Dissertations / Theses on the topic 'Helmholtz Model'
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Scheiman, Kevin S. "A Parallel Spectral Method Approach to Model Plasma Instabilities." Wright State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=wright1527424992108785.
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Liu, Bing. "Properties Model for Aqueous Sodium Chloride Solutions near the Critical Point of Water." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1034.pdf.
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Gernert, Georg Johannes [Verfasser], Roland [Gutachter] Span, and Eckhard [Gutachter] Weidner. "A new Helmholtz energy model for humid gases and CCS mixtures / Georg Johannes Gernert ; Gutachter: Roland Span, Eckhard Weidner ; Fakultät für Maschinenbau." Bochum : Ruhr-Universität Bochum, 2013. http://d-nb.info/1212661400/34.
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Völker, Doris [Verfasser]. "Chemical-sensitive genes in zebrafish (Danio rerio) early development - identification and characterisation of differential expression in embryos exposed to the model compound 3,4-dichloroaniline / Doris Völker. [Helmholtz Centre for Environmental Research, UFZ]." Leipzig : Helmholtz Centre for Environmental Research, 2007. http://d-nb.info/1007282541/34.
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Sargent, Cristina Vasilica. "Trapped modes of the Helmholtz equation." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/11115.
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In the framework of the classical theory of linearised water waves in unbounded domains, trapped modes consist of non-propagating, localised oscillation modes of finite energy occurring at some well-defined frequency and which, in the absence of dissipation, persist in time even in the absence of external forcing. Jones (1953) proved the existence of trapped modes for problems governed by the Helmholtz equation in semi-infinite domains. Trapped modes have been studied in quantum mechanics, elasticity and acoustics and are known, depending on the context, as bound states, acoustic resonances, Rayleigh-Bloch waves, sloshing modes and motion trapped modes. We consider trapped modes in two dimensional infinite waveguides with either Neumann or Dirichlet boundary conditions. Such problems arise when considering obstacles in acoustic waveguides or bound states in quantum wires for example. The mathematical model is a boundary value problem for the Helmholtz equation. Under the usual assumptions of potential theory, the solution is written in terms of a boundary integral equation. We develop a Boundary Element Method (BEM) program which we use to obtain approximate numerical solutions. We extend existing results by identifying additional trapped modes for geometries already studied and investigate new structures. We also carry out a detailed investigation of trapped modes, using the planewave spectrum representation developed for various characteristic problems from the classical theories of radiation, diffraction and propagation. We use simple planewaves travelling in diverse directions to build a more elaborate solution, which satisfies certain conditions required for a trapped mode. Our approach is fairly flexible so that the general procedure is independent of the shape of the trapping obstacle and could be adapted to other geometries. We apply this method to the case of a disc on the centreline of an infinite Dirichlet acoustic waveguide and obtain a simple mathematical approximation of a trapped mode, which satisfies a set of criteria characteristic of trapped modes. Asymptotically, the solution obtained is similar to a nearly trapped mode, which is a perturbation of a genuine trapped mode.
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Liu, Guanhui. "Formulation of multifield finite element models for Helmholtz problems." Click to view the E-thesis via HKUTO, 2010. http://sunzi.lib.hku.hk/hkuto/record/B44204875.
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Liu, Guanhui, and 刘冠辉. "Formulation of multifield finite element models for Helmholtzproblems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44204875.
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FANTI, ALESSANDRO. "A generalized finite difference approach to the computation of modes." Doctoral thesis, Università degli Studi di Cagliari, 2012. http://hdl.handle.net/11584/266145.
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This thesis deals with numerical techniques for the computation of modes in electromagnetic structures with arbitrary geometry. The approach proposed in
this work is based on the Finite Difference (FD) and Vector Finite Difference (VFD), which are applied to rectangular, circular, elliptical geometries, and to combination of them. The FD is applied using a 2D cartesian, polar and elliptical grid in the waveguide section. A suitable Taylor expansion of the mode function allows, either for scalar and for vector FD, to take exactly into account the
boundary condition. To prevent the raising of spurious modes, the VFD approximation results in a constrained eigenvalue problem, that has been solved using a decomposition method. All approaches presented have been validated comparing the results to the analytical modes of rectangular and circular waveguide, and to known data for
the elliptic case. The standard calculation of the waveguide modes using FD requires the use of two different grids, namely one for TE modes and the other for TM modes, due to the different boundary condition. It has been shown that a single grid can be used for all modes, thus allowing an effective mode-matching solution. The FD approach has been extended to waveguides (and apertures) with irregular boundaries, and therefore non-regular discretization grids. It has been shown that a suitable FD approximation of the Laplace operator is still possible. A ridged-waveguide, with trapezoidal ridges, and a rounded-ended waveguide
have been considered in detail.
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Faure, Cédric. "Contrôle de la diffusion par des façades : cas des métasurfaces et des guides d'ondes ouverts inhomogènes." Thesis, Le Mans, 2017. http://www.theses.fr/2017LEMA1033/document.
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L’objectif de ce travail est le développement de dispositifs de contrôle de la diffusion des ondes acoustiques à l’aide de surfaces hétérogènes, pour des applications à l’acoustique urbaine. Pour remplir cet objectif, deux méthodes sont employées. La première à l’aide d’une métasurface, la direction d’une onde réfléchie est contrôlée. La seconde étude concerne l’influence d’un traitement inhomogène aux parois d’un guide ouvert sur les effets conjoints ou compétitifs d’absorption, de confinement et de rayonnement de l’onde. Nous montrons expérimentalement la possibilité de dissimuler un objet disposé sur un mur pour une onde acoustique audible. Pour y parvenir, une métasurface composée de différents résonateurs de Helmholtz est conçue et est réalisée de façon à être la plus fine possible. Ces travaux sont réalisés dans le domaine fréquentiel mais également dans le domaine temporel, ce qui permet de mettre en avant le caractère large bande de la métasurface. Il est démontré numériquement et expérimentalement que la direction des ondes réfléchies peut être contrôlée. Enfin la dernière partie est consacrée à l’influence d’une paroi hétérogène sur la propagation d’une onde acoustique à l’intérieur d’une rue. Une rue pouvant être assimilée à un guide d’onde ouvert engendre donc des modes de propagation complexes, dus aux pertes par rayonnement. La présence d’un matériau poreux sur les parois d’un guide vient perturber fortement la localisation spatiale des modes, ce qui les rend plus ou moins fuyantsThe aim of this thesis is to develop a scheme for controling the propagation of acoustic waves using heteregenous surfaces. Its results can be applied in the field of urban acoustic. The thesis is composed of two sections, each of them employing a different method. The first section focuses on controling the direction of a reflected wave, using a metasurface. The second concentrates on the influence of an inconsistent treatment to the side of an open waveguide on the wave joint and competitive effects of absorption, confinement and radiation. Part one provides experimental evidence that it is possible to conceal an object placed on a wall from an audible acoustic wave. To prove it, the thinest possible metasurface was constructed with Helmholtz resonators. The experimental results were compared to a numerical study realized with finite elements. This work was made in both temporal and frequency domains, allowing to point out the wide frequency characteristics of the metasurface. The numerical and experimental results show that the direction of a reflected wave can, indeed, be controled. Part two analyse the impact of a heterogeneous wall on the spreadinf of an acoustic wave in a street. Due to radiation losses, the street produces complex ways of propagation. The presence of a porous material on a waveguide‘ side deeply disrupt the spatial location of these waves, making them more or less fleeting. In particular, depending on the position of the material in the street, certain waves will be more confined to the inside of the street, radiating less towards the open external environment. They are consequently, less cushioned
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Djoudi, Adel. "Binary level static analysis." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX093.
