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1
Semmler, Gunter. "Nonlinear Riemann-Hilbert Problems." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:swb:105-7341443.
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Riemann-Hilbert-Probleme sind Randwertaufgaben für im Einheitskreis $\mathbb D$ holomorphe Funktionen $w$, deren Randwerte $w(t)$ auf gewissen Kurven $M_t$ liegen sollen. Ein Teil der Untersuchungen ist dem Fall explizit gegebener Kurven gewidmet. Dabei werden bekannte Resultate über glatte Kurven auf stetige Restriktionskurven erweitert, und die Existenz von Lösungen in gewissen Hardy-Räumen gezeigt. Die Eindeutigkeitsfrage führt auf ein Gegenbeispiel, das zugleich eine Vermutung aus einer Dissertation von Belch widerlegt. Der andere Teil der Untersuchungen ist dem klassischen Fall geschlossener Restriktionskurven gewidmet. Hier steht statt der Abschwächung von Glattheitsvoraussetzungen die Formulierung geeigneter Nebenbedingungen im Mittelpunkt. Die Abhängigkeit der Lösung von Zusatzbedingungen erweist sich als Verallgemeinerung des Verhaltens von Blaschkeprodukten. Für drei Interpolationpunkte kann charakterisiert werden, wann durch sie eine Lösung mit Windungszahl 1 verläuft, durch $k$ Interpolationspunkte wird die Existenz einer Lösung mit Windungszahl $k-1$ gezeigt.
2
Dewaal, Nicholas. "The Importance of the Riemann-Hilbert Problem to Solve a Class of Optimal Control Problems." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1759.pdf.
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Fernández, Sánchez Percy. "El problema de Riemann Hilbert : sobre superficies de Riemann no compactas." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96150.
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En el ICM (Intemational Congress of Mathematicians) de 1900, Hilbert presenta 23 problemas que establecieron el curso de gran parte de las investigaciones matemáticas del siglo XX. El 21° problema es la existencia de ecuaciones diferenciales lineales, con un grupo de monodromía y singularidades prescritas. Este artículo trata este problema sobre superficies de Riemann no compactas.
4
Gu, Xiang. "Hamiltonian structures and Riemann-Hilbert problems of integrable systems." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7677.
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We begin this dissertation by presenting a brief introduction to the theory of solitons and integrability (plus some classical methods applied in this field) in Chapter 1, mainly using the Korteweg-de Vries equation as a typical model. At the end of this Chapter a mathematical framework of notations and terminologies is established for the whole dissertation.
In Chapter 2, we first introduce two specific matrix spectral problems (with 3 potentials) associated with matrix Lie algebras $\mbox{sl}(2;\mathbb{R})$ and $\mbox{so}(3;\mathbb{R})$, respectively; and then we engender two soliton hierarchies. The computation and analysis of their Hamiltonian structures based on the trace identity affirms that the obtained hierarchies are Liouville integrable. This chapter shows the entire process of how a soliton hierarchy is engendered by starting from a proper matrix spectral problem.
In Chapter 3, at first we elucidate the Gauge equivalence among three types $u$-linear Hamiltonian operators, and construct then the corresponding B\"acklund transformations among them explicitly. Next we derive the if-and-only-if conditions under which the linear coupling of the discussed u-linear operators and matrix differential operators with constant coefficients is still Hamiltonian. Very amazingly, the derived conditions show that the resulting Hamiltonian operators is truncated only up to the 3rd differential order. Finally, a few relevant examples of integrable hierarchies are illustrated.
In Chapter, 4 we first present a generalized modified Korteweg-de Vries hierarchy. Then for one of the equations in this hierarchy, we build the associated Riemann-Hilbert problems with some equivalent spectral problems. Next, computation of soliton solutions is performed by reducing the Riemann-Hilbert problems to those with identity jump matrix, i.e., those correspond to reflectionless inverse scattering problems. Finally a special reduction of the original matrix spectral problem will be briefly discussed.
5
Desideri, Laura. "Problème de Plateau, équations fuchsiennes et problème de Riemann-Hilbert." Phd thesis, Université Paris-Diderot - Paris VII, 2009. http://tel.archives-ouvertes.fr/tel-00452508.
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Ce mémoire est consacré à la résolution du problème de Plateau à bord polygonal dans l'espace euclidien et dans l'espace de Minkowski de dimension trois. Il s'appuie sur la méthode de résolution proposée par René Garnier dans le cas euclidien dans un article publié en 1928 et qui a été oublié depuis, voire ignoré à l'époque. Plus géométrique et constructive que la méthode variationnelle, l'approche de Garnier est cependant parfois très compliquée, voire obscure et incomplète. On retranscrit sa démonstration dans un formalisme moderne, tout en proposant de nouvelles preuves plus simples, et en en complétant certaines lacunes. Ce travail repose principalement sur l'utilisation plus systématique des systèmes fuchsiens et la mise en évidence du lien entre la réalité de ces systèmes et leur monodromie. Ceci nous permet d'étendre le résultat de Garnier dans l'espace de Minkowski. La méthode de Garnier repose sur le fait que, par la représentation de Weierstrass spinorielle des surfaces minimales, on peut associer une équation fuchsienne réelle du second ordre définie sur la sphère de Riemann à tout disque minimal à bord polygonal. La monodromie de cette équation est déterminée par les directions orientées des côtés du bord. Pour résoudre le problème de Plateau, on est donc amené à résoudre un problème de Riemann-Hilbert. On procède ensuite en deux étapes : on construit d'abord, par déformations isomonodromiques, la famille de tous les disques minimaux dont le bord est un polygone de directions orientées données. Puis on montre, en étudiant les longueurs des côtés des bords polygonaux, qu'on obtient ainsi tout polygone comme bord d'un disque minimal.
6
TINTAYA, PERCY ALEXANDER CACERES. "RIEMANN HILBERT PROBLEMS IN RANDOM MATRIX THEORY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26432@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Estudamos as noções básicas da Teoria das Matrizes Aleatórias e
em particular discutimos o Emsemble Unitário Gaussiano. A continuação
descrevemos o gaz de Dyson em equilíbrio e fora do equilíbrio que permite
interpretar a informação estatística dos autovalores das matrizes aleatórias.
Além desso mostramos descrições alternativas dessa informação estatística.
Em seguida discutimos aspectos diferentes dos polinômios ortogonais. Uma
dessas caracterizações é dada pelos problemas de Riemann-Hilbert. As
técnicas dos problemas de Riemann-Hilbert são uma ferramenta eficaz e
potente na Teoria das Matrizes Aleatórias a qual discutimos com mais
cuidado. Finalmente usamos o método de máxima gradiente na análise
assintótico dos polinômios ortogonais.<br>We review the basic notions of the Random Matrix Theory and in
particular the Gaussian Unitary Ensemble. In what follows we describe the
Dyson gas in equilibrium and nonequilibrium that allows one to interpret the
statistical information of the eigenvalues of random matrices. Furthermore
we show alternative descriptions of this statistical information. In the
following we discuss different aspects of orthogonal polynomials. One of
these caracterizations is given by a Riemann Hilbert problem. Riemann
Hilbert problem techniques are an efficient and powerfull tool for Random
Matrix Theory which we discuss in more detail. In the final part we
use the steepest descent method in the asymptotic analysis of orthogonal
polynomials.
7
Belch, Rudiger. "Extremal interpolation and nonlinear Riemann-Hilbert problems." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624100.
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Campana, Camilo. "O problema de Riemann-Hilbert para campos vetoriais complexos." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-25072017-111735/.
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Este trabalho trata de problemas de contorno definidos no plano. O problema central desta tese é chamado Problema de Riemann-Hilbert, o qual pode ser descrito como segue. Seja L um campo vetorial complexo não singular definido em uma vizinhança do fecho de um aberto simplesmente conexo do plano com fronteira suave. O Problema de Riemann-Hilbert para o campo L consiste em obter uma solução para a equação Lu = F(x, y, u) no aberto em estudo, sendo dada uma função F mensurável. Pede-se também que a solução tenha extensão contínua até a fronteira e que satisfaça lá uma condição adicional; trabalha-se aqui no contexto das funções Hölder contínuas. Foram obtidos resultados para o problema acima no caso em que L pertence a uma classe de campos hipocomplexos. O caso clássico conhecido é quando o campo vetorial é o operador de Cauchy-Riemann, ou, mais geralmente, quando é um campo elítico.<br>This work deals with boundary problems in the plane. The central problem in this thesis is the so-called Riemann-Hilbert problem, which may be described as follows. Let L be a non-singular complex vector field defined on a neighborhood of the closure of a simply connected open subset of the plane having smooth boundary. The Riemann-Hilbert problem for the vector field L consists in finding a solution to the equation Lu = F(x, y, u) on the open set under study, where the given function F is measurable. It is also required that the solution have a continuous extension up to the boundary and satisfy an additional condition there. Results were obtained for the above problem when L belongs to a class of hypocomplex vector fields. The well-known classical case is the one in which the vector field under study is the Cauchy-Riemann operator, or more generally when it is an elliptic vector field.
