Dissertations / Theses on the topic 'Spectral Fourier Method'

As computer hardware has evolved, the time required to perform numerical simulations has reduced, allowing investigations of a wide range of new problems. This thesis focuses on algorithm optimization, to minimize run-time, when solving the incompressible Navier-Stokes equations. Aspects affecting performance related to the discretisation and algorithm parallelization are investigated in the context of high-order methods. The roles played by numerical approximations and computational strategies are highlighted and it is recognized that a versatile implementation provides additional benefits, allowing an ad-hoc selection of techniques to fit the needs of heterogeneous computing environments. We initially describe the building blocks of a spectral/hp element and pure spectral method and how they can be encapsulated and combined to create a 3D discretisation, the Fourier spectral/hp element method. Time-stepping strategies are also described and encapsulated in a flexible framework based on the General Linear Method. After implementing and validating an incompressible Navier-Stokes solver, two canonical turbulent flows are analyzed. Afterward a 2D hyperbolic equation is considered to investigate the efficiency of low- and high-order methods when discretising the spatial and temporal derivatives. We perform parametric studies, monitoring accuracy and CPU-time for different numerical approximations. We identify optimal discretisations, demonstrating that high-order methods are the computationally fastest approach to attain a desired accuracy for this problem. Following the same philosophy, we investigate the benefits of using a hybrid parallel implementation. The message passing model is introduced to parallelize different kernels of an incompressible Navier-Stokes solver. Monitoring the parallel performance of these strategies the most efficient approach is highlighted. We also demonstrate that hybrid parallel solutions can be used to significantly extend the strong scalability limit and support greater parallelism.

Une methode de mesure par intercorrelation utilisant l'intercomparaison de trois oscillateurs deux a deux, permet de mesurer les fluctuations de phase ou de frequence des oscillateurs ultrastables. Nous presentons l'etude et la realisation d'un analyseur de spectre par correlation. Cet appareil permet d'analyser la fonction de correlation ou de calculer la densite spectrale de puissance du bruit de phase de l'oscillateur a mesurer

Abstract Cognitive Radio (CR) improves the efficiency of spectrum utilization by allowing non- licensed users to utilize bands when not occupied by licensed users. In this thesis, we address several challenges currently limiting the wide use of cognitive radios. These challenges include identification of unoccupied bands, energy consumption and other technical challenges. Improved accuracy edge detection techniques are developed for CR to mitigate both noise and estimation error variance effects. Next, a reduced complexity Simplified DFT (SDFT) is proposed for use in CR. Then, a sub-Nyquist rate A to D converter is introduced to reduce energy consumption. Finally, a novel multi-resolution PSD estimation based on expectation-maximization algorithm is introduced that can obtain a more accurate PSD within a specified sensing time.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The present work is dedicated to perform the mathematical modeling and DNS and LES simulations of a three-dimensional, temporally evolving incompressible plane wake are performed, seeking to evidence differences in stability, transition and onset of both coherent and small scale structures, when the flow is subjected to random perturbations of different amplitudes. The perturbations are generated using the Random-Flow-Generator (RFG) technique, being imposed to the flow as initial conditions. The Navier-Stokes equations are solved in a prismatic domain, with periodic boundary conditions in all directions, using Fourier pseudospectral method. The invariants of the velocity gradient tensor, Q and R, are analyzed for random perturbations with magnitudes 10−3, 10−4 and 10−5, showing the onset of their characteristic teardrop correlation map. Moreover, maps of the second and third invariants of the rate-of-strain tensor, QS and RS, are shown, in order to evidence the differences in local flow strain and topological characteristics of the dissipation of kinetic energy. Isosurface plots of Q and QW, as well as vorticity contours are shown, allowing visual identification of the coherent structures and confirming patterns predicted by the invariant maps.
O presente trabalho se dedica a modelagem matemática e a simulações numéricas DNS e LES de uma esteira tridimensional, incompressível, em desenvolvimento temporal, buscando evidenciar diferenças na estabilidade, transição e no desenvolvimento de estruturas coerentes e de pequena escala, quando o escoamento é submetido a perturbações randômicas de diferentes amplitudes. As perturbações são geradas utilizando-se a técnica Random Flow Generator (RFG), sendo sobrepostas à condição inicial do escoamento. As equações de Navier-Stokes são resolvidas em um domínio prismático, com condições de contorno periódicas em todas as direções, utilizando-se o método pseudoespectral de Fourier. Os invariantes do tensor gradiente de velocidade, Q e R, são analisados para perturbações de magnitude 10−3, 10−4 and 10−5, mostrando a formação de uma correlação no formato de gota, característica da resolução das equações de Navier-Stokes. Além disso, são apresentados mapas do segundo e terceiro invariante do tensor taxa de deformação, QS e RS, a fim de evidenciar as diferenças locais no escoamento e as características topológicas na taxa de dissipação de energia cinética. Isosuperfícies de Q e QW, bem como contornos de vorticidade são apresentados, possibilitando a identificação visual das estruturas coerentes, e confirmando os padrões de estruturas previstos pelos mapas de invariância.
Mestre em Engenharia Mecânica