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Les méthodes de vérification automatique des logiciels connaissent un succès croissant depuis le début des années 2000, suite à plusieurs succès industriels (Microsoft, Airbus, etc.). L'analyse statique vise, à partir d'une description du programme, à inférer automatiquement des propriétés vérifiées par celui-ci. Les techniques standards d'analyse statique travaillent sur le code source du logiciel, écrit par exemple en C ou Java. Cependant, avoir accès au code source n'est pas envisageable pour de nombreuses applications relatives à la sécurité, soit que le code source n'est pas disponible (code mobile, virus informatiques), soit que le développeur ne veut pas le divulguer (composants sur étagère, certification par un tiers).Nous nous intéressons dans cette thèse à la conception et au développement d'une plate-forme d'analyse statique de code binaire à des fins d'analyse de sécurité. Nos principales contributions se font à trois niveaux: sémantique, implémentation et analyse statique.Tout d'abord, la sémantique des programmes binaires analysés est basée sur un formalisme générique appelé DBA qui a été enrichi avec des mécanismes de spécification et d'abstraction. La définition de la sémantique des programmes binaires requiert aussi un modèle mémoire adéquat.Nous proposons un modèle mémoire adapté au binaire, inspiré des travaux récents sur le code C bas-niveau. Ce nouveau modèle permet de profiter de l'abstraction du modèle à régions tout en gardant l'expressivité du modèle plat.Ensuite, notre plate-forme d'analyse de code binaire nommée BinSec offre trois services de base: désassemblage, simulation et analyse statique.Chaque instruction machine est traduite vers un bloc d'instructions DBA avec une sémantique équivalente. Une large partie des instructions x86 est gérée par la plateforme. Une passe de simplification permet d'éliminer les calculs intermédiaires inutiles afin d'optimiser le fonctionnement des analyses ultérieures. Nos simplifications permettent notamment d'éliminer jusqu'à75% des mises à jours de flags.Enfin, nous avons développé un moteur d'analyse statique de programmes binaires basé sur l'interprétation abstraite. Outre des domaines adaptés aux spécificités du code binaire, nous nous sommes concentrés sur le contrôle par l'utilisateur du compromis entre précision/correction et efficacité. De plus, nous proposons une approche originale de reconstruction de conditions dehaut-niveau à partir des conditions bas-niveau afin de gagner plus de précision d'analyse. L'approche est sûre, efficace, indépendante de la plateforme cibleet peut atteindre des taux de reconstruction très élevésAutomatic software verification methods have seen increasing success since the early 2000s, thanks to several industrial successes (Microsoft, Airbus, etc.).Static program analysis aims to automatically infer verified properties of programs, based on their descriptions. The standard static analysis techniques apply on the software source code, written for instance in C or Java. However, access to source code is not possible for many safety-related applications, whether the source code is not available (mobile code, computer virus), or the developer does not disclose it (shelf components, third party certification).We are interested in this dissertation in design and development of a static binary analysis platform for safety analysis. Our contributions are made at three levels: semantics, implementation and static analysis.First, the semantics of analyzed binary programs is based on a generic, simple and concise formalism called DBA. It is extended with some specification and abstraction mechanisms in this dissertation. A well defined semantics of binary programs requires also an adequate memory model. We propose a new memory model adapted to binary level requirements and inspired from recent work on low-level C. This new model allows to enjoy the abstraction of the region-based memory model while keeping the expressiveness of the flat model.Second, our binary code analysis platform BinSec offers three basic services:disassembly, simulation and static analysis. Each machine instruction is translated into a block of semantically equivalent DBA instructions. The platform handles a large part of x86 instructions. A simplification step eliminates useless intermediate calculations in order to ease further analyses. Our simplifications especially allow to eliminate up to 75% of flag updates.Finally, we developed a static analysis engine for binary programs based on abstract interpretation. Besides abstract domains specifically adapted to binary analysis, we focused on the user control of trade offs between accuracy/correctness and efficiency. In addition, we offer an original approach for high-level conditions recovery from low-level conditions in order to enhance analysis precision. The approach is sound, efficient, platform-independent and it achieves very high ratio of recovery
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Olivares, Nicole Michelle. "Accuracy of Wave Speeds Computed from the DPG and HDG Methods for Electromagnetic and Acoustic Waves." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/2920.
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We study two finite element methods for solving time-harmonic electromagnetic and acoustic problems: the discontinuous Petrov-Galerkin (DPG) method and the hybrid discontinuous Galerkin (HDG) method.
The DPG method for the Helmholtz equation is studied using a test space normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. We find that, as the parameter approaches zero, better results are obtained, under some circumstances. A dispersion analysis on the multiple interacting stencils that form the DPG method shows that the discrete wavenumbers of the method are complex, explaining the numerically observed artificial dissipation in the computed wave approximations. Since the DPG method is a nonstandard least-squares Galerkin method, its performance is compared with a standard least-squares method having a similar stencil.
