Orientador: Alberto Vazquez Saa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T03:54:09Z (GMT). No. of bitstreams: 1 Leal_Isabel_M.pdf: 984828 bytes, checksum: b0a33558ae8b5683163892248364a85b (MD5) Previous issue date: 2012 / Resumo: Nesta dissertação, fazemos uma revisão da literatura existente sobre vórtices em superfícies de curvatura constante, dando especial atenção às questões de integrabilidade e não integrabilidade. Além disso, apresentamos alguns resultados originais sobre o movimento de vórtices no plano hiperbólico que indicam um possível caminho para demonstrar a não integrabilidade de um sistema de quatro vórtices nessa superfície / Abstract: In this thesis, we review the existing literature on vortices on surfaces of constant curvature, giving special attention to the issues of integrability and non-integrability. In addition, we present some original results on the motion of vortices on the hyperbolic plane that indicate a possible way to demonstrate the non-integrability of a system of four vortices on that surface / Mestrado / Matematica / Mestre em Matemática

Conventional interferometry is widely used to measure spherical and flat surfaces with nanometer level precision but is plagued by back reflections. We describe a new method of isolating the measurement surface by controlling spectral properties of the source (Spectrally Controlled Interferometry - SCI). Using spectral modulation of the interferometer's source enables formation of localized fringes where the optical path difference is non-zero. As a consequence it becomes possible to form white-light like fringes in common path interferometers, such as the Fizeau. The proposed setup does not require mechanical phase shifting, resulting in simpler instruments and the ability to upgrade existing interferometers. Furthermore, it allows absolute measurement of distance, including radius of curvature of lenses in a single setup with possibility of improving the throughput and removing some modes of failure.

Cette thèse est consacrée à l'étude d'une famille des flots géométriques associés au problème de la courbure scalaire prescrite sur une variété riemannienne compacte. Plus précisément, si on désigne par (M,g0) une variété riemannienne compacte de dimension n≥3, et si F∈C∞ (M) est une fonction donnée, le problème de la courbure scalaire prescrite consiste à trouver une métrique g conforme à g0 telle que F soit sa courbure scalaire. Ce problème est équivalent à la résolution de l'EDP suivante :-4 (n-1)/(n-2) ∆u+R0 u=Fu((n+2)/(n-2 )) , u>0 , (E), Où R0 est la courbure scalaire de la métrique initiale g0 et ∆ est le laplacien associé à g0. Il s'agit d'une équation elliptique non-linéaire dont la difficulté principale provient du terme u((n+2)/(n-2 )). Hormis le cas de la sphère standard Sn , tous les travaux consacrés à l'étude de l'équation (E) sont basés sur la méthode variationnelle. Dans cette thèse, on développe une autre approche basée sur l'étude d'une famille de flots géométriques qui permet, entre autres, de résoudre l'équation (E). La question dépend bien entendu de la métrique initiale g0 et en particulier du signe de sa courbure scalaire R0. Les flots introduits sont des flots de gradient associés à deux fonctionnelles distinctes dépendant du signe de R0. La première partie de cette thèse est consacrée au cas R0<0 et dans la deuxième partie on traite le cas R0>0. Dans les deux cas, on démontre l'existence globale du flot et on étudie son comportement asymptotique à l'infini. / This thesis is devoted to the study of a family of geometric flows associated with the prescribed scalar curvature problem. More precisely, if we denote by (M,g0) a compact riemannian manifold with dimension n≥3, and if F∈C∞ (M) is a given function, the prescribed scalar curvature problem consists of finding a conformal metric g to g0 such that F is its scalar curvature. This problem is equivalent to the resolution of the following PDE : -4 (n-1)/(n-2) ∆u+R0 u=Fu((n+2)/(n-2 )) , u>0 , (E), Where R0 is the scalar curvature of the initial metric g0 and ∆ is the laplacian associated with g0.It is a nonlinear elliptic equation, whose the main difficulty comes from the term u((n+2)/(n-2 )). Apart from the case of the standard sphere Sn all the works that study the equation (E) are based on the variational method. In this thesis, we develop another approach based on the study of a family of geometric flows which allows to solve equation (E).The flows introduced are gradient flows associated with two distinct functional functions depending on the sign of R0.The first part of this thesis is devoted to the case R0<0 and in the second part we treat the case R0>0. In both cases, our aim is to proof the global existence of the flow and study its asymptotic behavior at infinity.