9
Hays, Christopher. "Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2917.
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Let Σ<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, for each <em>g</em> ≥ 1 and <em>h</em> ≥ 0 we construct an infinite set of infinite families of homotopic but pairwise non-isotopic symplectic surfaces inside the product symplectic manifold Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>. In particular, we achieve all positive genera from these families, providing first examples of infinite families of homotopic but pairwise non-isotopic symplectic surfaces of even genera inside Σ<em><sub>g</sub></em> ×Σ<em><sub>h</sub></em>.
10
Vitti, Ana Paula. "PROBLEMA DE RIEMANN PARA LEIS DE CONSERVAÇÃO ESCALARES." Universidade de São Paulo, 1995. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-24042018-145013/.
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Este trabalho apresenta um estudo sobre a existência, unicidade e comportamento assintótico de soluções para uma lei de conservação escalar da forma ut+ f (u)x = O. Esta solução satisfaz a desigualdade de entropia, e além disso é a única solução com esta propriedade. O problema é estudado via o método das diferenças finitas.<br>In this work we studied the existence, uniqueness and asymptotic behavior of solutions for a single conservation law in the form ut + f (u)x = 0. This solution satisfies the entropy inequality, and furthermore is the unique solution with this propriety. The problem was studied using the finite-difference method.
11
Sousa, Vítor Luís Pereira de. "O problema de Riemann Hilbert para polinómios ortogonais." Master's thesis, Universidade de Aveiro, 2004. http://hdl.handle.net/10773/16686.
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Mestrado em Matemática<br>Nesta dissertação estudamos a aplicação do Problema de Riemann-Hilbert
na teoria de Polinómios Ortogonais. Com esse efeito, abordamos vários
tópicos essenciais para clarificar esta técnica. O texto está dividido em quatro
capítulos, Preliminares de Análise Complexa, Problemas de Valores de
Fronteira, Teoria Geral dos Polinómios Ortogonais, e O Problema de
Riemann-Hilbert nos Polinómios Ortogonais.
Apresentamos uma série de resultados fundamentais de Análise Complexa,
entre os quais, uma extensão do teorema de Riemann em singularidades
removíveis, a fórmula de Cauchy em domínios ilimitados, o principio do
prolongamento analítico, e exemplos de Superfícies de Riemann.
Formulamos o Problema de Riemann-Hilbert, e estudamos a sua solução
típica, a Transformada de Cauchy, sobre vários tipos de curvas e famílias de
funções. A este propósito definimos o integral singular no sentido de Cauchy,
e o seu valor principal, e deduzimos as designadas fórmulas de Sokhotski-
Plemelj .
Sobre a teoria de Polinómios Ortogonais, apresentamos alguns resultados
básicos de polinómios ortogonais sobre a recta real e sobre a circunferência
unitária. Estudamos, também, a teoria apresentada por Szegö e mostramos
resultados sobre o comportamento assimptótico dos polinómios ortogonais
que esta teoria permite obter.
Finalmente, estudamos o designado por método de Riemann-Hilbert, que
usamos para determinar o comportamento assimptótico (forte) dos polinómios
ortogonais. Este método consiste em caracterizar os polinómios ortogonais
em termos de um problema de Riemann-Hilbert (i.e., em termos de uma
matriz de funções analíticas com um salto sobre uma curva γ ) e, depois, em
transformar sucessivamente o problema de Riemann-Hilbert inicial noutros
problemas de Riemann-Hilbert sobre um conjunto de curvas deformadas com
saltos mais simples. Fazemos a aplicação deste método aos polinómios
ortogonais correspondentes à função peso
w(x) ( x ) h(x) 1 2 1/ 2 − = −
(onde x∈[−1,1] e h é uma função real, analítica e estritamente positiva sobre
[−1,1]), e obtemos resultados assimptóticos para os polinómios ortogonais
mónicos e para os coeficientes principais dos polinómios ortonormais.<br>In this dissertation we study the application of the Riemann-Hilbert problem
in the theory of Orthogonal Polynomials. With that objective, we board several
essential subject helpful to clarify this technique. This work is divided in four
chapters, Preliminaries of Complex Analysis, Boundary Value Problems,
General Theory of Orthogonal Polynomials, The Riemann-Hilbert problem in
Orthogonal Polynomials.
We present a number of basic facts of Complex Analysis, such as the
Riemann’s theorem on removable singularities, the Cauchy’s formula for
unbounded domains, the analytic continuation principle, and some examples
of Riemann Surfaces.
We formulate the Riemann-Hilbert problem, and study its typical solution,
the Cauchy transform on several kind of contours and families of functions. We
also define the singular integral in Cauchy sense, and the main principal value,
and we deduce the Sokhotski-Plemelj formulas.
About the Orthogonal Polynomials theory, we present some basic results on
orthogonal polynomials on the real line and on the unit circle. We also study
the Szegö’s theory and show some results about the asymptotic behaviour of
orthogonal polynomials that are possible to get with this theory.
Finally we study the so-called Riemann-Hilbert method, that we use its for
finding the (strong) asymptotic behaviour of orthogonal polynomials. This
method consist in characterising the Orthogonal Polynomials in terms of the
Riemann-Hilbert problem (i.e., as a boundary value problem for a matrix
valued analytic functions with jump on a contour γ ), and then to transform
successively the initial Riemann-Hilbert problem to another equivalent
Riemann-Hilbert problem on a deformed set of contours with simpler jumps.
We apply this method to the orthogonal polynomials corresponding to the
weight function
w(x) ( x ) h(x) 1 2 1/ 2 − = −
(with x∈[−1,1] and h real analytic function and strictly positive on [−1,1]), and
we get asymptotics formulas for the monic orthogonal polynomials and for the
leading coefficients of the orthonormal polynomials.
12
Sambou, Salomon. "Equation de Cauchy-Riemann pour les courants prolongeables." Université Joseph Fourier (Grenoble ; 1971-2015), 2001. http://www.theses.fr/2001GRE10081.
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Soient x une variete analytique complexe et un domaine de x. On resout le pour les courants prolongeables definis sur sous des hypotheses de convexite ou concavite sur. On applique les resultats ainsi obtenus a l'etude de l'isomorphisme de dolbeault entre les groupes de b-cohomologie des formes c et des courants definis sur une hypersurface reelle dont la forme de levi a un certain nombre de valeurs propres strictement positives et de valeurs propres strictement negatives. Dans le cas ou est completement strictement pseudoconvexe a bord c , nous obtenons aussi les deux applications suivantes : 1) l'annulation du r-ieme groupe de cohomologie des formes differentielles de classe c a valeurs dans le faisceau des fonctions holomorphes sur qui ont une valeur au bord au sens des courants. 2) la resolution de l'equation pour une donnee qui est une (1, 1)-forme differentielle c , d-fermee qui a une valeur au bord au sens des courants sur.
13
Zhang, Lun. "Global asymptotics of orthogonal polynomials via Riemann-Hilbert approach /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749453f.pdf.
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Thesis (Ph.D.)--City University of Hong Kong, 2009.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [95]-100)
14
Jardim, Luiz Guilherme Chagas Moraes. "Uma nova descrição para a transferência de massa em meios porosos com transição saturado-insaturado." Universidade do Estado do Rio de Janeiro, 2014. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=8096.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Esse texto trata do problema de um fluido contaminado escoando por um meio poroso, tratando os componentes na mistura como meios contínuos. Na primeira parte, desenvolvemos a teoria de misturas de meios contínuos e discutimos equações da continuidade, momento linear e momento angular. A seguir, descrevemos o problema em detalhe e fazemos hipóteses para simplificar o escoamento. Aplicamos as equações encontradas anteriormente para encontrarmos um sistema de equações diferenciais parciais. Desse ponto em diante, o problema se torna quase puramente matemático. Discutimos o caso insaturado, e depois a saturação do meio poroso. Finalmente, adicionamos um contaminante à mistura e, em seguida, N contaminantes.<br>This text treats the problem of a contaminated fluid flowing through a porous medium, treating the components in the mixture as continuum media. In the first part, we develop the continuum mixture theory and discuss equations for continuity, linear momentum and angular momentum. Next, we describe the problem in detail and make hypotheses to simplify the flow. We apply the equations found previously to a system of partial diferential equations. From then on, the problem becomes almost purely mathematical. We discuss the unsaturated case, then the saturation of the porous medium. Finally, we add a contaminant to the mixture and, then, N contaminants.
15
Kozlowska, Katarzyna. "Riemann-Hilbert problems and their applications in mathematical physics." Thesis, University of Reading, 2017. http://centaur.reading.ac.uk/73488/.
