-métrique, répondant ainsi à une question d'I. Kapovich. / In a paper published in 2003, M.Gromov proposes a rewording of the small cancellation theory in geometric group theory. In this version, a finite graph defines a finitely presented group; generators of the group are the labels of the graph; relators are the words associated with cycles; pieces, "short" words which allow small cancellations in a group, are words which label two distinct paths in the graph.Our thesis relies on a brief description of this theory published in2006 by Y.Ollivier. The concept of finitely presented "small cancellation" group, developed by R.Lyndon, M.Greendlinger and others in the 60's and 70's, is a precursor of Gromovword-hyperbolic groups in the late of the 80's, for which combinatorial properties of the presentation imply algebraic properties of the group. In our work, we build a rigorous small cancellation theory in terms of graphs, and develop the basic concept of "megatiles", implicitly used by Y. Ollivier in his article. We extend his results to non-hyperbolic and non-metric cases (eg. $C(4)-T(4)$). This point of view allows a new proof, more natural, of thesolvability of word and conjugacy problems for presentations of prime alternating link groups. We also extend the results of a M.Greendlinger theorem to thenon-metric case, in response to a question of I. Kapovich.

Orientador: Antonio Carlos Bannwart / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências / Made available in DSpace on 2018-08-22T09:34:42Z (GMT). No. of bitstreams: 1 Gaspari_EduardoFerreira_D.pdf: 3211545 bytes, checksum: 80820e359cf9df0a39b228d34978524f (MD5) Previous issue date: 2013 / Resumo: Utilizando um método numérico especializado em problemas hiperbólicos chamado Riemann Solver, é feito um estudo para avaliar o processo de evolução de roll waves em canais fechados. Todo o estudo se baseia em fenômenos de propagação de ondas hiperbólicas do tipo ondas de gravidade. Foi utilizado um modelo unidimensional para representar a dinâmica das roll waves. Inicialmente foi feita uma análise das velocidades características envolvidas, a qual indicou, para o arranjo estratificado, um fraco acoplamento entre os fenômenos de propagação de onda mais relacionados com a compressibilidade dos fluidos e os fenômenos de propagação de ondas mais relacionados com a variação hidrostática na seção transversal do canal. Os resultados desta análise foram utilizados para justificar uma modelagem de roll wave considerando os fluidos como incompressíveis. Testes numéricos também foram feitos, demonstrando que a hipótese de fluidos incompressíveis não leva a uma perda de qualidade na modelagem de ondas de gravidade em canais fechados. Foi observada a fragilidade da hipótese de perfil hidrostático de pressão nos modelos de dois fluidos e é proposta uma modificação para este perfil de pressão considerando os efeitos dinâmicos devido à forma rugosa da interface em um escoamento estratificado instável. São feitas comparações com resultados experimentais de literatura para o filme de líquido em regime laminar e foram feitos experimentos para o filme de líquido em regime turbulento. As comparações entre as simulações e os resultados experimentais demonstrando que o modelo proposto é consistente / Abstract: Using a Riemann Solver numerical method, a study to evaluate the process of evolution of roll waves in closed channels was implemented. The whole study is based on the phenomena of hyperbolic gravity waves propagation. It was used a one-dimensional model to represent the dynamics of roll waves. Initially an analysis of the propagation wave velocities involved on to the stratified flow was done, a weak coupling between the wave propagation phenomena more closely related to fluid compressibility and wave propagation phenomena more closely related to the change in the void fraction, due the gravity waves, was verified. The results of this analysis were used to justify a roll wave modeling considering the fluids as incompressible. Numerical tests were also performed, showing that the hypothesis of incompressible fluids does not lead to a loss of quality in the modeling of gravity waves in closed channels. It was observed a fragility of the hydrostatic pressure profile assumption to modeling unstable stratified flow. It was proposed a modification to this pressure profile, considering the dynamic effects of the roughness interface. Comparisons were made with experimental results from the literature for the liquid film in laminar and experiments made for the film of liquid in turbulent flow. This comparison between simulations and experimental results demonstrate that the proposed model is consistent / Doutorado / Explotação / Doutor em Ciências e Engenharia de Petróleo

Neste trabalho mostramos que dado um domínio exterior de classe C0 contido em uma superfície umb lica de H3; com curvatura média constante H 2 [0; 1); existe uma família de gracos de Killing com curvatura média constante H: O bordo de cada um destes gracos está contido nesta superfície umbílica e a norma do gradiente da função no bordo pode ser prescrita por um certo valor s 0. / In this paper we show that given an exterior domain of class C0 contained in an umbilical surface of H3; with constant mean curvature H 2 [0; 1); there exists a family of Killing graphs with constant mean curvature H: The boundary of each of these graphs is contained in this umbilical surface and the norm of the gradient of the function in the boundary can be prescribed by a certain value s 0:

Deux méthodes de construction de représentations de groupes sont présentées. La première propose une stratégie essayant de déterminer les représentations de groupes libres de type fini à valeurs dans tout réseau de groupes de Lie réel. La seconde, après avoir revu une construction d'une surface hyperbolique complexe, c'est-à-dire le quotient du plan hyperbolique complexe par un réseau, et examiné soigneusement ses propriétés, produit une infinité de représentations non-conjuguées, à valeurs dans un réseau du groupe des isométries du plan hyperbolique complexe, de groupes fondamentaux de variétés hyperboliques fermées de dimension 3, obtenues comme des fibrés en surfaces sur le cercle. / Two construction methods of group representations are presented. The first one proposes a strategy to try to determine the representations of finitely generated free groups into any lattice in real Lie groups. The second, after reviewing a construction of a complex hyperbolic surface, that is the quotient of the complex hyperbolic plane by a lattice, and examining its properties carefully, yields infinitely many non-conjugate representations into a lattice in the group of isometries of the complex hyperbolic plane, of fundamental groups of closed hyperbolic 3-dimensional manifolds, obtained as surface bundles over the circle.