Cette Thèse de Doctorat est dédiée à la simulation numérique des détonations, et plus particulièrement aux détonations confinées par un gaz inerte. Cette configuration correspond en partie à l’écoulement rencontré au sein des moteurs à détonations rotatives, dans lesquels le combustible est confiné par les gaz brûlés issus du cycle précédent. Le code de calcul employé s’appuie sur des schémas numériques d’ordre élevé adaptés à la capture des discontinuités (interpolation MP d’ordre 9, solveur HLLC et intégration temporelle d’ordre3). Une attention particulière a été portée à la caractérisation de l’écoulement au travers de son évolution moyenne dans le repère de la détonation. Les simulations ont été réalisées pour différentes valeurs de l’énergie d’activation, qui traduit la sensibilité du milieu réactif,pour des couches réactives de dimensions variées et enfin pour des confinements inertes à différentes températures. La base de données résultante démontre l’existence de deux comportements distincts suivant l’énergie d’activation du milieu réactif. Le déficit de la célérité de la détonation peut être globalement appréhendé comme fonction du ratio de l’épaisseur hydrodynamique par le rayon de courbure sur l’axe. Enfin, la présence d’une couche inerte à haute température modifie de façon importante la topologie de la détonation et en étend les limites de propagation. / This dissertation is devoted to the numerical study of detonation waves, and more specifically to the dynamics of detonations bounded by an inert gaseous layer. This configuration is similar to the flow field within the rotating detonation engines, in which the fuel is confined by the burned gases produced during the previous combustion cycle. The computational solver is based on high-order schemes designed for capturing discontinuities (9thorder MP interpolation, HLLC solver and 3rd order temporal integration). The detonation was investigated by calculating the averaged profile in the shock frame of reference. The simulations were performed for various values of the activation energy, which control the mixture sensitivity, for different heights of the reactive layer and for different temperature of the inert medium. The resulting database shows that according to the activation energy, two different behaviors can be observed. The presence of a high-temperature inert layer strongly affects the detonation structure and extends the propagation limits. The detonation deficit can be globally expressed as a function of the ratio of the hydrodynamic thickness to the radius of curvature on the axis.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17106号 / 工博第3617号 / 新制||工||1549(附属図書館) / 29836 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 杉浦 邦征, 教授 白土 博通, 教授 河野 広隆 / 学位規則第4条第1項該当

Contorted polycyclic aromatic hydrocarbons have found increasing utility in the application of molecular electronics due to the surpamolecular properties that result from these non-planar structures. The [n]circulene series of molecules are particularly attractive members of the contorted aromatic family due to the unique structural implications that result from their changing value of n. For example, when n ≤ 5, the structures adopt a bowl-like shape; when n = 6, a planar structure is observed; and when 7 ≤ n ≤ 16, the compounds assume a saddle-like shape. Very few molecules exhibit the structural contortions that these contorted aromatics do – primarily because aromatic molecules desire to adopt highly planar conformations. Following the model of aromaticity developed by Erich Clar, we set our sights on the synthesis of tetrabenzo[8]circulene, the stabilized form of [8]circulene established through the addition of four fused benzenoid rings around the periphery of the molecule. The initial approach towards this structure employs a Diels-Alder [4 + 2] cycloaddition reaction and a palladium catalyzed arylation reaction as the key transformation steps. The results of these studies were promising, establishing the structural characterization of this new molecule and providing access to functionalized derivatives of the saddle-shaped structure. However, access towards these functionalized derivatives proved limiting, compelling us to investigate alternative synthetic methodologies. In the course of our studies, we established a new methodology towards 2,5-diarylthiophene-1-oxides, a key precursor to the Diels-Alder cycloaddition reaction. These reactive dienes are prepared from readily available arylacetylene precursors via zirconacyclopentadiene intermediates. The isolated yields of the desired thiophene-1-oxides are comparable to those obtained from previously established oxidation strategies while avoiding the formation of over-oxidation products. Of significant importance to scope of our work, this newly established methodology offers broader versatility providing products outfitted with electron-donating or electron-withdrawing groups. These new methodologies provided access to functionalized derivatives of the saddle-shaped molecule tetrabenzo[8]circulene in improved yield when coupled with a revised Diels-Alder/oxidative cyclodehydrogenation approach. This methodology affords products containing both electron-rich and electron-poor functional groups in a more efficient manner. The optoelectronic effects that result from the introduction of this functionality and investigations into the development of larger contorted aromatic systems are also discussed.