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The aim of this thesis is to present the reader with the very effective and rigorous Riemann-Hilbert approach of solving asymptotic problems. We consider a transition problem for a Toeplitz determinant; its symbol depends on an additional parameter t. When t > 0, the symbol has one Fisher-Hartwig singularity at an arbitrary point z1 6= 1 on the unit circle (with associated α1, β1 ∈ C strengths) and as t → 0, a new Fisher-Hartwig singularity emerges at the point z0 = 1 (with α0, β0 ∈ C strengths). The asymptotics we present for the determinant are uniform for sufficiently small t. The location of the β-parameters leads to the consideration of two cases, both of which are addressed in this thesis. In the first case, when | Re β0 − Re β1| < 1 we see a transition between two asymptotic regimes, both given by the same result by Ehrhardt, but with different parameters, thus producing different asymptotics. In the second case, when | Re β0 − Re β1| = 1 the symbol has Fisher-Hartwig representations at t = 0, and the asymptotics are given the Tracy-Basor conjecture. These double scaling limits are used to explain transition in the theory of XY spin chains between different regions in the phase diagram across critical lines.
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ARAÚJO, Juliana Aragão de. "O Problema de Riemann para um escoamento bifásico em meios porosos com histerese nas duas fases." Universidade Federal de Campina Grande, 2005. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1108.
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Previous issue date: 2005-05<br>Neste trabalho é apresentada a solução do problema de Riemann associado a um
sistema de leis de conservação. Este sistema é proveniente de um escoamento bifásico
unidimensional em meios porosos e considera os efeitos de histerese nas curvas de
permeabilidade das fases. A principal contribuição deste trabalho é que a solução do
problema de Riemann é obtida para um modelo que leva em conta a histerese nas duas
fases e que considera as curvas de embebição e de drenagem distintas sempre que haja
uma reversão de regime de drenagem para embebição e vice-versa. Os resultados obtidos aqui ampliam aqueles obtidos para um modelo mais simplificado em que a histerese era considerada apenas numa das fases e as curvas de permeabilidade eram tomadas coincidentes após urna segunda reversão. Uma vez obtida a solução do problema de Riemann, base para a construção de simuladores numéricos de alta precisão, é feita uma comparação entre esta solução e aquela obtida anteriormente, para os mesmo dados iniciais, mostrando que não só as velocidades de ondas podem ser distintas, mas também as próprias sequências de ondas que formam tais soluções.<br>In this work we prasent the Riemann solution for a system of conservation laws
associatcd to an unidimensional two-ph&sc fiow in a porous media taking into account
the hysteresis effects on the permeability curves. Our main contribution in this work
is that the solution of the Riemann problem is obtained for a model that takes into account
the hysteresis in both wetting and non-wetting phases and considers the scanning
curves of embebition and drainagc distincts whenever there is a reversion of regime.
The results obtained here improve those obtained for a simplified model where hysteresis
is considered only on the non-wetting phase and the scanning curves coincide aftcr
a second reversion of regime. Once obtained the solution of the Riemann problem,
which is basic for the construction of high aceurate numeric simulators, we compare
this solution and that one already obtained, for the same initial data. showing that
not only the speeds of waves can be distinct, but also the sequences of waves in such
Solutions.
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Renaut, Gilles-Alexis. "Schémas d'ordre élevé pour la méthode SPH-ALE appliquée à des simulations sur machines hydrauliques." Thesis, Ecully, Ecole centrale de Lyon, 2015. http://www.theses.fr/2015ECDL0053/document.
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Ce travail traite des méthodes de calcul numérique pour les simulations hydrodynamiques appliquées principalement sur des produits développés par ANDRITZ HYDRO. Il s’agit ici de mettre en place des schémas d’ordre élevé pour des simulations CFD en utilisant le code de calcul ASPHODEL développé et utilisé par ANDRITZ HYDRO. Les principales motivations sont l’augmentation de la fiabilité des résultats de calculs numériques avec un coût de calcul raisonnable. Cette fiabilité s’exprime à travers l’augmentation de la précision et de la robustesse des schémas numériques. Le code de calcul ASPHODEL est basé sur la méthode sans maillage SPH-ALE. Mélange entre les volumes finis et la méthode SPH (Smoothed Particle Hydrodynamics), la méthode SPH-ALE emploie un ensemble de points appelés particules servant à la discrétisation du domaine fluide. Elle permet en particulier de par son caractère sans maillage, un suivi des surfaces libres sans effort de calcul supplémentaire. Cet aspect est véritablement attrayant pour bon nombre d’applications industrielles notamment la simulation des écoulements à surface libre se produisant dans une turbine Pelton, mais également le remplissage d’une turbine Francis. Cependant, le bémol à cette méthode est son manque de précision spatiale. En effet les points de calcul étant mobiles, les opérateurs spatiaux doivent être en mesure de conserver leur précision et leur robustesse au cours du temps. La qualité des résultats en est du coup impactée, en particulier le champ de pression souvent excessivement bruité. La montée en ordre et l’amélioration de la consistance des opérateurs pour un vaste panel de configurations géométriques sont donc les enjeux de ce travail. En utilisant des outils inspirés par les volumes finis non-structurés, il est possible d’améliorer les opérateurs spatiaux. En effet, la montée en ordre ou p-raffinement peut notamment se faire avec des reconstructions d’ordres élevés pour évaluer les états aux interfaces des problèmes de Riemann. La sommation des flux numériques résolus par un solveur de Riemann est ensuite retravaillée pour obtenir un schéma numérique d’ordre global cohérent. Le même soucis de cohérence avec les schémas en temps doit d’ailleurs être pensé. Le gain de précision apporté par les schémas numériques d’ordre élevé est comparé avec un raffinement spatial, c’est à dire une augmentation du nombre des particules de taille plus petite, aussi appelé h-raffinement. La méthode SPH-ALE améliorée est ensuite testée sur des cas représentatifs des applications visées. En conclusion, les développements effectués dans cette étude ont été guidés par l’application en turbine Pelton principalement mais il va de soi qu’ils sont applicables à des écoulements sans surface libre dans les turbines Francis par exemple. Ce travail montre les possibilités d’une méthode sans maillage pour des cas d’écoulements complexes autour de géométrie tournantes<br>This work deals with numerical methods for hydrodynamic testing applied mainly on products developed by ANDRITZ HYDRO. This is to put in place high order schemes for CFD simulations using the ASPHODEL calculation code developed and used by ANDRITZ HYDRO. The main reasons are the increased reliability of the results of numerical calculations with a reasonable computational cost. This reliability is expressed through increasing the accuracy and robustness of numerical schemes. The ASPHODEL computer code is based on the meshfree method SPH-ALE. Mix between finite volume method and SPH (Smoothed Particle Hydrodynamics), the SPH-ALE method uses a set of points called particles serving as the fluid domain discretization. It allows track free surfaces without additional computational effort. This is truly attractive for many industrial applications including the simulation of free surface flows occurring in a Pelton turbine, but also filling a Francis turbine. However, the downside of this method is its lack of spatial accuracy. Indeed calculation points are mobile, space operators must be able to keep their accuracy and robustness over time. The quality of results is impacted especially the pressure field is often excessively noisy. The rise in order and improving the consistency of the operators for a wide range of geometric configurations are the challenges of this work. Using tools inspired by the unstructured finite volume, it is possible to improve the spatial operators. Indeed, the increasing order or p-refinement particular can be done with reconstructions of high order to assess the conditions at the interfaces of Riemann problems. The summation of discret fluxes solved by Riemann solver is then reworked to obtain a coherent global order scheme. The same concern for consistency with temporal schemes should also be considered. The precision gain provided by numerical schemes of higher orders is compared with a spatial refinement ie an increase in the number of smaller particles ; also called h -refinement . Improved SPH -ALE method is then tested on representative cases of intended applications. In conclusion, the developments made in this study were guided in accordance mainly with the Pelton turbine but it goes without saying that they are applicable to non- free surface flows in Francis turbines for example. This work shows the possibilities of a free mesh method for cases of complex flow around rotating geometry
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CARVALHO, Maur?cio de. "Fluxo de solu??o salinizada com ?ons dissolvidos em um meio poroso unidimensional." Universidade Federal Rural do Rio de Janeiro, 2016. https://tede.ufrrj.br/jspui/handle/jspui/2095.
