Dissertations / Theses on the topic 'Hodge decomposition'
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Eriksson, Olle. "Hodge Decomposition for Manifolds with Boundary and Vector Calculus." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-328318.
Full textCARMO, FABIANO PETRONETTO DO. "POISSON EQUATION AND THE HELMHOLTZ-HODGE DECOMPOSITION WITH SPH OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=12140@1.
Full textFUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
A equação diferencial parcial de Poisson é de fundamental importância em várias áreas de pesquisa, dentre elas: matemática, física e engenharia. Para resolvê-la numericamente utilizam-se vários métodos, tais como os já tradicionais métodos das diferenças finitas e dos elementos finitos. Este trabalho propõe um método para resolver a equação de Poisson, utilizando uma abordagem de sistema de partículas conhecido como SPH, do inglês Smoothed Particles Hydrodynamics. O método proposto para a solução da equação de Poisson e os operadores diferenciais discretos definidos no método SPH, chamados de operadores SPH, são utilizados neste trabalho em duas aplicações: na decomposição de campos vetoriais; e na simulação numérica de escoamentos de fluidos monofásicos e bifásicos utilizando a equação de Navier-Stokes.
Poisson`s equation is of fundamental importance in many research areas in engineering and the mathematical and physical sciences. Its numerical solution uses several approaches among them finite differences and finite elements. In this work we propose a method to solve Poisson`s equation using the particle method known as SPH (Smoothed Particle Hydrodynamics). The proposed method together with an accurate analysis of the discrete differential operators defined by SPH are applied in two related situations: the Hodge-Helmholtz vector field decomposition and the numerical simulation of the Navier-Stokes equations.
RIBEIRO, PAULA CECCON. "UNCERTAINTY ANALYSIS OF 2D VECTOR FIELDS THROUGH THE HELMHOLTZ-HODGE DECOMPOSITION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2016. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=29431@1.
Full textCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
PROGRAMA DE EXCELENCIA ACADEMICA
PROGRAMA DE DOUTORADO SANDUÍCHE NO EXTERIOR
Campos vetoriais representam um papel principal em diversas aplicações científicas. Eles são comumente gerados via simulações computacionais. Essas simulações podem ser um processo custoso, dado que em muitas vezes elas requerem alto tempo computacional. Quando pesquisadores desejam quantificar a incerteza relacionada a esse tipo de aplicação, costuma-se gerar um conjunto de realizações de campos vetoriais, o que torna o processo ainda mais custoso. A Decomposição de Helmholtz-Hodge é uma ferramenta útil para a interpretação de campos vetoriais uma vez que ela distingue componentes conservativos (livre de rotação) de componentes que preservam massa (livre de divergente). No presente trabalho, vamos explorar a aplicabilidade de tal técnica na análise de incerteza de campos vetoriais 2D. Primeiramente, apresentaremos uma abordagem utilizando a Decomposição de Helmholtz-Hodge como uma ferramenta básica na análise de conjuntos de campos vetoriais. Dado um conjunto de campos vetoriais epsilon, obtemos os conjuntos formados pelos componentes livre de rotação, livre de divergente e harmônico, aplicando a Decomposição Natural de Helmholtz- Hodge em cada campo vetorial em epsilon. Com esses conjuntos em mãos, nossa proposta não somente quantifica, por meio de análise estatística, como cada componente é pontualmente correlacionado ao conjunto de campos vetoriais original, como também permite a investigação independente da incerteza relacionado aos campos livre de rotação, livre de divergente e harmônico. Em sequência, propomos duas técnicas que em conjunto com a Decomposição de Helmholtz-Hodge geram, de forma estocástica, campos vetoriais a partir de uma única realização. Por fim, propomos também um método para sintetizar campos vetoriais a partir de um conjunto, utilizando técnicas de Redução de Dimensionalidade e Projeção Inversa. Testamos os métodos propostos tanto em campos sintéticos quanto em campos numericamente simulados.