We study the HDG method for complex wavenumber cases and show how the HDG stabilization parameter must be chosen in relation to the wavenumber. We show that the commonly chosen HDG stabilization parameter values can give rise to singular systems for some complex wavenumbers. However, this failure is remedied if the real part of the stabilization parameter has the opposite sign of the imaginary part of the wavenumber. For real wavenumbers, results from a dispersion analysis for the Helmholtz case are presented. An asymptotic expansion of the dispersion relation, as the number of mesh elements per wave increase, reveal values of the stabilization parameter that asymptotically minimize the HDG wavenumber errors. Finally, a dispersion analysis of the mixed hybrid Raviart-Thomas method shows that its wavenumber errors are an order smaller than those of the HDG method.
We conclude by presenting some contributions to the development of software tools for using the DPG method and their application to a terahertz photonic structure. We attempt to simulate field enhancements recently observed in a novel arrangement of annular nanogaps.
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Marinho, Leonardo Ribeiro. "Análise Completa das Fibras de Bragg de Núcleo Oco." Universidade do Estado do Rio de Janeiro, 2013. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=8141.
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A evolução nos sistemas digitais de comunicação está intrinsicamente relacionada ao desenvolvimento da tecnologia de fibras ópticas. Desde a sua criação, na década de 60, inúmeras pesquisas vem sendo realizadas com o intuito de aumentar a capacidade de informação transmitida, por meio da redução da atenuação, controle da dispersão cromática e eliminação das não-linearidades. Neste contexto, as Fibras de Bragg surgem como uma estrutura de grande potencialidade para se minimizar tais inconvenientes. As fibras de Bragg possuem um mecanismo de operação diferente em relação às fibras tradicionais
de suportar os modos confinados. Nelas, o núcleo possui um baixo índice de refração, e a casca é constituída por anéis dielétricos de diferentes índices de refração, alocados alternadamente. Para uma fibra de Bragg com núcleo oco, como a considerada neste trabalho,
há perdas decorrentes dos modos de fuga. Portanto, a análise da dispersão destas estruturas se situa no plano complexo, tornando-a muito difícil. Esta dissertação será fundamentada em uma estratégia imprescindível à análise dos modos transversais TE0m, TM0m e dos híbridos. Os resultados encontrados são validados confrontando-os com os obtidos na literatura. O trabalho discutirá as perdas e dispersões dos modos citados, e os resultados obtidos poderão nortear as pesquisas das fibras de Bragg.The evolution of digital communication systems is intrinsically related to the development of optical fiber technology. Since its creation in the 1960s, many studies have been conducted in order to increase the system capacity, such as the attenuation reduction, chromatic dispersion control and elimination of nonlinearities. In this context, Bragg fibers appear as a structure with great potential to mitigate these drawbacks. Bragg fibers have a different operational mechanism with respect to traditional fibers to support the confined modes. Their core has a low refractive index, and the cladding consists of dielectric rings of different refractive indices, allocated alternately. For a Bragg fiber with hollow core, as considered in this paper, there are losses due to the occurrence of leaky modes. Therefore, the dispersion analysis of these structures falls in the complex plane, making it even harder. This dissertation will be based on a strategy essential to the analysis of transverse modes: TE0m, TM0m and hybrids. The found results have been validated by comparing them with those obtained in the literature. The paper discusses the losses and dispersions of the mentioned modes, and the results obtained will serve to guide the research on Bragg fibers.
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Soussi, Sofiane. "Quelques Modélisations Mathématiques en Optique." Phd thesis, Ecole Polytechnique X, 2004. http://tel.archives-ouvertes.fr/tel-00008756.
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La première partie de la thèse est consacrée à l'étude de la diffraction d'ondes électromagnétiques par des objets bornés recouverts de couches minces de diélectriques non linéaires. Un développement asymptotique de l'onde fondamentale et de la seconde harmonique est donné en utilisant des techniques d'équations intégrales.Dans la deuxième partie de la thèse, on s'intéressé à la méthode dite de la (\em supercell) qui est utilisée par les physiciens afin de donner une approximation des modes introduits par un défaut à support compact dans un cristal photonique. On étudie la convergence de cette méthode donnant un sens à la convergence du spectre de l'opérateur approché. La convergence exponentielle des valeurs propres dues au défaut est démontrée.
La troisième partie de la thèse est consacrée à l'étude de la propagation d'ondes électromagnétiques dans les fibres optiques photoniques. On dérive une modélisation mathématique de ces fibres dont l'enveloppe est constituée d'un cristal photonique bidimensionnel invariant selon l'axe de la fibre. Les modes guidés par la fibre sont caractérisés comme étant les valeurs propres d'opérateurs intégraux.
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Costa, Ricardo Gomes da. "Estudo dos modos de Plasmon em Fibras fracamente guiadas com camadas dielétricas sobre Filme Metálico." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=7456.
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Neste trabalho são analisados os quatro modos de plasmon, ligados simétrico (Sb) e
assimétrico (ab), fuga pelo núcleo (ln) e fuga pela cobertura (lc), que se propagam em uma
fibra óptica fracamente guiada envolta por um filme metálico. No filme metálico é depositada
uma camada dielétrica extra e acima desta, uma outra denominada cobertura. A análise será
desenvolvida para filmes metálicos de prata, paládio e ouro.
Esta estrutura é muito útil na confecção de sensores ópticos.In this work the four Plasmon modes are analyzed, the symmetrical (Sb) and asymmetrical bounded (ab); the core (ln) and covering leaky modes (lc), that propagate in weakly guided optical fibers with a metallic film around that. In the metallic film a layer extra dielectric is deposited and above this, another layer denominated covering. The analysis will be developed for metallic films of the Silver, Palladium and Gold. This structure is very useful to making optical sensors.
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Vianna, Pedro Arlindo Barroso Hardman. "Análise dos Modos de Plasmon em Fibras Ópticas com Contraste Arbitrário de Índices de Refração." Universidade do Estado do Rio de Janeiro, 2009. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=7541.
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Neste trabalho, é feita a análise dos modos de plasmon que se propagam em um filme
metálico que cobre uma fibra óptica generalizada. Os modos de plasmon estudados são: Fuga
pela Cobertura (lcv), Ligado Simétrico (Sb), Fuga pelo Núcleo (lcr) e Ligado Assimétrico (ab).
Os filmes metálicos, para efeito de comparação, utilizados neste trabalho, são: a prata, o ouro
e o paládio.
Desenvolveu-se um modelo matemático do fenômeno eletromagnético e um software,
que gerou um banco de dados que facilitasse a análise de estruturas, com diversas
combinações de parâmetros.