FundaÃÃo de Amparo à Pesquisa do Estado do CearÃ
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Neste trabalho analisou-se a integridade mecÃnica do material compÃsito constituÃdo por uma matriz polimÃrica, resina epoxi DER 331, e por fibra de vidro tipo âEâ como agente de reforÃo. Esta anÃlise foi realizada utilizando-se o ensaio de emissÃo acÃstica, com o objetivo de correlacionar as formas de onda dos sinais com os mecanismos de falhas associados aos esforÃos de traÃÃo e flexÃo aplicados a espÃcimes fabricados com tal material. Na anÃlise dos sinais como funÃÃo do tempo foram utilizados os mÃtodos de contagem de caixas, que fornece a dimensÃo fractal, e o do intervalo re-escalado de Hurst, sendo tambÃm utilizado o mÃtodo espectral de Fourier para a anÃlise no domÃnio da freqÃÃncia. Mostrou-se que os expoentes calculados pelos mÃtodos espectral de Fourier e re-escalado de Hurst estÃo correlacionados com a dimensÃo fractal obtida pelo mÃtodo de contagem de caixa, e satisfazem as relaÃÃes previstas pelas leis de escala. Os resultados mostraram tambÃm a existÃncia de duas regiÃes de escala distintas, sendo uma caracterizada pela persistÃncia do sinal e outra por um comportamento aleatÃrio caracterÃstica do ruÃdo presente. As dimensÃes fractais obtidas apresentaram-se independentes da taxa de aquisiÃÃo da forma da onda emitida indicando a propriedade de auto-similaridade dos sinais estudados, o que confirma a sua caracterÃstica fractal. Finalmente, Ã conjecturado uma correlaÃÃo entre o coeficiente de Hurst/dimensÃo fractal e as falhas mecÃnicas observadas.
In this work it is analysed the mechanical integrity of the composite material constituted of a polymeric matrix, epoxy resin DER 331, reinforced by glass fiber type E. This analysis has been done by using the acoustic emission testing with the aim to correlating the wave-form of the pulse with the flaw mechanisms associated to the tensile and bending loads applied to the samples. The analysis of the pulses as a function of time has been made by using box counting method, which provides the fractal dimension, and the rescaled Hurst analysis. The analysis in the frequency domain has been made by using the spectral Fourier method It has been shown that the exponents obtained from the spectral Fourier method and the rescaled Hurst analysis are correlated to the box counting fractal dimension, and satisfy the known relations obtained from the scaling laws. The results have also shown the existence of two scaling regions, characterized by the persistence of the pulse and by a random behaviour, respectively. The fractal dimensions have also been shown to be independent of time acquisition of the emitted pulse, and this indication of self-similarity confirms its fractal characteristics. Finally, it is conjectured a correlation between the Hurst coefficient/fractal dimension and the mechanical flaws observed.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Modern engineering increasingly requires the comprehension of phenomena related to combustion, aeroacustics, turbulence transition, among others. For these purposes the Computational Fluids Dynamics (CFD) requires the used high order methods. One of these methods is the Fourier pseudo-spectral method, that provides an excellent numerical accuracy, and with the use of the Fast Fourier Transform algorithm (FFT), it presents a low computational cost in comparison to anothers high-order methods. Another important issue is the projection method of the pression term, which does not require the pressure computation from the Navier-Stokes equations. The procedure to calculate the pression field is usually the most onerous in classical methodologies. Nevertheless, the pseudo-spectral method can be only applied to periodic boundary flows, thus limiting its use. Aiming to solve this restriction, a new methodology is proposed at the present work, which has the objective of simulating nonperiodic flows using the Fourier pseudo-spectral method. For this purpose the immersed boundary method, that represents the boundary conditions through a force field imposed at Navier-Stokes equations is used. As a test to this new methodology, a classic problem of Computational Fluid Dynamics, The Lid Driven Cavity was simulated. The obtained results are promising and demonstrate the possibility to simulating non-periodic flows making use of the Fourier pseudo-spectral method.
Para compreender fenômenos relacionados à combustão, aeroacústica, transição a turbulência entre outros, a Dinâmica de Fluídos Computacional (CFD) utiliza os métodos de alta ordem. Um dos mais conhecidos é o método pseudo-espectral de Fourier, o qual alia: alta ordem de precisão na resolução das equações, com um baixo custo computacional. Este está ligado à utilização da FFT e do método da projeção do termo da pressão, o qual desvincula os cálculos da pressão da resolução das equações de Navier-Stokes. O procedimento de calcular o campo de pressão, normalmente é o mais oneroso nas metodologias convencionais. Apesar destas vantagens, o método pseudo-espectral de Fourier só pode ser utilizado para resolver problemas com condições de contorno periódicas, limitando o seu uso no campo da dinâmica de fluídos. Visando resolver essa restrição uma nova metodologia é proposta no presente trabalho, que tem como objetivo simular escoamentos não-periódicos utilizando o método pseudo-espectral de Fourier. Para isso, é utilizada a metodologia da Fronteira Imersa, a qual representa as condições de contorno de um escoamento através de um campo de força imposto nas equações de Navier-Stokes. Como teste, para essa nova metodologia, foi simulada uma cavidade com tampa deslizante (Lid Driven Cavity), problema clássico da mecânica de fluídos, que objetiva validar novas metodologias e códigos computacionais. Os resultados obtidos são promissores e demostram que é possível simular um escoamento não-periódico com o método pseudo-espectral de Fourier.
Mestre em Engenharia Mecânica