Vector field plays an essential role in a large range of scientific applications. They are commonly generated through computer simulations. Such simulations may be a costly process because they usually require high computational time. When researchers want to quantify the uncertainty in such kind of applications, usually an ensemble of vector fields realizations are generated, making the process much more expensive. The Helmholtz-Hodge Decomposition is a very useful instrument for vector field interpretation because it traditionally distinguishes conservative (rotational-free) components from mass-preserving (divergence-free) components. In this work, we are going to explore the applicability of such technique on the uncertainty analysis of 2-dimensional vector fields. First, we will present an approach of the use of the Helmholtz-Hodge Decomposition as a basic tool for the analysis of a vector field ensemble. Given a vector field ensemble epsilon, we firstly obtain the corresponding rotational-free, divergence-free and harmonic component ensembles by applying the Natural Helmholtz-Hodge Decomposition to each1 vector field in epsilon. With these ensembles in hand, our proposal not only quantifies, via a statistical analysis, how much each component ensemble is point-wisely correlated to the original vector field ensemble, but it also allows to investigate the uncertainty of rotational-free, divergence-free and harmonic components separately. Then, we propose two techniques that jointly with the Helmholtz-Hodge Decomposition stochastically generate vector fields from a single realization. Finally, we propose a method to synthesize vector fields from an ensemble, using both the Dimension Reduction and Inverse Projection techniques. We test the proposed methods with synthetic vector fields as well as with simulated vector fields.
Strang, Alexander. "Applications of the Helmholtz-Hodge Decomposition to Networks and Random Processes." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1595596768356487.
Full textRibeiro, Carlos Augusto David. "Teorema de Hodge e aplicaÃÃes." Universidade Federal do CearÃ, 2008. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=4360.
Full textO presente trabalho aborda um teorema classico de decomposiÃÃo do espaÃo das p-formas suaves sobre uma variedade Riemaniana compacta e orientada, conhecido como teorema da decomposiÃÃo de Hodge, assim como suas consequÃncias. No decorrer do mesmo, foi feita uma passagem por diversas ferramentas interessantes, como espaÃos Sobolev (capÃtulo 2) e EDP elÃptica (capÃtulo 3), assim como uma abordagem suscinta de formas diferenciÃveis.
This dissertation presents a classical theorem of decomposition of the space of smooths p-forms on compact oriented Riemannian manifold , known as the theorem of Hodge decomposition, and its consequences. During the same was made a passage for several interesting tools, such as Sobolev spaces(Chapter 2) and elliptical PDE (Chapter 3), as well as a succinct approach about diferenciable forms (Chapter 1).
Lemoine, Antoine. "Décomposition de Hodge-Helmholtz discrète." Thesis, Bordeaux, 2014. http://www.theses.fr/2014BORD0227/document.
Full textWe propose in this thesis a methodology to compute the Helmholtz-Hodge decomposition on discrete polyhedral meshes. The challenge of this work isto preserve the properties of the decomposition at the discrete level. In our literature survey, we have identified the need of mimetic schemes to achieve our goal. The description and validation of our implementation of these schemes are presented inthis document. We revisit and improve the methods of decomposition we then study through numerical experiments. In particular, we detail our choice of linear solvers and the convergence of extracted quantities on various series of polyhedral meshes and boundary conditions. Finally, we apply the Helmholtz-Hodge decomposition to the study of two turbulent flows: a turbulent channel flow and a homogeneous isotropic turbulent flow
Schüler, Axel. "Äußere Algebren, de-Rham-Kohomologie und Hodge-Zerlegung für Quantengruppen." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-218057.