Com o banco de dados, foram obtidos diversos gráficos, que permitiram: analisar os
modos de plasmon, verificar a atenuação das ondas e o comportamento do campo
eletromagnético em cada região da estrutura.
As confrontações entre as estruturas com filmes de: prata, ouro e paládio, permitiram
concluir que aquelas elaboradas com os filmes de prata e de ouro são as que apresentam
menores perdas, portanto, as recomendadas na confecção de sensores. Como a prata é mais
acessível que o ouro, aconselha-se a sua utilização.
A análise e os resultados deste trabalho são originais na literatura especializada.In this work it is done the analysis of the ways of plasmon that developed themselves in a mettalic film that covers an optic and generalized fiber. The studied ways of plasmon are: Cover-Leaky (lcv), Symmetric Bounded (Sb), Core-Leaky (lcr) and Asymmetrical Bounded (ab). The metallic films, for reason of comparison, used in this work, are: the silver, the gold and the paladium. It was developed a mathematical model of the electricmagnetic phenomenon and a software, that created a database which could make it easy the analysis of structures with several combinations of parameters. With the database have been got several graphs that let: analyse the types of plasmon, see the reduction of waves and the behaviour of the electricmagnetic field in each area of the structure. The confrontations between the structures with films of silver, gold and paladium made it possible to conclude that those elaborated with films of silver and gold are those that present smaller losses, so, are recommended in the confection of sensors. As silver is more accecible than gold it is advisable its utilization. The analysis and the results of this work are original in the specialized literature.
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Williams, Paul David. "Nonlinear interactions of fast and slow modes in rotating, stratified fluid flows." Thesis, University of Oxford, 2003. http://ora.ox.ac.uk/objects/uuid:5365c658-ab60-41e9-b07b-0f635909835e.
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This thesis describes a combined model and laboratory investigation of the generation and mutual interactions of fluid waves whose characteristic scales differ by an order of magnitude or more. The principal aims are to study how waves on one scale can generate waves on another, much shorter scale, and to examine the subsequent nonlinear feedback of the short waves on the long waves. The underlying motive is to better understand such interactions in rotating, stratified, planetary fluids such as atmospheres and oceans. The first part of the thesis describes a laboratory investigation using a rotating, two-layer annulus, forced by imposing a shear across the interface between the layers. A method is developed for making measurements of the two-dimensional interface height field which are very highly-resolved both in space and time. The system's linear normal modes fall into two distinct classes: 'slow' waves which are relatively long in wavelength and intrinsic period, and 'fast' waves which are much shorter and more quickly-evolving. Experiments are performed to categorize the flow at a wide range of points in the system's parameter space. At very small background rotation rates, the interface is completely devoid of waves of both types. At higher rates, fast modes only are generated, and are shown to be consistent with the Kelvin-Helmholtz instability mechanism based on a critical Richardson number. At rotation rates which are higher still, baroclinic instability gives rise to the onset of slow modes, with subsequent localized generation of fast modes superimposed in the troughs of the slow waves. In order to examine the generation mechanism of these coexisting fast modes, and to assess the extent of their impact upon the evolution of the slow modes, a quasi-geostrophic numerical model of the laboratory annulus is developed in the second part of the thesis. Fast modes are filtered out of the model by construction, as the phase space trajectory is confined to the slow manifold, but the slow wave dynamics is accurately captured. Model velocity fields are used to diagnose a number of fast wave radiation indicators. In contrast to the case of isolated fast waves, the Richardson number is a poor indicator of the generation of the coexisting fast waves that are observed in the laboratory, and so it is inferred that these are not Kelvin-Helmholtz waves. The best indicator is one associated with the spontaneous emission of inertia-gravity waves, a generalization of geostrophic adjustment radiation. A comparison is carried out between the equilibrated wavenumbers, phase speeds and amplitudes of slow waves in the laboratory (which coexist with fast modes), and slow waves in the model (which exist alone). There are significant differences between these wave properties, but it is shown that these discrepancies can be attributed to uncertainties in fluid properties, and to model approximations apart from the neglect of fast modes. The impact of the fast modes on the slow modes is therefore sufficiently small to evade illumination by this method of inquiry. As a stronger test of the interaction, a stochastic parameterization of the inertia-gravity waves is included in the model. Consistent with the laboratory/model intercomparison, the parameterized fast waves generally have only a small impact upon the slow waves. However, sufficiently close to a transition curve between two different slow modes in the system's parameter space, it is shown that the fast modes can exert a dominant influence. In particular, the fast modes can force spontaneous transitions from one slow mode to another, due to the phenomenon of stochastic resonance. This finding should be of interest to the meteorological and climate modelling communities, because of its potential to affect model reliability.
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Vegh, Viktor. "Numerical modelling of industrial microwave heating." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/37144/7/37144_Digitised%20Thesis.pdf.
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The numerical modelling of electromagnetic waves has been the focus of many research areas in the past. Some specific applications of electromagnetic wave scattering are in the fields of Microwave Heating and Radar Communication Systems. The equations that govern the fundamental behaviour of electromagnetic wave propagation in waveguides and cavities are the Maxwell's equations. In the literature, a number of methods have been employed to solve these equations. Of these methods, the classical Finite-Difference Time-Domain scheme, which uses a staggered time and space discretisation, is the most well known and widely used. However, it is complicated to implement this method on an irregular computational domain using an unstructured mesh.
In this work, a coupled method is introduced for the solution of Maxwell's equations. It is proposed that the free-space component of the solution is computed in the time domain, whilst the load is resolved using the frequency dependent electric field Helmholtz equation. This methodology results in a timefrequency domain hybrid scheme. For the Helmholtz equation, boundary conditions are generated from the time dependent free-space solutions. The boundary information is mapped into the frequency domain using the Discrete Fourier Transform. The solution for the electric field components is obtained by solving a sparse-complex system of linear equations. The hybrid method has been tested for both waveguide and cavity configurations. Numerical tests performed on waveguides and cavities for inhomogeneous lossy materials highlight the accuracy and computational efficiency of the newly proposed hybrid computational electromagnetic strategy.
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Méry, Fabien. "Instabilités linéaires et rayonnement acoustique d'un écoulement sur une paroi présenatant une cavité." Toulouse, ISAE, 2010. http://www.theses.fr/2010ESAE0017.