La description magnétohydrodynamique est utilisée pour étudier les plasmas de fusion par confinement magnétique dans deux configurations: tokamak et reversed field pinch. Une méthode de Fourier pseudo-spectrale et une technique de pénalisation en volume sont employées pour résoudre les équations. La méthode de pénalisation permet d'introduire des conditions aux limites de Dirichlet et donc de faire varier facilement la géométrie considérée. Les simulations dans des géométries toroïdales de type tokamak montrent l'apparition spontanée de vitesses. Une importante composante toroïdale se développe si le système est peu dissipatif. Il est aussi montré que la brisure de symétrie dans la forme de la section du tore fait apparaitre un moment angulaire toroïdal. Pour le Reversed Field Pinch on montre l'émergence de structures hélicoïdales. La forme de ces structures varie en fonction des coefficients de transport ainsi que du paramètre de pincement du champ magnétique imposé. Pour compléter l'étude on compare les résultats du tore aux calculs dans un cylindre périodique. Les différences dans la dynamique des deux cas sont mises en avant. Finalement les simulations sont confrontées à des expériences et un meilleur accord est observé entre simulation et expérience pour la géométrie toroïdale que pour la géométrie cylindrique.

This document introduces a brand new method of the 1D, 2D and 3D decomposition with the use of local Fourier basis, its implementation and comparison with the currently used global 1D domain decomposition. The new method was designed, implemented and tested primarily for future use in the simulation software called The k-Wave toolbox, but it can be applied in many other spectral methods. Compared to the global 1D domain decomposition, the Local Fourier decomposition is up to 3 times faster and more efficient thanks to lower inter-process communication, however it is a little inaccurate. The final part of the thesis discusses the limitations of the new method and also introduces best practices to use 3D Local Fourier decomposition to achieve both more speed and accuracy.

Etude d'un algorithme pour le traitement d'un signal. Cet algorithme est composé de différents programmes indépendants permettant le calcul des polynômes orthonormaux, le calcul récursif, le calcul de la transformée de Fourier, de densité spectrale, réponse impulsionnelle d'un filtre numérique. Application à la reconnaissance des formes et simulation du processus de Lévy

Ziel der vorliegenden Arbeit ist es, Rühr- und Mischungsvorgänge in Flüssigmetallströmungen zu untersuchen, die mittels rotierender und wandernder Magnetfelder bzw. deren Kombination induziert werden. Im Mittelpunkt steht dabei die Charakterisierung der dreidimensionalen Strömungsstrukturen innerhalb zylindrischer Geometrien bei der Verwendung überkritischer Magnetfelder. Neben der Untersuchung der Strömungseigenschaften stellen die physikalische Modellierung der angreifenden Kräfte, die geeignete Wahl und Validierung eines effizienten numerischen Lösungsverfahrens und dessen Erweiterung für die Durchführung von Large Eddy Simulationen wesentliche Eckpfeiler dieser Arbeit dar.

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CNPq
Neste trabalho deduzimos o sistema de Equações de Águas Rasas na forma Lagrangeana e obtemos a sua solução analítica. Aplicamos o Método Espectral na análise numérica deste sistema e mostramos que a propagação de ondas de águas rasas não depende do meio em que ela se propaga.
In this work we deduce the system of Shallow Water Equations in the Lagrangian form and we obtain its analytical solution. We have applied the spectral method in the numerical analysis of this system and we have shown that the propagation of the shallow water waves doesn't depend on the medium in which it spreads.