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Previous issue date: 2016-04-12<br>CAPES<br>In this work we consider the injection of water with dissolved ions into a linear horizontal porous rock cylinder with constant porosity and absolute permeability initially containing oil and water in several proportions. The water is assumed to have low salinity concentration, where some ions are dissolved. We disregard that there is in the rocks some possible minerals that can dissolve or precipitate in water phase. There are two chemical fluid components as well as two immiscible phases: water and oil, (w, o). The dissolved ions are: positive divalent ions: calcium ions, Ca2+ and magnesium ions, Mg2+; negative divalent ions: sulphate ions, SO42?; positive monovalent ions: sodium ions, Na+; negative monovalent ions: cloride ions, Cl?. The cations are modeled to be involved in fast ion exchange process with a surface negative X? which can absorb the positive ions, Ca2+, Mg2+ and Na+. We use simple mixing rules and we disregard any heat of precipitation/dissolution of substance reactions or ion desorption. Moreover we disregard any volume contraction efects resulting from mixing and reactions in any phase. We are going to solve in this work, the Riemann problem and we are going to discuss some features about the studied model.<br>Neste trabalho consideramos a inje??o de ?gua com ?ons dissolvidos em um meio po-roso linear horizontal cil?ndrico com porosidade e permeabilidade absoluta constantes, inicialmente, contendo ?leo e ?gua em v?rias propor??es. A ?gua ? assumida ter baixa concentra??o de sais, onde alguns ?ons est?o dissolvidos. Desconsideramos a exist?ncia de alguns poss?veis minerais na rocha que possam dissolver ou precipitar na fase da ?gua. Existem dois componentes qu?micos fluidos assim como duas imisc?veis fases: ?gua e ?leo,(w, o). Os ?ons dissolvidos s?o: ?ons divalentes positivos: ?ons c?lcio, Ca2+ e ?ons magn?sio, Mg2+; ?ons negativos divalentes: ?ons sulfato, SO42?; ?ons positivos monovalentes: ?ons s?dio, Na+; ?ons negativos monovalentes: ?ons cloro, Cl?. Os c?tions est?o envolvidos em um processo r?pido de troca de ?ons com a superf?cie do meio poroso carregada eletronega-tivamente X?, onde o meio absorver? os ?ons positivos Ca2+, Mg2+ e Na+. Usando regras simples de misturas e desconsiderando qualquer calor de precipita??o ou dissolu??o de rea??es de subst?ncias ou dessor??o de ?ons. Al?m disso, desconsideramos quaisquer efeitos de contra??o de volume resultante das misturas e rea??es em qualquer fase. Resolveremos neste trabalho, o Problema de Riemann e discutiremos algumas caracter?sticas do modelo estudado.
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SILVA, Keytt Amaral da. "O problema de Riemann para um modelo de injeção de polímero." Universidade Federal de Campina Grande, 2015. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1405.
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Previous issue date: 2015-08<br>Neste trabalho apresentamos a construção detalhada da solução do Problema de
Riemann associado à um sistema de leis de conservação de um problema não estritamente hiperbólico, proveniente da modelagem matemática de um escoamento unidimensional bifásico num meio poroso em que as fases são óleo e água com polímero
dissolvido, para dados iniciais arbitrários no espaço de estados. A construção da solução
do sistema é baseada na solução da equação de Buckley−Leverett para cada nível de
concentração constante de polímero e nas curvas integrais de uma campo característico
linearmente degenerado que dá origem as chamadas ondas de contato.<br>We present the detailed construction of the Riemann problem solution associate to
a system of conservation laws of a non−strictly hyperbolic problem, from mathematical
modeling of a one-dimensional two-flow in a porous medium filled by oil and water with
dissolved polymer, for arbitrary initial data in the state space. The construction of the
system solution is based on the solution Buckley−Leverett equation for each level
constant polymer concentration and on the integral curves of a linearly degenerated
field characteristic that gives rise to the so-called contact waves.
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Usatine, Jeremy. "Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/57.
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If R is a list of positive integers with greatest common denominator equal to 1, calculating the Frobenius number of R is in general NP-hard. Dino Lorenzini defines the arithmetical graph, which naturally arises in arithmetic geometry, and a notion of genus, the g-number, that in specific cases coincides with the Frobenius number of R. A result of Dino Lorenzini's gives a method for quickly calculating upper bounds for the g-number of arithmetical graphs. We discuss the arithmetic geometry related to arithmetical graphs and present an example of an arithmetical graph that arises in this context. We also discuss the construction for Lorenzini's Riemann-Roch structure and how it relates to the Riemann-Roch theorem for finite graphs shown by Matthew Baker and Serguei Norine.
We then focus on the connection between the Frobenius number and arithmetical graphs. Using the Laplacian of an arithmetical graph and a formulation of chip-firing on the vertices of an arithmetical graph, we show results that can be used to find arithmetical graphs whose g-numbers correspond to the Frobenius number of R. We describe how this can be used to quickly calculate upper bounds for the Frobenius number of R.
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Percca, Edwin Marcos Maraví. "Resolução do problema de Riemann através de um método variacional." Universidade Federal de Juiz de Fora (UFJF), 2017. https://repositorio.ufjf.br/jspui/handle/ufjf/4037.
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Previous issue date: 2017-02-20<br>As leis de balanço expressam de uma maneira mais geral as leis de conservação e, portanto, é natural que coincidam em algumas definições ou resultados que vamos mostrar aqui. Um sistema de leis de conservação estritamente hiperbólico numa dimensão espacial sob certas condições é um sistema simetrizável, portanto, possui uma entropia convexa. Isto induz a definiroparentropia-fluxodeentropiaeaproduçãodeentropia,ingredientesmínimospara usar o critério de admissibilidade da taxa de entropia e conferir se a solução do problema de Riemann respectivo é ótimo. A taxa de entropia definida aqui em termos da entropia é um funcional que pode ser minimizada nos leques de ondas com estados constantes do problema de Riemann, usando as equações de Euler-Lagrange. Primeiramente, mostramos que as soluções do problema de Riemann são funções de variação limitada, resultando num método variacional para resolver o problema. Neste trabalho será mostrado que a solução obtida pelo método variacional, coincide com a solução obtida pelo método das curvas caraterísticas.<br>The balance laws express in a more general way the conservation laws and therefore it is naturalthattheycoincideinsomedefinitionsorresultsthatwewillshowhere. Thestrictly hyperbolic systems of conservation laws in a spatial dimension under certain conditions is a symmetrizable system, therefore it has a convex entropy. This induces to define the entropy-entropy flux pair and the entropy production, minimum ingredients to use the Entropy rate admissibility criterion and check whether the solution of the respective Riemann problem is optimal. The entropy rate defined here in terms of entropy is a functional that can be minimized in the wave fans with constant states of the Riemann problem using the Euler-Lagrange equations, we show that the solutions of the Riemann problem are functions of bounded variation, resulting in a variational method to solve the respective problem. In this work it will be shown that the solution obtained by the variational method, coincides with the solution obtained by the method of characteristics.
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Alcántara, Bode Julio. "Un problema de completación relacionado con la hipótesis de Riemann." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95425.
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Jousse, Nicolas. "Etude d'un problème de continuité lié à l'hypothèse de Riemann." Bordeaux 1, 2004. http://www.theses.fr/2004BOR12812.
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This work is devoted to a problem linked to the Beurling-Nyman's criterion about the Riemann hypothesis. We study the continuity of the projection of the characteristic function of (0,1) on a subspace of the square-integrable functions generated by dilated functions of the fractionnal part function. In the first part of this work, we give a general result about the projection P of a vector belonging to a Hilbert space H on a variable subspace of H. We proove a continuity criterion about P under some weak convergence hypothesis. In the second part, we specify those last results in the case where H is a L2(Y) space. In the third part, we suppose that Y is a commutative, locally compact, sigma-compact and metrisable group, and we project on a subspace of L2(Y) generated by dilated functions of a given function in L2(Y). At last, we apply all our results in the fourth part, in the scope of the Beurling-Nyman criterion as far as zeta is concerned, and more generally, with regard to functions in Selberg's class<br>Cette thèse est consacrée à l'étude d'un problème lié au critère de Beurling Nyman sur l'hypothèse de Riemann. On y étudie la continuité de la projection de la fonction indicatrice de l'intervalle ]0,1] sur un sous-espace vectoriel variable de l'ensemble des fonctions dont le carré est intégrable sur la demi-droite réelle engendré par des fonctions dilatées de la fonction partie fractionnaire. Dans la première partie de la thèse, on établit un résultat général sur la projection P d'un vecteur d'un espace de Hilbert H sur un sous-espace de H dépendant d'une variable. On démontre un critère de continuité sur P à l'aide d'hypothèses de convergence faible. Dans la deuxième partie, on précise ces résultats généraux au cas où H est de la forme L2(Y). Dans la troisième partie, on approfondit encore notre étude lorsque Y est un groupe abélien localement compact, sigma-compact et métrisable, et on projette sur un sous-espace de L2(Y) engendré par des dilatées d'une fonction donnée f dans L2(Y). La dernière partie met en application ce qui précède dans le cadre du critère de Beurling-Nyman pour la fonction zeta, et plus généralement, pour les fonctions de la classe de Selberg
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Pocchiola, Samuel. "Le problème d’équivalence pour les variétés de Cauchy-Riemann en dimension 5." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112340/document.