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L'aéroacoustique des cavités constitue une problématique majeure pour l'industrie aéronautique en ce qui concerne la réduction du bruit d'un avion en phase d'atterrissage. Parmi les différents outils d'analyse d'un tel écoulement, la théorie de stabilité linéaire fournit un moyen simple d'investigation. Dans la bibliographie afférente, on trouve surtout des études fondamentales (bas nombres de Reynolds, cavités rectangulaires). Notre étude s'est concentrée sur la stabilité d'un cas plus appliqué issu d'expérimentations réalisées à l'ECL dans le cadre du projet AEROCAV. Précisément, nous étudions l'écoulement sur une paroi plane présentant une cavité cylindrique pour une vitesse incidente de 70 [m/s] correspondant à un nombre de Reynolds important basé sur le diamètre de la cavité (460 000). Une simulation des grandes échelles a par ailleurs été réalisée à l'ONERA DSNA. La partie moyenne de cette simulation sert d'écoulement de base pour l'étude de stabilité, la partie instationnaire d'éléments de comparaison. L'étude de stabilité est conduite dans le plan médian à la cavité situé dans l'axe de l'écoulement principal. Dans ce plan, l'écoulement présente deux directions d'inhomogénéité, c'est pourquoi une théorie dite globale 2D a été mise en œuvre pour l'étude de stabilité d'une telle configuration. La g"ométrie utilisée (plan médian de la cavité cylindrique) présente l'intérêt d'avoir des résultats de mesure mais l'inconvénient de nécessitéer une modélisation limitée au plan médian. Pour cette raison, nous avons souhaité appliquer la même approche de stabilité à des écoulements sur des cavités rectangulaires. Une étude paramétrique vis-à-vis de la vitesse incidente a été réalisée et confirme les résultats de la cavité cylindrique. Le calcul de stabilité a permis de mettre en évidence l'émergence des modes de Kelvin-Helmholtz qui semblent coïncider avec les modes dits de Rossiter. Cela permet une réinterprétation de la formule de Rossiter d'un point de vue stabilité. Par ailleurs, une simulation sur cavité rectangulaire avec vitesse incidente variable a permis de mettre en évidence le changement de mode impliqué dans la résonance de la cavité par une analyse HR d'un senseur de pression. Ce calcul permet une caractérisation et une compréhension du phénomène de sélection de mode émis par la cavité.
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Goursaud, Benjamin. "Etude mathématique et numérique de guides d'ondes ouverts non uniformes, par approche modale." Phd thesis, Ecole Polytechnique X, 2010. http://pastel.archives-ouvertes.fr/pastel-00546093.
Full textAbstract:
Cette thèse s'inscrit dans le cadre de l'étude, à la fois théorique et numérique, de la diffraction d'une onde harmonique par la jonction entre deux guides d'ondes ouverts. Nous démontrons que ce problème est bien posé. Pour cela, nous utilisons des conditions de rayonnement modales, qui sont fondées sur la représentation de la solution dans un guide droit à l'aide des modes guidés (liés au spectre ponctuel de l'opérateur transverse) et des modes de radiation (liés au spectre continu de l'opérateur transverse). Cette représentation semble difficile à mettre en oeuvre dans une méthode numérique, à cause du continuum des modes de radiation. Comme alternative, nous utilisons des PMLs (Perfectly Matched Layers) pour borner le domaine de calcul dans les directions transverses, ce qui modifie singulièrement la nature de l'opérateur transverse : il perd son caractère autoadjoint et son spectre devient exclusivement discret. Parmi ses nouveaux modes, se trouvent désormais des modes à fuite, dont les propriétés sont étudiées. Nous expliquons en quoi la perte du caractère autoadjoint implique que le calcul des modes peut être délicat. Nous expliquons ensuite comment utiliser ces nouveaux modes (formant maintenant un ensemble discret) dans des méthodes numériques pour la jonction entre deux guides d'ondes ouverts (conditions aux limites transparentes fondées sur des opérateurs de Dirichlet-to-Neumann, méthode multimodale).
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Basley, Jérémy. "An Experimental Investigation on Waves and Coherent Structures in a Three-Dimensional Open Cavity Flow." Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112245/document.
Full textAbstract:
Une écoulement de cavité ouverte tridimensionnel saturé non-linéairement est étudié par une approche spatio-temporelle utilisant des données expérimentales résolues à la fois en temps et en espace. Ces données ont été acquises dans deux plans longitudinaux, respectivement perpendiculaire et parallèle au fond de la cavité, dans le régime incompressible, en air ou en eau. À l'aide de multiples méthodes de décompositions globales en temps et en espace, les ondes et les structures cohérentes constituant la dynamique dans le régime permanent et pouvant être produites par des mécanismes d'instabilités différents sont identifiées et caractérisées.Tout d'abord, on approfondit la compréhension de l'effet des non-linéarités sur les oscillations auto-entretenues de la couche cisaillée impactante et leurs interactions avec l'écoulement intra-cavitaire. En particulier, l'analyse spectrale d'une portion de l'espace des paramètres permet de mettre en évidence un lien entre l'accrochage des modes d'oscillations auto-entretenues, la modulation d'amplitude au niveau du coin impactant et l'intermittence de ces modes. De plus, l'observation des basses fréquences intéragissant fortement avec les oscillations de la couche de mélange démontre l'existence d'une dynamique tridimensionnelle intrinsèque à l'intérieur de la cavité malgré les perturbations causées par la couche cisaillée instable.Les analyses de stabilité linéaire ont montré que des instabilités centrifuges peuvent résulter de la courbure induite par la recirculation. L'étude de la dynamique après saturation révèle de nombreuses structures cohérentes dont les propriétés sont quantifiées et classées en s'appuyant sur la forme des instabilités sous-jacentes: des ondes transverses progressives ou stationnaires. Enfin, certains comportements des structures saturées suggèrent que les mécanismes non-linéaires gouvernant le développement de l'écoulement une fois sorti du régime linéaire pourraient être étudiés dans le cadre des équations d'amplitudeA space-time study of a three-dimensional nonlinearly saturated open cavity flow is undertaken using time-resolved space-extended experimental data, acquired in both cross-stream and spanwise planes, in incompressible air and water flows. Through use of multiple modal decompositions in time and space, the waves and coherent structures composing the dynamics in the permanent regime are identified and characterised with respect to the instabilities arising in the flow.Effects of nonlinearities are thoroughly investigated in the impinging shear layer, regarding the self-sustained oscillations and their interactions with the inner-flow. In particular, the analysis conducted throughout the parameter space enlightens a global connection between the selection of locked-on modes and the amplitude modulation at the impingement and the mode switching phenomenon. Furthermore, observations of low frequencies interacting drastically with the shear layer flapping motion underline the existence of intrinsic coherent three-dimensional dynamics inside the cavity in spite of the shear layer disturbances.Linear stability analyses have demonstrated that centrifugal instabilities are at play along the main recirculation. The present investigation of the dynamics after onset of the saturation reveals numerous space-time coherent structures, whose properties are quantified and classified with respect to the underlying instabilities: travelling or standing spanwise waves. Finally, some patterns exhibited by the saturated structures suggest that the nonlinear mechanisms governing the mutations of the flow after the linear regime could gain more insight in the frame of amplitude equations
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Basley, Jérémy. "Étude Expérimentale des Ondes et Structures Cohérentes dans un Écoulement Tridimensionnel de Cavité Ouverte." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00822898.