Ces deux dernières décennies, les techniques de somme connexe essentiellement basées sur des outils d'analyse ont permis de faire des progrès importants dans la compréhension de nombreux problèmes non linéaires issus de la géométrie (étude des métriques à courbure scalaire constante en géométrie Riemannienne, métriques auto-duales, métrique ayant des groupes d'holonomie spéciaux, métriques extrémales en géométrie Kaehlerienne, équations de Yang-Mills, étude des surfaces minimales et des surfaces à courbure moyenne constante, métriques d'Einstein, etc.). Ces techniques se sont avérées être un outil puissant pour démontrer l'existence de solutions à des problèmes hautement non linéaires. Si les techniques permettant d'effectuer des sommes connexes en des points isolés sont bien comprises et fréquemment utilisées, les techniques permettant d'effectuer des sommes connexes le long de sous-variétés ne sont pas encore bien maîtrisées. Le principal objectif de cette thèse est de combler (partiellement) cette lacune en développant de telles techniques applicables dans le cadre de l'étude des métriques à courbure scalaire constante et aussi dans le cadre de l'étude des équations de comptabilité d'Einstein en relativité générale / These last two decades the connected sum techniques, essentially based on analytical tools, are revealed to be a powerful instrument to understand solutions of several nonlinear problem issued from the geometry (constant scalar curvature metrics in Riemannian geometry, self-dual metrics, metrics with special holonomy group, extremal Kaehler metrics, Yang-Mills equations, minimal and constant mean curvature surfaces, Einstein metrics, etc.). Even tough the techniques which allows one to consider the connected sum at points for solutions of nonlinear PDE's are frequently used and deeply understood, the analogous techniques for connected sums along sub-manifolds have not been mastered yet. The main purpose of this thesis is to (partially) plug this gap by developing such techniques in the context of the constant scalar curvature metrics and the Einstein constraint equations in general relativity

Master of Science / Department of Geology / Abdelmoneam Raef / Matthew W. Totten / This work focuses on the use of advanced seismically driven technologies to estimate the distribution of key reservoir properties which mainly includes porosity and hydrocarbon reservoir pay. These reservoir properties were estimated by using a multitude of seismic attributes derived from post-stack high resolution inversions, spectral imaging and volumetric curvature. A pay model of the reservoir in the Wierman field in Ness County, Kansas is proposed. The proposed geological model is validated based on comparison with findings of one blind well. The model will be useful in determining future drilling prospects, which should improve the drilling success over previous efforts, which resulted in only few of the 14 wells in the area being productive. The rock properties that were modeled were porosity and Gamma ray. Water saturation and permeability were considered, but the data needed were not available. Sequential geological modeling approach uses multiple seismic attributes as a building block to estimate in a sequential manner dependent petrophysical properties such as gamma ray, and porosity. The sequential modelling first determines the reservoir property that has the ability to be the primary property controlling most of the other subsequent reservoir properties. In this study, the gamma ray was chosen as the primary reservoir property. Hence, the first geologic model built using neural networks was a volume of gamma ray constrained by all the available seismic attributes. The geological modeling included post-stack seismic data and the five wells with available well logs. The post-stack seismic data was enhanced by spectral whitening to gain as much resolution as possible. Volumetric curvature was then calculated to determine where major faults were located. Several inversions for acoustic impedance were then applied to the post-stack seismic data to gain as much information as possible about the acoustic impedance. Spectral attributes were also extracted from the post-stack seismic data. After the most appropriate gamma ray and porosity models were chosen, pay zone maps were constructed, which were based on the overlap of a certain range of gamma ray values with a certain range of porosity values. These pay zone maps coupled with the porosity and gamma ray models explain the performance of previously drilled wells.