Full textConsider one of the standard bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or SPq(N), where q is a transcendental complex number. It is shown that the de Rham cohomology of Woronowicz' external algebra coincides with the de Rham cohomologies of its left-invariant, its right-invariant and its bi-invariant subcomplexes. In the cases GLq(N) and SLq(N), the cohomology ring is isomorphic to the left-invariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. As in the classical case all three spaces of differential forms coincide: bi- invariant forms, harmonic forms and the de-Rham-cohomology. For orthog- onal and symplectic quantum groups there is no complete Hodge decompo- sition. In case of the standard calculi on the quantum groups GLq(N) and SLq(N), the size of exterior algebra is computed. The space of left-invariant k-forms has dimension C(N², k) (binomial coefficient). The algebra of bi-invariant forms is graded commutative with Poincaré series (1+t)(1+t³) ... (1+t^(2N-1)). Bi-invariant forms are closed
Arnold, Rachel Florence. "Complex Analysis on Planar Cell Complexes." Thesis, Virginia Tech, 2008. http://hdl.handle.net/10919/32230.
Full textMaster of Science
Seyfert, Anton [Verfasser], Matthias [Akademischer Betreuer] Hieber, and Hideo [Akademischer Betreuer] Kozono. "The Helmholtz-Hodge Decomposition in Lebesgue Spaces on Exterior Domains and Evolution Equations on the Whole Real Time Axis / Anton Seyfert ; Matthias Hieber, Hideo Kozono." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2018. http://d-nb.info/1166315320/34.
Full textSuda, Tomoharu. "On some methods for the analysis of continuous dynamical systems." Kyoto University, 2020. http://hdl.handle.net/2433/253357.
Full text0048
新制・課程博士
博士(人間・環境学)
甲第22521号
人博第924号
新制||人||221(附属図書館)
2019||人博||924(吉田南総合図書館)
京都大学大学院人間・環境学研究科共生人間学専攻
(主査)准教授 木坂 正史, 教授 角 大輝, 教授 足立 匡義
学位規則第4条第1項該当
Shen, Xu. "Filtrations de Hodge-Newton, décomposition cellulaire et cohomologie de certains espaces de modules p-adiques." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00764117.
Full textHe, Bo. "Compatible discretizations for Maxwell equations." The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1143171299.
Full textSims, John Andrew. "Directional analysis of cardiac left ventricular motion from PET images." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-05092017-093020/.
Full textA quantificação do movimento cardíaco do ventrículo esquerdo (VE) a partir de imagens médicas fornece um método não invasivo para o diagnóstico de doenças cardiovasculares (DCV). O estudo aqui proposto continua na mesma linha de pesquisa do nosso grupo sobre quantificação do movimento do VE por meio de técnicas de fluxo óptico (FO), aplicando estes métodos para quantificar o movimento do VE em sequências de imagens associadas às substâncias de cloreto de rubídio-82Rb (82Rb) e fluorodeoxiglucose-18F (FDG) PET. Com a extração dos campos vetoriais surgiram os seguintes desafios: (i) o campo vetorial de movimento (motion vector field, MVF) deve ser feito da forma mais precisa possível para maximizar a sensibilidade e especificidade; (ii) o MVF é extenso e composto de vetores 3D no espaço 3D, dificultando a análise visual de informações por observadores humanos para o diagnóstico médico. Foram desenvolvidas abordagens para melhorar a precisão da quantificação de movimento, considerando que o volume de interesse seja a região do MVF correspondente ao miocárdio do VE, em que valores de movimento não nulos existem fora deste volume devido aos artefatos do método de detecção de movimento ou de estruturas vizinhas, como o ventrículo direito. As melhorias na precisão foram obtidas segmentando o VE e ajustando os valores de MVF para zero fora do VE. O miocárdio VE foi segmentado automaticamente em fatias de eixo curto usando a Transformada de Hough na detecção de círculos para fornecer uma inicialização ao algoritmo de curvas de nível, um tipo de modelo deformável. A segmentação automática do VE atingiu 93,43% de medida de similaridade Dice, quando foi testado em 395 fatias de eixo menor de FDG, comparado com a segmentação manual. Estratégias para melhorar o desempenho do algoritmo OF nas bordas de movimento foram investigadas usando spatially varying averaging filters, aplicados em seqüências de imagens sintéticas. Os resultados mostraram melhorias na precisão de quantificação de movimento utilizando estes métodos. O Índice de Energia Cinética (KEf), um indicador de motilidade cardíaca, foi utilizado para avaliar 63 sujeitos com função cardíaca normal e alterada / baixa de uma base de dados de