Full textAbstract:
Une écoulement de cavité ouverte tridimensionnel saturé non-linéairement est étudié par une approche spatio-temporelle utilisant des données expérimentales résolues à la fois en temps et en espace. Ces données ont été acquises dans deux plans longitudinaux, respectivement perpendiculaire et parallèle au fond de la cavité, dans le régime incompressible, en air ou en eau. À l'aide de multiples méthodes de décompositions globales en temps et en espace, les ondes et les structures cohérentes constituant la dynamique dans le régime permanent et pouvant être produites par des mécanismes d'instabilités différents sont identifiées et caractérisées.Tout d'abord, on approfondit la compréhension de l'effet des non-linéarités sur les oscillations auto-entretenues de la couche cisaillée impactante et leurs interactions avec l'écoulement intra-cavitaire. En particulier, l'analyse spectrale d'une portion de l'espace des paramètres permet de mettre en évidence un lien entre l'accrochage des modes d'oscillations auto-entretenues, la modulation d'amplitude au niveau du coin impactant et l'intermittence de ces modes. De plus, l'observation des basses fréquences intéragissant fortement avec les oscillations de la couche de mélange démontre l'existence d'une dynamique tridimensionnelle intrinsèque à l'intérieur de la cavité malgré les perturbations causées par la couche cisaillée instable.Les analyses de stabilité linéaire ont montré que des instabilités centrifuges peuvent résulter de la courbure induite par la recirculation. L'étude de la dynamique après saturation révèle de nombreuses structures cohérentes dont les propriétés sont quantifiées et classées en s'appuyant sur la forme des instabilités sous-jacentes: des ondes transverses progressives ou stationnaires. Enfin, certains comportements des structures saturées suggèrent que les mécanismes non-linéaires gouvernant le développement de l'écoulement une fois sorti du régime linéaire pourraient être étudiés dans le cadre des équations d'amplitude.
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Beale, Jennifer Claire. "Modeling fuel injection using Kelvin-Helmholtz/Rayleigh-Taylor hybrid atomization model in KIVA-3V." 1999. http://catalog.hathitrust.org/api/volumes/oclc/42012813.html.
Full textAbstract:
Thesis (M.S.)--University of Wisconsin--Madison, 1999.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 101-105).
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Boruah, Buddha Deka. "Coupled Optical and Electrochemical Properties of ZnCo2O4 for Radiation Sensitive Supercapacitor : An Approach Towards Self-powered Photosensitive Energy Storage." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4242.
Full textAbstract:
Recently, the fields of energy conversion and storage have drawn great interests in the research community due to the wide range of practical applications in the society. Among them, photodetector (PD) and supercapacitor (SC) have attracted potential imprints for energy conversion and storage applications. This thesis is thus focused on the fabrication of efficient self-powered ultraviolet (UV) PD and SC based on optically and electrochemically active heterostructure materials.
Firstly, self-powered UV PD is explored based on one dimensional zinc oxide (ZnO) nanorods (NRs). The charge carrier density of ZnO NRs was modified by doping of halogen elements to enhance the self-powered photo response. Interestingly, 5.5 times enhancement in the photo response of halogen doped ZnO NRs was noticed as compared to pristine ZnO NRs. Further charge carrier modification of ZnO NRs was performed via hydrogenation process of ZnO NRs. Efficient increase in the carrier density of hydrogenated ZnO (H: ZnO) NRs allows enhancing the photo response to nearly 900% and 82% as compared to pristine ZnO NRs and halogen doped ZnO NRs, respectively. The optically as well as electrochemically active heterostructure was then introduced by integrating zinc cobalt oxide (ZnCo2O4) with H: ZnO NRs to form ZnCo2O4/H: ZnO NRs for the applications of UV PD and SC. Further enhancement of 75% in the photo response of ZnCo2O4/H: ZnO NRs was obtained as compared to H: ZnO NRs in self-powered configuration. The photo response behaviour of the ZnCo2O4/H: ZnO NRs PD was investigated under different UV illumination intensities in absence of external bias voltage. A power law dependence of the response of the PD on UV illumination intensity was displayed. Moreover, faster photon detection speed in the order of few milliseconds was also achieved for the self-powered PD. Furthermore, efficient UV detection efficiency for the PD was obtained.
The electrochemical performance of the ZnCo2O4/H: ZnO NRs was then investigated in detail. Efficient energy storage performance of ZnCo2O4/H: ZnO NRs was obtained where 63% enhancement in energy storage performance of ZnCo2O4/H: ZnO NRs electrode was observed as compared to ZnCo2O4 alone. For the investigation of energy storage performance of ZnCo2O4/H: ZnO NRs in presence of UV illumination, a solid-state symmetric SC (SSC) was fabricated composed of ZnCo2O4/H: ZnO NRs electrodes. The energy storage performance of the SSC was analysed both in the absence and the presence of UV illumination. An appreciable, 2.7 times enhancement in specific capacitance of the SSC was noticed under UV illumination as compared to the absence of UV. It was found that with the increase in UV illumination intensity, the electrochemical performance of the SSC increases linearly. The capacitance stability of the SSC was further studied for 4000 cycles both in the presence and the absence of UV. Notably, only 2% degradation of the capacitive response of the SSC was noticed under UV illumination as compared to absence of UV. Moreover, 175% enhancement in energy density of the SSC was obtained in presence of UV.