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Ce mémoire est une contribution à la résolution du problème d'équivalence pour les variétés de Cauchy-Riemann en dimension inférieure ou égale à 5. On traite d'abord du cas des variétés CR de dimension 5, qui sont 2-nondégénérées et de rang de Levi constant égal à 1. Pour une telle variété, on obtient deux invariants, J et W, dont l'annulation simultanée caractérise l'équivalence locale à une variété modèle, le tube au-dessus du cône de lumière. Si l'un des deux invariants ne s'annule pas, on construit un parallélisme absolu, i.e. on montre que le problème d'équivalence se réduit à un problème d'équivalence entre {e}-structures de dimension 5. On étudie ensuite le problème d'équivalence pour certaines variétés CR de dimension 4 appelées variétés de Engel. Ce problème est résolu par la construction d'une connexion de Cartan sur un fibré principal de dimension 5. On traite ensuite du cas de variétés CR de dimension 5 dont le fibré CR vérifie une certaine hypothèse de dégénérecence. Le problème d'équivalence est résolu dans ce cas par la construction d'une connexion de Cartan sur un fibré de dimension 6. Enfin, on détermine les algèbres de Lie des automorphismes infinitésimaux des modèles pour les trois classes de variétés CR étudiées<br>This memoir contributes to solve the equivalence problem for CR-manifolds in dimension up to 5. We first deal with the equivalence problem for 5-dimensional CR-manifolds which are 2-nondegenerate and of constant Levi rank 1. For such a manifold M, we find two invariants, J and W, the annulation of which gives a necessary and sufficient condition for M to be locally CR-equivalent to a model hypersurface, the tube over the light cone. If one of the invariants does not vanish on M, we construct an absolute parallelism on M, that is we show that the equivalence problem reduces to an equivalence problem between 5-dimensional {e}-structures. We then study the equivalence problem for 4-dimensional CR-manifolds which are known as Engel manifolds. This problem is solved by the construction of a canonical Cartan connection on a 5-dimensional bundle through Cartan's equivalence method. We also study the equivalence problem for 5-dimensional CR-manifolds whose CR-bundle satisfies a certain degeneracy assumption, and show that in this case, the problem is solved by the construction of a Cartan connection on a 6-dimensional bundle. The last part of this memoir is devoted to the determination of the Lie algebra of infinitesimal automorphisms for the model manifolds of the three previous classes
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Hank, Sarah. "Modélisation et simulation de la dispersion de fluide en milieu fortement hétérogène." Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4765/document.
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Ces travaux portent sur la modélisation et la simulation numérique de la dispersion de matériaux nocifs (pulvérisations liquides ou gazeuses) en milieu urbain ou naturel (attentat ou explosion accidentelle survenant en zone peuplée, fuites de produits toxiques gazeux ou liquides, éclatement de réservoir..). Afin de prédire ces risques un outils de simulation tridimensionnel a été développé. Celui-ci est basé sur un modèle de milieu hétérogène afin de traiter des phénomènes dont la durée et les distances associées peuvent être très grandes. La topographie des milieux étudiées est prise en compte grâce à des données numériques d'´elévation ainsi que les conditions météo permettant l'utilisation de profils de température et de vent complexes. Les transferts de chaleur et de masse sont considérés, notamment au niveau des obstacles. Un schéma numérique d'ordre élevé en temps et en espace est utilisé pour calculer les concentrations massiques de polluants. Par ailleurs, un modèle d'écoulement gaz-particule a été développé et implémenté dans le code de calcul. L'instabilité d'une couche de fluide soumise à un important gradient de pression est également étudiée, ceci afin de mieux comprendre et de caractériser les conditions initiales à utiliser pour ce type d'écoulement, impliquant des couches de particules<br>This work deals with the modeling and the numerical simulation of the dispersion of toxic cloud of dropplets or gas in uneven geometry such as urban environment, industrial plants and hilly environment. Examples of phenomena under study are the dispersion of chemical products from damaged vessels, gas diffusion in an urban environment under explosion conditions, shock wave propagation in urban environment etc. A 3D simulation code has been developed in this aim. To simplify the consideration of complex geometries, a heterogeneous discrete formulation has been developed. When dealing with large scale domains, such as hilly natural environment, the topography is reconstructed with the help of numerical elevation data. Meteorological conditions are also considered, concerning temperature and wind velocity profiles. Heat and mass transfers on subscale objects, such as buildings are studied. A high order numerical scheme in space and time is used to compute mass concentration of pollutant. A two-phase model for dilute gas-particles flow has been developed and implemented in the 3D simulation code. The instability of a fluid layer appearing under high pressure gradient is also studied. This analysis allows us a better understanding of initial conditions for similar problems involving particles layer
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VANDAMME, JULIETTE. "Probleme de riemann-hilbert pour une representation de monodromie triangulaire superieure." Nice, 1998. http://www.theses.fr/1998NICE5165.
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On etudie le probleme de riemann-hilbert (prh) pour une representation de monodromie triangulaire superieure de dimension 5 et 6. Le prh peut etre formule comme suit : existe-t-il un systeme fuchsien ayant des points singuliers et une representation de monodromie donnes ?. Dans le cas d'une representation de monodromie triangulaire superieure il est connu que la reponse au prh est positive en dimension 2, 3, 4 et qu'elle est negative en dimension 7. On montre que la reponse au prh depend des structures de jordan des matrices de monodromie et de leurs valeurs propres ; de plus on peut remplacer ces matrices par des matrices diagonales de memes valeurs propres. D'autre part le prh peut etre reduit au probleme d'existence d'une solution entiere d'un systeme d'equations lineaires algebriques associe a la representation. En dimension 5 on montre que le probleme general peut etre reduit au cas ou la representation a au plus 8 points singuliers. Les systemes algebriques associes aux representations sont etudies cas par cas et admettent toujours une solution entiere. On en deduit que le prh en dimension 5, pour une representation triangulaire superieure, admet une solution. En dimension 6 on utilise le logiciel mathematica pour montrer que si le systeme algebrique associe a la representation est de rang 1, 2, 3, 4 ou 6 alors le prh admet une solution. Mais il existe une representation de monodromie triangulaire superieure de dimension 6 qui ne peut etre realisee par aucun systeme fuchsien (le systeme algebrique associe est de rang 5). Finalement la plus petite dimension pour avoir une reponse negative au prh pour une representation triangulaire superieure est 6.
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Martin, Frank. "Analytische und numerische Verfahren zur Berechnung der Hilbert-Transformation und zur Lösung funktionentheoretischer Randwertaufgaben." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2011. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-65398.
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In der Arbeit werden effektive Verfahren zur Auswertung der Hilbert-Transformation entwickelt und zur Lösung nichtlinearer Randwertaufgaben der Funktionentheorie eingesetzt. Die Verwendung polynomialer Spline-Wavelets und geeignet modifizierter Wavelet-Algorithmen ermöglichen die schnelle Berechnung auf gleichmäßigen und ungleichmäßigen Gittern sowie deren automatische Anpassung an lokale Besonderheiten der Lösung. Die detaillierte Untersuchung des Zusammenhangs zwischen der Glattheit, der Größe des Trägers des Splines, der Anzahl verschwindender Momente und des asymptotischen Verhaltens der Hilbert-Transformierten erlaubt die Anpassung der Parameter des Verfahrens in Bezug auf Genauigkeit und Effektivität. Im zweiten Teil der Arbeit werden verschiedene Algorithmen zur Lösung von Riemann-Hilbert Probleme vorgeschlagen und deren Konvergenzverhalten untersucht. Die theoretischen Ergebnisse werden durch numerische Experimente bestätigt.
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Reid, Cynthia 1958. "A class of solutions in non-homogeneous fluid dynamics obtained by the Riemann-invariant method /." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66007.
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Nardulli, Stéfano. "Le profil isopérimétrique d'une variété riemannienne compacte pour les petits volumes." Paris 11, 2006. http://www.theses.fr/2006PA112344.