imagens PET de 82Rb. Foram realizados testes de sensibilidade e especificidade para avaliar o potencial de KEf para classificar a função cardíaca, utilizando a fração de ejeção do VE como padrão ouro. Foi construída uma curva ROC, que proporcionou uma área sob a curva de 0,906. A análise do movimento do VE pode ser simplificada pela visualização de componentes de campo de movimento direcional, ou seja, radial, rotacional (ou circunferencial) e linear, obtidos por decomposição automatizada. A decomposição discreta de Helmholtz Hodge (DHHD) foi utilizada para gerar estes componentes de forma automatizada, com uma validação utilizando campos de movimento cardíaco sintéticos a partir do conjunto Extended Cardiac Torso Phantom. Finalmente, o método DHHD foi aplicado a campos de FO, criado a partir de imagens FDG, permitindo uma análise de componentes direcionais de um indivíduo com função cardíaca normal e um paciente com baixa função e utilizando um marca-passo. A quantificação do campo de movimento a partir de imagens PET possibilita o desenvolvimento de novos indicadores para diagnosticar DCVs. A capacidade destes indicadores de motilidade depende na precisão da quantificação de movimento que, por sua vez, pode ser determinado por características das imagens de entrada como ruído. A análise de movimento fornece um promissor e sem precedente método para o diagnóstico de DCVs.
Du, Dong. "Contributions to Persistence Theory." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338304358.
Full textHaufe, Daniel. "Untersuchung optischer Verfahren zur gleichzeitigen Messung von Strömungs- und Schallfeldern an aeroakustischen Schalldämpfern." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-197742.
Full textPnevmatikos, Nikolaos. "Contributions à la théorie des jeux : valeur asymptotique des jeux dépendant de la fréquence et décompositions des jeux finis." Thesis, Paris 1, 2016. http://www.theses.fr/2016PA01E026/document.
Full textThe problems addressed and results obtained in this thesis are divided in two parts. The first part concerns the study of the asymptotic value of frequency-dependent games (FD-games). We introduce a differential game associated to the FD-game whose value leads to a Hamilton-Jacob-Bellman-lsaacs equation. Although an irregularity occurs at the origin, we prove existence of the value in the differential game played over [0.1 ], which allows to prove that the value of the FD-game, as the number of stages tend to infinity, converges to the value of the continuous-time game with initial state 0. ln the second part, the objective is the decomposition of the space of finite games in subspaces of suitable games which admit disguised equilibria and more tractable analysis. This part is divided in two chapters. In the first chapter, we establish a canonical decomposition of an arbitrary game into three components and we characterize the approximate equilibria of a given game in terms of the uniform equilibrium and the equilibrium in dominant strategies that appear in its components. In the second part, we introduce a family of inner products in the space of finite games and we define the class of harmonic games relatively to the chosen inner product. Inspired of the Helmholtz-Hodge decomposition applied to games by Candogan et al (2011 ), we establish an orthogonal decomposition of the space of finite games with respect to the chosen inner product, in the subspaces of potential harmonic and non-strategic games and we further generalize several results of Candogan et al (2011)
Sacchetto, Lucas Kaufmann. "Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-18062012-194224/.
Full textThe main goal of this work is to present a detailed study of the foundations of Complex Geometry, highlighting its geometric, topological and analytical aspects. Beginning with a preliminary material, such as the basic results on holomorphic functions in one or more variables and the definition and first examples of a complex manifold, we move on to an introduction to sheaf theory and its cohomology, an essential tool to the rest of the work. After a discussion on divisors and line bundles we turn attention to Kähler Geometry and its central results, such as the Hodge Decomposition Theorem, the Hard Lefschetz Theorem and the Lefschetz Theorem on $(1,1)$-classes. After that, we study complex vector bundles and its geometry, focusing on the concepts of connections, curvature and Chern classes. Finally, we finish by describing some aspects of the topology of complex manifolds, such as the Lefschetz Hyperplane Theorem and some of its consequences.