Nous considérons dans cette thèse le problème de Cauchy pour des systèmes d'EDP quasilinéaires, du premier ordre. Dans le cas initialement elliptique, c'est-à-dire un spectre non-réel pour le symbole principal du système à t=0, nous prouvons un résultat d'instabilité au sens d'Hadamard. La preuve est basée sur la construction d'une famille de solutions présentant une croissance exponentielle en temps et fréquence. Cette famille invalide la régularité Hölder du flot, partant d'espaces de Gevrey vers L². Nous prouvons un résultat analogue pour différents cas de transition de l'hyperbolique vers l'elliptique, avec une restriction possible sur l'indice Gevrey pour lequel l'instabilité est observée. Dans un second temps, nous considérons le cas faiblement hyperbolique et semilinéaire. Grâce à des estimations d'énergie dans les espaces de Gevrey et à la construction d'un symétriseur adapté, nous prouvons le caractère localement bien-posé pour un tel système. Pour ce faire, nous utilisons et démontrons aussi un résultat d'action d'opérateurs pseudo-différentiels dont le symbole possède une régularité Gevrey dans la variable d'espace. / We consider the Cauchy problem for first-order, quasilinear systems of PDEs. In the initially elliptic case, that is when the principal symbol of the system has nonreal spectrum at time t=0, we prove an instability result in the sense of Hadamard. The proof is based on the construction of a family of exact solutions which exhib an exponential growth, both in time and frequency. That family leads to a defect of Hölder regularity of the flow, starting from evrey spaces to L² space. We prove analogous results for some cases of transition from hyperbolicity to ellipticity, with a potential restriction on the Gevrey index for which we may observe the instability. In a second time, we consider weakly hyperbolic systems. Thanks to an energy estimate in Gevrey spaces and the construction of a suitable symetriser, we prove local well-posedness for such a system. In doing so we use and prove a result on actions of pseudo-differential operators whose symbols have Gevrey regularity in the spatial variable

This thesis explores problematics of speaker localization using microphone array. Aim of this thesis is implementation of algorithms for speaker localization and experiments with those algorithms. Calculation of TDOA was done using cross-correlation and hyperbolic method was used to calculate position estimation. Finished microphone array is able to locate speaker within certain variance. Results of this thesis allow reader to make assumptions regarding accuracy of localisation using microphone array and ARM kit with limited performance. Precision of position estimation using microphone array reached several decimeters, but this precision is dependent on distance from microphone array.

The subject of this final thesis was to elaborate variant proposal and to assess supporting steel structure roof bus station in the shape of a hyperbolic paraboloid. 2 variants were proposed, one of which was chosen as a more appropriate and this was processed details and drawings. Both variants are used as cover glass panels. Structures are made of steel with 235J0.

<p>In the first part, the pressureless gas dynamic system with source (body force) is examined and solved by using Shadow Waves. The source represents gravity and Shadow Wave solution (containing the delta function) shows acceleration (contrary to shocks, for example). In the second part, one will nd numerical calculations that conrms the above results.</p> / <p>Rad je posvecen analizi modela gasa bez pritiska uz dodatak izvora. Model je resen koriscenjem senka talasa. U ovom slucaju, izvor predstavlja uticaj gravitacije na cestice u modelu. Za razliku od udarnih talasa, talasi senke koje sadrze delta funkciju, krecu se ubrzano pod gravitacionim uticajem. U drugom delu rada su naprevljeni numericki eksperimenti koji potvrdjuju teoijske rezultate.</p>

In dieser Arbeit werden wir Systeme von Erhaltungsgleichungen betrachten. Dabei handelt es sich um hyperbolische Systeme erster Ordnung. Durch hyperbolische Differentialgleichungen werden Wellen und deren Ausbreitung beschrieben, skalare Differentialgleichungen erster Ordnung sind immer hyperbolisch. Wichtige Beispiele für hyperbolische Erhaltungsgleichungen sind die nichtviskose Burgersgleichung, die Buckley-Leverett-Gleichung zur Beschreibung von Zweiphasenströmungen, die Eulergleichungen der nichtviskosen Strömungsmechanik und bestimmte Gleichungen der Magnetohydrodynamik. Ausserdem finden sie auch Anwendung in Verkehrsflussmodellen, beispielsweise beim Modell von Lighthill, Whitham und Richards.

The investigation of the latent geometrical space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarity-optimization (PSO) generative model is able to grow random geometric graphs in the hyperbolic space with realistic properties such as clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex systems, which is the community organization. Here, we introduce the nonuniform PSO (nPSO) generative model, a generalization of the PSO model with a tailored community structure, and we provide an efficient algorithmic implementation with a O(EN) time complexity, where N is the number of nodes and E the number of edges. Meanwhile, in recent years, the inverse problem has also gained increasing attention: given a network topology, how to provide an accurate mapping into its latent geometrical space. Unlike previous attempts based on a computationally expensive maximum likelihood optimization (whose time complexity is between O(N^3) and O(N^4)), here we show that a class of methods based on nonlinear dimensionality reduction can solve the problem with higher precision and reducing the time complexity to O(N^2).