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Cette thèse porte sur une question de calcul des variations motivée par la géométrie riemannienne, le problème isopérimétrique. On montre que les solutions du probème isopérimétrique proches en norme flat d’une sous-variété lisse sont elle-meˆmes lisses et C2,-proches de la sous-variéte donnée. En particulier, les solutions du problème isopérimétrique pour les petits volumes sont C2,-proches de petites sphères. Par ailleurs, on définit une classe de sous-variétés appelées pseudo-bulles, définies par une équation plus faible que la constance de la courbure moyenne. On montre qu’au voisinage de chaque point d’une variété riemannienne compacte, nait une unique famille de pseudo-bulles concentriques, conte- nant toutes les pseudo-bulles C2,-proches de petites sphères. Cela permet de ramener le problème isopérimétrique pour les petits volumes à un problème variationnel en dimension finie. En particulier, lorsque les maxima de la courbure scalaire sont non dégénérés, le problème isopérimétrique se ramène à un problème d’optimisation sur un ensemble fini. Les techniques utilisées sont, outre les outils standard d’analyse linéaire elliptique et les théorèmes de comparaison de la géométrie riemannienne, – le théorème de compacité des courants en norme flat, – le théorème de régularité d’Allard pour les varifolds minimisantes, - la caractérisation par Taylor des courants solutions du problème isopérimétrique euclidien, – le théorème de plongement isométrique de Nash et une version à paramètres du à Gromov<br>In this thesis we consider a question in the calculus of variations motivated by riemannian geometry, the isoperimetric problem. We show that solutions to the isoperimetric problem, close in the flat norm to a smooth submani- fold, are themselves smooth and C2,-close to the given sub manifold. In particular, the solutions of the isoperimetric problem for small volumes are C2,-close to small spheres. On the way, we define a class of submanifolds called pseudo balls, defined by an equation weaker than constancy of mean curvature. We show that in a neighborhood of each point of a compact rie- mannian manifold, there is a unique family concentric pseudo balls which contains all the pseudo balls C2,-close to small spheres. This permit us to reduce the isoperimetric problem for small volumes to a variational problem in finite dimension. In particular, when the maxima of the scalar curvature function are non degenerate the isoperimetric reduces to a problem of opti- mum on a finite set. The techniques used are, among other, les outils standard of linear elliptic analysis and comparison theorems of riemannian geometry, 1. Compactness theorems for currents in flat norm, 2. Allard’s regularity theorem for minimizing varifolds, 3. Jean Taylor’s caracterization for currents that are solution of the eucli- dean isoperimetric problem, 4. The isometric immersion theorem of Nash and a parametric version due to Gromov
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Prosmans, Fabienne. "Algèbre homologique topologique et problème de Riemann-Hilbert pour les D-modules." Paris 13, 1998. http://www.theses.fr/1998PA132040.
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Cette these est composee de quatre parties. Dans la premiere partie, nous etudions les foncteurs derives des limites projectives dans les categories quasi-abeliennes generales en utilisant le langage des categories derivees. Nous etablissons notamment l'existence de ces foncteurs derives lorsque la categorie consideree a des produits exacts. Nous montrons egalement l'invariance des limites projectives derivees par composition avec un foncteur cofinal et en tirons qu'elles peuvent s'exprimer en termes de pro-objets. La theorie developpee dans la premiere partie nous permet d'etablir dans la seconde quelques proprietes d'exactitude du foncteur limite projective dans le cas plus specifique des groupes abeliens topologiques. La troisieme partie est consacree a l'etude de la derivee la categorie t c des espaces vectoriels topologiques localement convexes. Nous degageons en particulier la notion de completude cohomologique et montrons que la sous-categorie de la categorie derivee de t c formee de complexes cohomologiquement complets est equivalente a la categorie derivee de la categorie des pro-espaces de banach. Nous montrons egalement comment notre point de vue permet de clarifier divers resultats de palamodov sur l'homologie des espaces localement convexes. Enfin, dans la quatrieme partie, en travaillant dans la categorie derivee des faisceaux a valeurs dans les ind-espaces de banach et en utilisant certains resultats de schneiders concernant la dualite de poincare dans cette categorie, nous etablissons un theoreme de reconstruction topologique pour les complexes parfaits de d#-modules. Ce resultat repose sur des theoremes d'acyclicite que nous demontrons en faisant appel aux techniques developpees dans les trois premieres parties.
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Ziti, Chérif. "Analyse et simulation numérique d'un système hyperbolique modélisant le comportement d'une population bactérienne." Saint-Etienne, 1987. http://www.theses.fr/1987STET4004.
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Silva, Guilherme Lima Ferreira da [UNESP]. "Universalidade em matrizes aleatórias via problemas de Riemann-Hilbert." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/86512.
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silva_glf_me_sjrp.pdf: 4891307 bytes, checksum: d50ac695507aa5097767c494c073e3f8 (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Neste trabalho estudaremos a relação existente entre polinômios ortogonais e matrizes aleatórias. Exibiremos uma caracterização de polinômios ortogonais via problemas de Riemann-Hilbert, a qual tem se mostrado uma ferramenta única para obtenção de assintóticas de polinômios ortogonais. Posteriormente, estudaremos a teoria básica dos ensembles unitários de matrizes aleatórias. Por fim, mostraremos como a teoria de assintóticas de polinômios ortogonais pode ser usada na análise assintótica de estatísticas de matrizes aleatórias, nos levando a resultados de universalidade para os ensembles unitários<br>We will exhibit a characterization of orthogonal p olynomials via Riemann-Hilbert problems, which has been shown a powerful to ol for studying asymptotics of orthogonal polynomials. Posteriorly we will review the basic theory of unitary ensembles of random matrices. At the end, we will show how asymptotics of orthogonal polynomials can be used to study asymptotics of several statistics in random matrix theory, obtaining universality results for the unitary ensembles
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Schulz-Rinne, Carsten Werner. "The Riemann problem for two-dimensional gas dynamics and new limiters for high-order schemes /." [S.l.] : [s.n.], 1993. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10297.
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Abadpour, Anahita. "Analyse asymptotique du problème de Riemann pour les écoulements compositionnels polyphasiques en milieux poreux et applications aux réservoirs souterrains." Thesis, Vandoeuvre-les-Nancy, INPL, 2008. http://www.theses.fr/2008INPL098N/document.
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Dans la première partie de cette thèse nous traitons l’écoulement diphasique compositionnel, partiellement miscible et compressible en milieux poreux. Déplacement d'une phase par un autre est analysé. Nous examinons les mélanges non idéals, la pression est variable, et les concentrations de phase, la densité et la viscosité sont les fonctions de la pression. Le processus est décrit par le problème de Riemann qui admet des solutions discontinues. Nous avons développé une méthode numérique-analytique de solution pour déterminer les paramètres à tous les chocs avant résoudre les équations de flux. Cette méthode est basée sur la séparation de thermodynamique et hydrodynamique, proposée dans [Oladyshkin, Panfilov 2006] et qui était inapplicable à problème de Riemann, en raison de manque des conditions d’Hugoniot. Dans cette thèse, nous avons construit les conditions supplémentaires d'Hugoniot. Dans la deuxième partie, nous examinons l'écoulement diphasique lors que les zones monophasique apparaissent, dans cette zone, le fluide est sur/sous-saturés et les équations diphasique dégénèrent.Nous avons proposé de décrire les zones diphasique et sur/sous-saturés avec un système uniforme des équations diphasique classique en étendant le concept de saturation d'être négatif et supérieur à un. Physiquement, cela signifie que les états monophasiques sont considérés comme des états diphasiques consistant une phase imaginaire avec la saturation négative. Une telle extension de la saturation exige développement des conditions de consistance qui sont fait dans cette thèse.La dernière partie est consacrée ensuite à étendre le modèle HT-split pour le cas d’écoulement triphasique compositionnel. Nous avons obtenu le modèle asymptotique, dans lequel la thermodynamique et l'hydrodynamique sont séparées<br>In the first part of thesis we deal with two-phase multicomponent, partially miscible, compressible flow in porous media. Displacement of one phase by another is analyzed. We examine non ideal solutions, pressure is variable, and phase compositions, densities and viscosities are variable functions of pressure.The process is described by Riemann problem which admits discontinuous solutions.We developed a numerical-analytical method of solution to explicitly determine all shock parameters before solving the flow equations. This method is based on splitting thermodynamics and hydrodynamics, suggested in [Oladyshkin, Panfilov 2006]. Earlier this method was inapplicable to Riemann problem, due to the lack of Hugoniot conditions. In this thesis we have constructed additional Hugoniot conditions.In the second part we examine two-phase flow when the single-phase zones appear, in this zone the fluid is over/under-saturated and two-phase flow equations degenerate and they cannot be used. We proposed to describe two-phase and over/under-saturated single-phase zones by uniform system of classic two-phase equations while extending the concept of phase saturation to be negative and higher than one. Physically it means that the oversaturated single-phase states are considered as pseudo two-phase states consisting an imaginary phase with negative saturation. Such an extension of saturation requires developing some consistence conditions which have developed in this thesis.The last part then is devoted to extend the HT-split model to the case of three-phase compositional flow. We have obtained the general asymptotic model, in which the thermodynamics and hydrodynamics are split
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Gaspareti, Leandro. "O Santo Graal da matemática: a hipótese de Riemann." Universidade Tecnológica Federal do Paraná, 2014. http://repositorio.utfpr.edu.br/jspui/handle/1/1015.
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CAPES<br>Este trabalho traz um relato a respeito da Hipótese de Riemann, com o objetivo de tornar os conceitos referentes a esse problema acessíveis ao professor da educação básica, que pretenda abordá-los em sala de aula quando tratar de conteúdos a ele relacionados. A pesquisa foi inteira bibliográfica, apoiada em sua grande parte em textos de História da Matemática, tornando este trabalho divulgador dos problemas que ocupam parte das pesquisas matemáticas deste século, em especial da Hipótese de Riemann.<br>This study presents a report about the Riemann Hypothesis, leaving the underlying concepts behind this problem more accessible to a high school teacher. The literature review was based mainly on History of Mathematics texts. This research aims to study significant topics of mathematical research throughout this century, particularly to popularize the Riemann Hypothesis.