To expand the working voltage of the SSC, an asymmetric solid-state SC (ASC) was fabricated composed of ZnCo2O4/H: ZnO NRs as positive electrode and activated carbon (AC) as negative electrode. The working voltage of the ASC is increased from 0.6 to 1.5 V, thus providing an increase in overall energy storage performance of the ASC as compared to SSC. The charge storage mechanism of the ASC was discussed in detail. For the direct practical implementation of the ASC, a PD was fabricated based on ZnCo2O4/H: ZnO NRs as photosensitive material and connected in series configuration with the ASC. As-fabricated ASC can easily offer desired power to the ZnCo2O4/H: ZnO NRs PD during the conversion of optical to electrical signal. Increase in the photo response of the PD was observed in presence of UV illumination.
For further expansion of the working voltage of ASC, three ASCs were connected internally in series to form solid-state asymmetric tandem SC (ATSC). The electrochemical response of the ATSC electrodes composed of hybrid reduced graphene oxide (rGO)-carbon nanotubes (CNTs)-ZnCo2O4 (rGO-CNTs-ZnCo2O4) as positive and rGO-CNTs-iron (III) oxide (rGO-CNTs- Fe2O3) negative electrodes were performed systematically. The efficient energy storage performance of the ATSC is due to the synergistic contribution of each of individual nanomaterials in the hybrid electrodes. The working voltage of the ATSC was measured to be 4.5 V which is three times larger than ASC. As a result, a significant increase in energy density (61%) and power density (33%) was noticed as compared to ASC. Moreover, the electrochemical measurement of the ATSC was also studied at different mechanical bending deformation angles ranging from 0 to 60o at a working voltage of 4.5 V. Interestingly, no significant deviation in electrochemical response was observed under the mechanical deformations of the ATSC. In addition, the energy storage performance of the ATSC was measured at different working voltage ranging from 1.5 to 4.5 V. With increase in the working voltage, the energy storage performances (energy density and power density) of the ATSC increase following a linear function. In addition, for the direct practical application, ZnCo2O4/H: ZnO NRs PD was driven by the ATSC used as a power source for the detection of UV light.
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Shabanian, Samira. "Bidirectional Helmholtz Machines." Thèse, 2016. http://hdl.handle.net/1866/16181.
Full textAbstract:
L'entraînement sans surveillance efficace et inférence dans les modèles génératifs profonds reste un problème difficile. Une approche assez simple, la machine de Helmholtz, consiste à entraîner du haut vers le bas un modèle génératif dirigé qui sera utilisé plus tard pour l'inférence approximative. Des résultats récents suggèrent que de meilleurs modèles génératifs peuvent être obtenus par de meilleures procédures d'inférence approximatives. Au lieu d'améliorer la procédure d'inférence, nous proposons ici un nouveau modèle, la machine de Helmholtz bidirectionnelle, qui garantit qu'on peut calculer efficacement les distributions de haut-vers-bas et de bas-vers-haut. Nous y parvenons en interprétant à les modèles haut-vers-bas et bas-vers-haut en tant que distributions d'inférence approximative, puis ensuite en définissant la distribution du modèle comme étant la moyenne géométrique de ces deux distributions. Nous dérivons une borne inférieure pour la vraisemblance de ce modèle, et nous démontrons que l'optimisation de cette borne se comporte en régulisateur. Ce régularisateur sera tel que la distance de Bhattacharyya sera minisée entre les distributions approximatives haut-vers-bas et bas-vers-haut. Cette approche produit des résultats de pointe en terme de modèles génératifs qui favorisent les réseaux significativement plus profonds. Elle permet aussi une inférence approximative amérliorée par plusieurs ordres de grandeur. De plus, nous introduisons un modèle génératif profond basé sur les modèles BiHM pour l'entraînement semi-supervisé.Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximate inference procedures. Instead of improving the inference procedure, we here propose a new model, the bidirectional Helmholtz machine, which guarantees that the top-down and bottom-up distributions can efficiently invert each other. We achieve this by interpreting both the top-down and the bottom-up directed models as approximate inference distributions and by defining the model distribution to be the geometric mean of these two. We present a lower-bound for the likelihood of this model and we show that optimizing this bound regularizes the model so that the Bhattacharyya distance between the bottom-up and top-down approximate distributions is minimized. This approach results in state of the art generative models which prefer significantly deeper architectures while it allows for orders of magnitude more efficient approximate inference. Moreover, we introduce a deep generative model for semi-supervised learning problems based on BiHM models.
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Karakoc, Kerem. "Modeling and design optimization of electromechanical brake actuator using eddy currents." Thesis, 2012. http://hdl.handle.net/1828/4289.
Full textAbstract:
A novel electromechanical brake (EMB) based on the eddy current principle is proposed for application in electrical vehicles. The proposed solution is a feasible replacement for the current conventional hydraulic brake (CHB) systems. Unlike CHBs eddy current brakes (ECBs) use eddy currents and their interaction with an externally applied magnetic field to generate braking torque. Due to their pure electrically controllable and contact free nature, ECBs have multiple advantages over the current CHB systems, such as faster response, reduced weight and number of components, ease of implementing various controllers (e.g., anti-lock braking), and reduced noise levels. However, the torque generated by a typical ECB at low speeds is insufficient to effectively and completely stop a moving vehicle. Therefore, an ECB is commonly used as an assistive brake to the CHB system in heavy vehicles, i.e. trains and trucks In order to overcome this shortcoming, the use of AC magnetic fields is proposed to realize a stand-alone ECB system in which sufficient braking torque can be generated at low speeds. To this end, eddy currents are modeled analytically using the governing Maxwell’s equations with the consideration of time varying field application. The analytical model was validated using finite element analysis. Results show that the braking torque increases with the application of a time varying field.
Various forms of time varying fields have been studied. It was found that the
frequency-modulated applied field in triangular waveform results in the highest braking torque. Next, the design was optimized to maximize the braking torque and an optimum configuration was obtained using multiple pole projection areas (PPAs). Optimization results show that the braking torque significantly increases with the introduction of additional PPAs to the configuration, and the braking torque generation for an optimum four-PPA ECB configuration exceeds the braking requirements for current passenger
vehicles.