Poelke, Konstantin [Verfasser]. "Hodge-Type Decompositions for Piecewise Constant Vector Fields on Simplicial Surfaces and Solids with Boundary / Konstantin Poelke." Berlin : Freie Universität Berlin, 2017. http://d-nb.info/1132547385/34.
Full textAxelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
Full textPearlstein, Gregory James. "The geometry of the Deligne-Hodge decomposition." 1999. https://scholarworks.umass.edu/dissertations/AAI9932337.
Full textSchüler, Axel. "Äußere Algebren, de-Rham-Kohomologie und Hodge-Zerlegung für Quantengruppen." Doctoral thesis, 2000. https://ul.qucosa.de/id/qucosa%3A15260.
Full textConsider one of the standard bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or SPq(N), where q is a transcendental complex number. It is shown that the de Rham cohomology of Woronowicz'' external algebra coincides with the de Rham cohomologies of its left-invariant, its right-invariant and its bi-invariant subcomplexes. In the cases GLq(N) and SLq(N), the cohomology ring is isomorphic to the left-invariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. As in the classical case all three spaces of differential forms coincide: bi- invariant forms, harmonic forms and the de-Rham-cohomology. For orthog- onal and symplectic quantum groups there is no complete Hodge decompo- sition. In case of the standard calculi on the quantum groups GLq(N) and SLq(N), the size of exterior algebra is computed. The space of left-invariant k-forms has dimension C(N², k) (binomial coefficient). The algebra of bi-invariant forms is graded commutative with Poincaré series (1+t)(1+t³) ... (1+t^(2N-1)). Bi-invariant forms are closed.
(6597026), Hongshan Li. "Vanishing Theorems for the logarithmic de Rham complex of unitary local system." Thesis, 2019.
Find full textSeyfert, Anton. "The Helmholtz-Hodge Decomposition in Lebesgue Spaces on Exterior Domains and Evolution Equations on the Whole Real Time Axis." Phd thesis, 2018. https://tuprints.ulb.tu-darmstadt.de/7725/1/20180801SeyfertAnton.pdf.
Full textHaufe, Daniel. "Untersuchung optischer Verfahren zur gleichzeitigen Messung von Strömungs- und Schallfeldern an aeroakustischen Schalldämpfern." Doctoral thesis, 2015. https://tud.qucosa.de/id/qucosa%3A29252.
Full textRioux-Lavoie, Damien. "Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre." Thèse, 2017. http://hdl.handle.net/1866/19377.
Full textThe objective of this thesis is to introduce a new implicit purely lagrangian smoothed particle hydrodynamics (SPH) method, for the resolution of the two-dimensional incompressible Navier-Stokes equations in the presence of a free surface. Our discretization scheme is based on that of Kéou Noutcheuwa et Owens [19]. We have treated the free surface by combining Yildiz et al. [43] multiple boundary tangent (MBT) method and boundary conditions on the auxiliary fields of Yang et Prosperetti [42]. In this way, we obtain a discretization scheme of order $\mathcal{O}(\Delta t ^2)$ and $\mathcal{O}(\Delta x ^2)$, according to certain constraints on the smoothing length $h$. First, we tested our scheme with a two-dimensional Poiseuille flow by means of which we analyze the discretization error of the SPH method. Then, we tried to simulate a two-dimensional Newtonian extrusion problem. Unfortunately, although the behavior of the free surface is satisfactory, we have encountered numerical problems on the singularity at the output of the die.
Axelsson, Andreas. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." Phd thesis, 2002. http://hdl.handle.net/1885/46056.
Full text