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Eaton, Matthew Denham. "A high-resolution Riemann method for solving radiation transport problems on unstructured meshes." Thesis, Imperial College London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.407250.
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Silva, Guilherme Lima Ferreira da. "Universalidade em matrizes aleatórias via problemas de Riemann-Hilbert /." São José do Rio Preto : [s.n.], 2012. http://hdl.handle.net/11449/86512.
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Orientador: Dimitar Kolev Dimitrov<br>Banca: Carlos Tomei<br>Banca: José Alberto Cuminato<br>Resumo: Neste trabalho estudaremos a relação existente entre polinômios ortogonais e matrizes aleatórias. Exibiremos uma caracterização de polinômios ortogonais via problemas de Riemann-Hilbert, a qual tem se mostrado uma ferramenta única para obtenção de assintóticas de polinômios ortogonais. Posteriormente, estudaremos a teoria básica dos ensembles unitários de matrizes aleatórias. Por fim, mostraremos como a teoria de assintóticas de polinômios ortogonais pode ser usada na análise assintótica de estatísticas de matrizes aleatórias, nos levando a resultados de universalidade para os ensembles unitários<br>Abstract: We will exhibit a characterization of orthogonal p olynomials via Riemann-Hilbert problems, which has been shown a powerful to ol for studying asymptotics of orthogonal polynomials. Posteriorly we will review the basic theory of unitary ensembles of random matrices. At the end, we will show how asymptotics of orthogonal polynomials can be used to study asymptotics of several statistics in random matrix theory, obtaining universality results for the unitary ensembles<br>Mestre
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Schlackow, Waldemar. "A sieve problem over the Gaussian integers." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:b7d4ff88-1f93-41b4-9f81-055f8f1b1c51.
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Our main result is that there are infinitely many primes of the form a² + b² such that a² + 4b² has at most 5 prime factors. We prove this by first developing the theory of $L$-functions for Gaussian primes by using standard methods. We then give an exposition of the Siegel--Walfisz Theorem for Gaussian primes and a corresponding Prime Number Theorem for Gaussian Arithmetic Progressions. Finally, we prove the main result by using the developed theory together with Sieve Theory and specifically a weighted linear sieve result to bound the number of prime factors of a² + 4b². For the application of the sieve, we need to derive a specific version of the Bombieri--Vinogradov Theorem for Gaussian primes which, in turn, requires a suitable version of the Large Sieve. We are also able to get the number of prime factors of a² + 4b² as low as 3 if we assume the Generalised Riemann Hypothesis.
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Dalpizol, Luiz Gustavo. "O conjunto excepcional do problema de Goldbach." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/180946.
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Seja E(X) a cardinalidade dos números pares menores ou iguais a X que não podem ser escritos como soma de dois primos. O objetivo central desta dissertação é apresentar uma demonstração de uma estimativa para E(X) dada por Hugh L. Montgomery e Robert C. Vaughan em [22]. Mais precisamente, estabeleceremos a existência de uma constante positiva (efetivamente computável) tal que E(X) X1 ; para todo X su cientemente grande.<br>Let E(X) the cardinality of even numbers not exceeding X which cannot be written as a sum of two primes. The main goal of this dissertation is to present a proof of an estimate for E(X) given by Hugh L. Montgomery e Robert C. Vaughan in [22]. More precisely, we will establish the existence of a positive constant (e ectively computable) such that E(X) X1 for all su ciently large X:
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Hitz, Timon [Verfasser]. "On the Riemann Problem and the Navier-Stokes-Korteweg Model for Compressible Multiphase Flows / Timon Hitz." München : Verlag Dr. Hut, 2020. http://d-nb.info/1222351846/34.
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Sousa, Vítor Luís Pereira Morais de. "The Riemann-Hilbert method applied to the theory of orthogonal polynomials." Doctoral thesis, Universidade de Aveiro, 2011. http://hdl.handle.net/10773/3871.
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Barbosu, Mihail. "Courbures riemanniennes dans le problème plan des trois corps : application à l'étude de la stabilité." Observatoire de Paris, 1995. https://tel.archives-ouvertes.fr/tel-01958569.
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Nous nous sommes intéressés à la théorie géométrique des systèmes dynamiques conservatifs. Pour toute valeur fixée, H, de la constante de l'énergie, les trajectoires d'un tel système dynamique sont des géodésiques de l'espace des configurations, muni de la métrique riemannienne de Maupertuis. Dans l'espace des phases, muni de la métrique de Sasaki, chaque géodésique est le relèvement d'une géodésique de l'espace des configurations. Nous avons développé une méthode pour étudier la courbure de l'espace des configurations et de l'espace des phases, en utilisant le logiciel de calcul formel Macsyma. Nous avons appliqué cette méthode dans le problème plan des trois corps pour déterminer les tenseurs de courbure et les courbures riemanniennes de l'espace des configurations ainsi que les composantes de la métrique de Sasaki dans l'espace des phases. Une discussion sur le signe des courbures riemanniennes et sur le tenseur de Ricci conduit à des conclusions concernant la stabilité des trajectoires de certaines configurations particulières. Nous avons montré ainsi, entre autres, que : dans le cas planétaire les courbures riemanniennes s'annulent si et seulement si la configuration est isocèle et que le tenseur de Ricci est négatif sous certaines conditions ; dans le cas du triangle équilatéral, même si le mouvement est homographique, nous avons trouvé des conditions dans lesquelles les courbures riemanniennes sont négatives. Dans le cas rectiligne, les courbures ne gardent pas un signe constant. Dans chacun de ces cas, nous avons déduit des résultats concernant la stabilité des configurations étudiées. Pour la plupart des calculs et des graphiques nous avons utilisé les logiciels de calcul formel Mathematica et Macsyma.
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Černigova, Sondra. "Moment problem for the periodic zeta-function." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141111_114553-36360.
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In the thesis, problems related to the moments of the periodic zeta-function are considered. The aim of the thesis is to obtain asymptotic formulae for some analytic objects related to the periodic zeta-function. The problems are the following: 1. To prove the Atkinson-type formula with a new error term in the critical strip for the periodic zeta-function with rational parameter. 2. To prove a mean square formula for the error term in the Atkinson-type formula on the critical line for the periodic zeta-function. 3. To prove a mean square formula for the error term in the Atkinson-type formula in the critical strip for the periodic zeta-function. 4. To obtain an asymptotic formula for the fourth power moment of the periodic zeta-function.<br>Disertacijos tyrimo objektas yra periodinė dzeta funkcija. Mokslinė problema - šios funkcijos momentų problema. Darbo tikslas - įrodyti asimptotines formules periodinės funkcijos momentams bei kai kuriems objektams, susijusiems su šios funkcijos momentais. Darbo uždaviniai yra šie: 1. Įrodyti Atkinsono tipo formulę su korektišku liekamuoju nariu kritinėje juostoje periodinei dzeta funkcijai su racionaliuoju parametru. 2. Įrodyti Atkinsono tipo formulės periodinei dzeta funkcijai kritinėje tiesėje vidurkio formulę liekamojo nario modulio kvadratui. 3. Įrodyti Atkinsono tipo formulės periodinei dzeta funkcijai kritinėje juostoje vidurkio formulę liekamojo nario modulio kvadratui. 4. Gauti asimptotinę formulę periodinės dzeta funkcijos ketvirtajam momentui.
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Gerber, Annelies. "The Weyl-Lanczos and Riemann-Lanczos problems as exterior differentia systems with applications to spacetimes." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.395471.
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ANDRADE, Patrício Luiz de. "O Problema de Riemann para um modelo matemático de um escoamento trifásico em meio poroso." Universidade Federal de Campina Grande, 2013. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1381.
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Previous issue date: 2013-05<br>Neste trabalho construímos uma solução do problema de Riemann para um sistema
de leis de conservação proveniente da modelagem matemática de um escoamento
trifásico num meio poroso representando a propagação de misturas do tipo água-gásóleo
num projeto de recuperação de um reservatório petrolífero. Usando métodos analíticos e
computacionais encontramos a geometria das curvas de onda sob a condição de entropia de viscosidade, com matriz de viscosidade sendo a identidade. Mostramos
que para dados à direita representando misturas próximas de óleo puro, a solução
do problema de Riemann consiste genericamente de uma sequência de dois grupos de
ondas relacionados às duas famílias caraterísticas, para quaisquer dados à esquerda
representando uma mistura água-gás. No entanto, para dados à direita representando
misturas ainda com óleo dominante, mas com uma composição maior de água e gás,
surge a necessidade de acrescentar um grupo de ondas transicional na sequência que
descreve a solução, para um pequeno conjunto de dados à esquerda.<br>In this work we construct a solution of the Riemann problem for a system of conservation laws arising from the mathematial modeling of a three-phase ow in a porous medium representing the propagation of water-gas-oil mixtures in a recovery project of a petroleum reservoir. Using analytical and computational methods we ndthe geometry of the wave
curves under the viscous pro le entropy condition, with theidentity as the viscosity matrix. We show that for the right data representing almost pure oil compositions the solution of the Riemann problem generically consists of a sequence of two wave groups, related to the two characteristics families, for any left data considered representing a water-gas mixture. However, for right data representing mixtures with oil still dominant, but with a larger proportion of gas and water, a transitional wave group is required in the sequen
e for a small subset of left data.