The thesis studies homogenization of Dirichlet boundary value problems for divergence type elliptic operators, and the associated boundary layer issues. This type of problems for operators with periodically oscillating coeffcients, and fixed boundary data are by now a classical topic largely due to the celebrated work by Avellaneda and Lin from late 80's. The case when the operator and the Dirichlet boundary data exhibit periodic oscillations simultaneously was a longstanding open problem, and a progress in this direction has been achieved only very recently, in 2012, by Gerard-Varet and Masmoudi who proved a homogenization result for the simultaneously oscillating case with an algebraic rate of convergence in L2. Aimed at understanding the homogenization process of oscillating boundary data, in the first part of the thesis we introduce and develop Fourier-analytic ideas into the study of homogenization of Dirichlet boundary value problems for elliptic operators in divergence form. In smooth and bounded domains, for fixed operator and periodically oscillating boundary data we prove pointwise, as well as Lp convergence results the homogenization problem. We then investigate the optimality (sharpness) of our Lp upper bounds. Next, for the above mentioned simultaneously oscillating problem studied by Gerard-Varet and Masmoudi, we establish optimal Lp bounds for homogenization in some class of operators. For domains with non smooth boundary, we study similar boundary value homogenization problems for scalar equations set in convex polygonal domains. In the vein of smooth boundaries, here as well for problems with fixed operator and oscillating Dirichlet data we prove pointwise, and Lp convergence results, and study the optimality of our Lp bounds. Although the statements are somewhat similar with the smooth setting, challenges for this case are completely different due to a radical change in the geometry of the domain. The second part of the work is concerned with the analysis of boundary layers arising in periodic homogenization. A key difficulty toward the homogenization of Dirichlet problem for elliptic systems in divergence form with periodically oscillating coefficients and boundary condition lies in identification of the limiting Dirichlet data corresponding to the effective problem. This question has been addressed in the aforementioned work by Gerard-Varet and Masmoudi on the way of proving their main homogenization result. Despite the progress in this direction, some very basic questions remain unanswered, for instance the regularity of this effective data on the boundary. This issue is directly linked with the up to the boundary regularity of homogenized solutions, but perhaps more importantly has a potential to cast light on the homogenization process. We initiate the study of this regularity problem, and prove certain Lipschitz continuity result. The work also comprises a study on asymptotic behaviour of solutions to boundary layer systems set in halfspaces. By a new construction we show that depending on the normal direction of the hyperplane, convergence of the solutions toward their tails far away from the boundaries can be arbitrarily slow. This last result, combined with the previous studies gives an almost complete picture of the situation.

In a foundational paper “Operators Possesing an Open Set of Eigenvalues” written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space ‘H possessing an open set Ω C of eigenvalues determines a holomorphic Hermitian vector bundle ET . One of the basic theorems they prove states that the unitary equivalence class of the operator T and the equivalence class of the holomorphic Hermitian vector bundle ET are in one to one correspondence. This correspondence appears somewhat mysterious until one detects the invariants for the vector bundle ET in the operator T and vice-versa. Fortunately, this is possible in some cases. Thus they point out that if the operator T possesses the additional property that the dimension of the eigenspace at ω is 1 for all ω Ω then the map ω ker(T - ω) admits a non-zero holomorphic section, say γ, and therefore defines a line bundle on Ω. As is well known, the curvature defined by the formula is a complete invariant for the line bundle . On the other hand, define and note that NT (ω)2 = 0. It follows that if T is unitarily equivalent to T˜, then the corresponding operators NT (ω) and NT˜(ω) are unitarily equivalent for all ω Ω. However, Cowen and Douglas prove the non-trivial converse, namely that if NT (ω) and NT˜(ω) are unitarily equivalent for all ω Ω then T and T˜ are unitarily equivalent. What does this have to do with the line bundles and .To answer this question, we must ask what is a complete invariant for the unitary equivalence class of the operator NT (ω). To find such a complete invariant we represent NT (ω) with respect to the orthonormal basis obtained from the two linearly independent vectors γ(ω),∂γ(ω) by Gram-Schmidt orthonormalization process. Then an easy computation shows that It then follows that is a complete invariant for NT (ω), ω Ω. This explains the relationship between the line bundle and the operator T in an explicit manner. Subsequently, in the paper ”Operators Possesing an Open Set of Eigenvalues”, Cowen and Douglas define a class of commuting operators possessing an open set of eigenvalues and attempt to provide similar computations as above. However, they give the details only for a pair of commuting operators. While the results of that paper remain true in the case of an arbitrary n tuple of commuting operators, it requires additional effort which we explain in this thesis.