For control purposes, a dynamic model for a novel stand-alone ECB system using AC fields for automotive applications has been successfully designed and evaluated. Also, a model-based predictive controller has been developed for the optimum ECB
configuration. Finally an experimental test-bed has been designed for experimentation of both DC and AC field application on ECB.Graduate
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Rotermund, Lina M. "The effects of sea ice on the tides in the Kitikmeot Sea: results using year–long current meter data from Dease Strait and tidal models." Thesis, 2019. http://hdl.handle.net/1828/11020.
Full textAbstract:
We examine the tides in the Kitikmeot Sea using year-long time-series from moored instrumentation in Dease Strait, and a 3D barotropic numerical tidal model of the region. The in-situ data show strong tidal damping during wintertime seasonal sea ice cover, with a 50-60% reduction in M2 and K1 tidal elevation and 65% reduction in M2 and K1 tidal velocities at the sea ice maximum. We hypothesize the damping largely occurs in Victoria Strait, the eastern gateway of the Kitikmeot Sea, where tidal-induced ridging causes thick, rough ice to accumulate over its shallow sill. Using the numerical model, FVCOM, we independently vary sea ice friction and sea ice thickness, and show that the observed wintertime tidal damping likely requires both very rough ice and a partial sea ice blockage in the sill region.
Analysis of the model shows different dynamics and dissipation of the dominant M2 and K1 tides. Both M2 and K1 tides are dominated by the Atlantic tides entering through Victoria Strait. Arctic tides, entering from the west, have a minor, but significant, contribution to the M2 tide. Overall, the K1 tide, after 19% dissipation in Victoria Strait and 24% in adjoining bays, propagates far into the region and behaves as a Helmholtz resonator in Dease Strait and Coronation Gulf. In contrast, 92% of the M2 tidal energy does not reach Dease Strait because, in addition to dissipation in Victoria Strait (29%), it is significantly diverted into adjoining bays and around an amphidrome in eastern Queen Maud Gulf. The K1 tide, with double the wavelength of the M2 tide, is less diverted.Graduate
2020-07-22
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Koch, Philipp. "Partikelmodellierung der Strukturbildung akustischer Kavitationsblasen in Wechselwirkung mit dem Schalldruckfeld." Doctoral thesis, 2006. http://www.gbv.de/dms/goettingen/524828539.pdf.
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Tylla, Alfred. "Erste Erfahrungen mit der Micro-Diagonalpumpe Deltastream® der Firma Medos (Helmholtz Institut Aachen) als linksventrikulärem Herzunterstützungssystem (LVAD) mit pulsatiler und laminarer Perfusion am Schafsmodell über sieben Tage." Doctoral thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-0006-B2B0-A.
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ARRIGHETTI, Walter. "Mathematical models and methods for Electromagnetism on fractal geometries." Doctoral thesis, 2007. http://hdl.handle.net/11573/1656600.
Full textAbstract:
This work summarizes the research path done by Walter Arrighetti during his three years of Doctorate of Research in Electromagnetism at Università degli Studi di Roma “La Sapienza,” Rome, under the guidance of Professor Giorgio Gerosa. This work was mainly motivated by the struggle to find simpler and simpler models to introduce complex geometries (like fractal ones, for example, which are complicated but far from being ‘irregular’) in physical field theories like the Classical Electrodynamics, and which stand at the base of most contemporary applied research activities: from antennas (of any sizes, bandwidths and operational distances) to waveguides & resonators (for devices ranging from IC motherboards , to high-speed fibre channel links), to magnetic resonance (RMI) devices (for both diagnostic and research purposes), all the way up to particle accelerators. All of these models need not only a solid physical base, but also a specifically crafted ensemble of mathematical methods, in order to tackle with problems which “standard-geometry” models (both in the continuum and the discrete cases) are not best-suited for. During his previous years of study towards the Laurea degree in Electronic Engineering, the author used different approaches toward Fractal Electrodynamics, form purely-analytical, to computer-assisted numerical simulations of applied electromagnetic structures (both radiating and wave-guiding), down to algebraic-topological ones. The latter approaches, more often than not, proved to be the best way to start with, because the author found out that self-similarity (a property which many complicated geometries —even non-fractal ones— seem to, at least, tend to possess) can be easily interpreted as a topological symmetry, wonderfully described using “ad hoc” nontrivial algebraic languages. Whatever can be successfully described in the language of Algebra (either via numbers, symmetry groups, graphs, polynomials, etc.) is then always simplified (or “quotiented” — so to speak in a more strict mathematical language) and, when numerical computation takes the way towards the solution of a specific applied problem, those simplifications turn in handy to reduce the complexity of it. For example, the strict self-similarity possessed by some fractals (like those generated via an Iterated Function System — or IFS) allows to numerically store the geometrical data for a fractal object in a sequence of simpler and simpler data which are, for example, instantly recovered by a computer starting from the simplest data (like simplices, squares/cubes, circles/spheres and regular polygons/polytopes). For the same reason, all the physical properties that depend on the geometry (or the topology — i.e. basically the number of “holes” or inner connections) of the domain can be reduced, estimated or be even completely known a priori, even before a numerical simulation is performed. In this work, several of these methods (coming from apparently different branches of pure and applied Mathematics) are presented and finally joined with Electromagnetism equations to solve some more or less applied problems. Since many of the mathematical tools used to build the studied models and methods are advanced and generally not sufficiently known to experts in either such different fields, the first two Chapters are devoted to a brief introduction of some purely mathematical topics. In that context, the author found that the best way to accomplish this was to re-write all those different results from different branches of both pure and applied Mathematics in a formalism as more solid and unified as possible, with continuous links back and forth to different topics (and to the next more applied Chapters). That approach is seldom found in most graduate-level texts. For example, very similar mathematical objects may be even called or classified in different ways, according to the different mathematical contexts they are introduced in, which is exactly the opposite philosophy which has guided underneath in writing these first Chapters. On the other end, simpler and more trivial mathematical definitions, formalisms or electromagnetic problems, when not elsewhere referenced to, can be found in [9], Arrighetti W., Analisi di Strutture Elettromagnetiche Frattali, the author’s Laurea degree dissertation (currently only in Italian language). The most original part of the work is in the last three Chapters where —always using the same “language” and helping with cross-links, as well as to the Bibliography— methods are introduced and then applied to model some electromagnetic problems (previously either unsolved — or already-known, but here solved with a different, usually simpler, or at least more elegant approach).
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Tsuji, Paul Hikaru. "Fast algorithms for frequency domain wave propagation." 2012. http://hdl.handle.net/2152/19533.
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High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of
metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime.
The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time.text