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LIMA, Erivaldo Diniz de. "O Problema de Riemann para um modelo de injeção de polímero em meio poroso com efeito de adsorção." Universidade Federal de Campina Grande, 2015. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1406.
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Previous issue date: 2015-08<br>Neste trabalho consideramos um sistema de leis de conservação proveniente da
modelagem matemática de um escoamento bifásico unidimensional num meio poroso,
preenchido de óleo e água com polímero dissolvido nela e levando em conta a adsorção
de parte do polímero pela rocha. Usando a técnica das curvas de onda apresentamos
a construção detalhada da solução do problema de Riemann para dados iniciais arbitrários no espaço de estados. Usamos a condição de entropia do per l viscoso para as
ondas de choque com salto na concentração do polímero e a condição de Oleinik-Liu
para os choques com concentração constante do polímero e salto na saturação da água<br>In this work we consider a system of conservation laws from the mathematical
modeling of a one-dimensional two-phase flow in porous media, filled with oil and water
with dissolved polymer in it and taking into account the adsorption of part of the
polymer by the rock. Using the wave curves technique, we present a detailed construction
of the Riemann problem solution for arbitrary initial data on the state space.
We use the entropy condition of the viscous pro le for the shock waves with jumps
in the polymer concentration and Oleynik-Liu condition for the shocks with constant
concentration of polymer and jumps on the water saturation.
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Brisson, Jade, and Jade Brisson. "Problèmes isopérimétriques et isospectralité pour le problème de Steklov." Master's thesis, Université Laval, 2019. http://hdl.handle.net/20.500.11794/37633.
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En géométrie spectrale, on s’intéresse aux liens entre le spectre d’une variété riemannienne et sa géométrie. On recherche notamment des bornes supérieures et inférieures pour les va-leurs propres qui font intervenir des quantités géométriques, comme l’aire et le périmètre. On se questionne aussi sur l’isospectralité : Quelles sont les variétés riemanniennes non iso-métriques qui possèdent le même spectre ? Au cours des dernières années, le problème de Steklov, problème introduit au tout début du 20e siècle en mécanique des fluides, a suscité l’intérêt de plusieurs mathématiciens. Le but de ce mémoire est de donner une banque de variétés riemanniennes Steklov-isospectrales. On y présente aussi une preuve d’une borne supérieure pour la première valeur propre de Steklov pour un domaine borné du plan, sans hypothèse sur sa connexité.<br>En géométrie spectrale, on s’intéresse aux liens entre le spectre d’une variété riemannienne et sa géométrie. On recherche notamment des bornes supérieures et inférieures pour les va-leurs propres qui font intervenir des quantités géométriques, comme l’aire et le périmètre. On se questionne aussi sur l’isospectralité : Quelles sont les variétés riemanniennes non iso-métriques qui possèdent le même spectre ? Au cours des dernières années, le problème de Steklov, problème introduit au tout début du 20e siècle en mécanique des fluides, a suscité l’intérêt de plusieurs mathématiciens. Le but de ce mémoire est de donner une banque de variétés riemanniennes Steklov-isospectrales. On y présente aussi une preuve d’une borne supérieure pour la première valeur propre de Steklov pour un domaine borné du plan, sans hypothèse sur sa connexité.<br>In spectral geometry, we are interested in the links between the spectrum of a Riemannian manifold and its geometry. We are looking for geometric upper and lower bounds for the eigenvalues. These bounds are geometric, for they involve geometric quantities such as area and perimeter. Isospectrality is also a subject of interest in spectral geometry: What are thenon isometric Riemannian manifolds that share the same spectrum? In the last few years, the Steklov problem, introduced in the beginning of the 20th century in fluid mechanics, raised the interest of many mathematicians. In this memoir, we present a bank of Steklov-isospectral Riemannian manifolds. We also give a proof of an upper bound for the first Steklov eigenvalue for a bounded domain of the plane without any connectedness assumption.<br>In spectral geometry, we are interested in the links between the spectrum of a Riemannian manifold and its geometry. We are looking for geometric upper and lower bounds for the eigenvalues. These bounds are geometric, for they involve geometric quantities such as area and perimeter. Isospectrality is also a subject of interest in spectral geometry: What are thenon isometric Riemannian manifolds that share the same spectrum? In the last few years, the Steklov problem, introduced in the beginning of the 20th century in fluid mechanics, raised the interest of many mathematicians. In this memoir, we present a bank of Steklov-isospectral Riemannian manifolds. We also give a proof of an upper bound for the first Steklov eigenvalue for a bounded domain of the plane without any connectedness assumption.
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Mondello, Ilaria. "Le problème de Yamabe sur les espaces stratifiés." Nantes, 2015. http://archive.bu.univ-nantes.fr/pollux/show.action?id=a82f7d20-528d-484f-a6dc-37dd590c9a54.
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On étudie une classe d’espaces métriques singuliers, les espaces stratifiés, et on se propose d’étendre à ces derniers des résultats de géométrie riemannienne et d’analyse sur les variétés. Dans une première partie, on montre l’existence d’une borne inférieure pour le bas du spectre du Laplacien, sous une hypothèse géométrique de minoration de la courbure de Ricci. Cela permet également de démontrer l’existence d’une inégalité de Sobolev dont les constantes dépendent uniquement du volume et de la dimension de l’espace, et d’une borne supérieure pour le diamètre. En outre, on prouve que la borne pour le diamètre est atteinte si et seulement si celle pour le bas du spectre l’est aussi. La deuxième partie de ce manuscrit est dédiée aux conséquences des résultats précédents sur le problème de Yamabe pour un espace stratifié : ce problème consiste à chercher une métrique conforme à courbure scalaire constante, et l’existence d’une solution dépend d’un invariant conforme, la constante de Yamabe locale, dont la valeur est en général inconnue. On montre que celle-ci peut-être calculée en un grand nombre de cas, lorsque une hypothèse géométrique sur le lieu singulier est vérifiée. On utilise des techniques liées aux inégalités isopérimétrique et de Sobolev. Enfin, on donne une classe d’exemples pour lesquels on peut prouver qu’une métrique conforme à courbure scalaire constante existe<br>We study a class of singular metric spaces, stratified spaces, with an approach whose goal is to extend to these latter some tools and results of Riemannian geometry and analysis on smooth manifolds. In a first part, we show the existence of a lower bound for the bottom of the spectrum of the Laplacian, under the assumption that the Ricci curvature is bounded by below. This allows us to prove also the existence of a Sobolev inequality whose constants only depend on the volume and of the dimension of the space, and of an upper bound for the diameter. Furthermore, we prove that the bound for the diameter is attained if and only if the one for the bottom of the spectrum is attained as well. The second part is devoted to the direct consequences of the previous results on the Yamabe problem on a stratified space: this problem consists in looking for a conformal metric with constant scalar curvature, and the existence of a solution depends on a conformal invariant, the local Yamabe constant, whose value is generally unknown. We show that this latter can be computed in a large number of cases, when a geometric hypothesis on the singular set is verified. We use techniques which are related to the Sobolev and the isoperimetric inequalities. Finally, we give a class of examples for which we can prove the existence of a conformal metric with constant scalar curvature
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Fardoun, Ali. "Applications p-harmoniques et harmoniques par rapport à un potentiel." Brest, 1995. http://www.theses.fr/1995BRES0001.
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Le but de cette thèse est d'étudier deux variantes de la fonctionnelle énergie classique, qui est définie pour des applications entre variétés riemanniennes. La première variante est la p-énergie. La seconde est l'énergie avec un potentiel. En particulier, nous obtenons des résultats d'existence et de non existence pour un problème de Dirichlet, et aussi de nouvelles applications de sphères qui sont harmoniques par rapport à un potentiel quadratique
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Kaye, Adelina E. "Singular integration with applications to boundary value problems." Kansas State University, 2016. http://hdl.handle.net/2097/32717.
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Master of Science<br>Mathematics<br>Nathan Albin<br>Pietro Poggi-Corradini<br>This report explores singular integration, both real and complex, focusing on the the Cauchy type integral, culminating in the proof of generalized Sokhotski-Plemelj formulae and the applications of such to a Riemann-Hilbert problem.