Une methode de type domaine fictif est proposee pour la resolution d'equations aux derivees partielles dans des geometries complexes. Elle est basee sur une decomposition du probleme de depart en un probleme periodique, pose sur un domaine fictif (cartesien) et resolu par une methode spectrale fourier, et en un probleme homogene resolu par elements de frontiere. Cette methode est en particulier appliquee a l'equation d'advection-diffusion et aux equations de navier-stokes incompressible. Differents tests sont menes pour evaluer ses capacites, ainsi que ses proprietes de precision et de stabilite. La resolution des equations de navier-stokes est envisagee en formulations tourbillon-fonction de courant et vitesse-pression. Elle est fondee sur des algorithmes de determination directe du tourbillon ou de la pression sur le bord. L'approche est validee en considerant des problemes classiques de la mecanique des fluides. Enfin, on presente une approche asymptotique permettant de traiter ces meme problemes de maniere tres efficace.

The Spectral and Photometric Imaging Receiver (SPIRE) is one of three scientific instruments on the European Space Agency's (ESA's) Herschel Space Observatory (HSO). The medium resolution spectroscopic capabilities of SPIRE are provided by an imaging Fourier transform spectrometer (IFTS). A software simulator of the SPIRE IFTS was written to generate realistic data products, making use of available qualification and test data. We present the design and implementation of the simulator. Component and end-to-end simulations were compared to results from the first SPIRE instrument proto-flight model (PFMI) test campaign conducted at the Rutherford Appleton Laboratory (RAL) in Oxford, England in 2005. Final characterization of the simulator involved the determination of astronomical quantities from the synthetic data products of a simple molecular cloud.
xix, 213 leaves : ill. (some col.) ; 29 cm.

Dans ce travail de thèse, un spectromètre FT-Raman a été développé dans l'intention de mesurer les substances dangereuses de manière propre et durable permettant à l'utilisateur un cout d'utilisation réduit (approche low cost). Dans ce but, le système FT- Raman a été développé en utilisant une combinaison originale de composants conventionnels d'optoméchatronique avec laquelle nous proposons une méthode d'évaluation du spectre. Ce système FT-Raman proposé n'inclut aucun composants spécialisé coûteux et permet la détection de la diffusion Raman et le suivi du chemin optique. Le dispositif a été testé lors d'analyses d'une série de composants chimiques standards largement utilisés dans la spectroscopie Raman (certains d'entre eux sont connus pour leur impact négatif sur la santé et l'environnement). Les résultats du spectre obtenus avec notre dispositif ont confirmé les valeurs signalées par le spectre Raman standard. Une comparaison des spectres avec des appareils commercialisés mesurant le FT-Raman a été également faite, et les résultats indiquent que notre combinaison de composants conventionnels et l'application de notre méthode d'évaluation peuvent être utilisées dans certaines surveillances d'applications demandant un haut degré de précision et la résolution sans toutefois présenter la charge financière que l'achat d'un instrument classique de mesure pourrait représenter
In this doctoral research project, a Fourier Trasform Raman spectrometer (FT-Raman spectrometer) instrument has been developed with the intention to perform the monitoring of certain materials having a contaminating and harmful nature, in a clean and sustainable manner, and without significantly affecting the financial aspect of the user (low-cost approach). For this purpose, the proposed FT-Raman system has been developed by using an original combination of conventional hardware (optomechatronics) parts and a method that we propose for spectral evaluations. In this FT-Raman system that we propose no specialized and costly hardware parts for optical path compensation, Raman scattering detection, optical path tracking, etc. have been used. The proposed FT-Raman device has been tested by analyzing a series of chemical components widely used in Raman spectroscopy as standard reference materials (some of them are also known due to their negative impact on health or on environment). The resulting spectra obtained using our proposed device have greatly agreed with the values of the standard Raman spectra. A comparison with spectral outputs from state-of-the-art FT-Raman devices has been also performed. These results indicate that our ``flexible" combination of conventional hardware parts and the applied evaluation method that we propose can be used in certain monitoring applications requiring a high degree of frequency accuracy and spectral resolution, without having the burden of a considerable expenditure that such a non-dispersive "classical" instrument might represent

Etude d'un profilometre optique base sur la defocalisation d'un faisceau de lumiere blanche. Etude de deux dispositifs optonumeriques d'analyse statistique utilisant les techniques de fourier optiques: un analyseur de particules et un dispositif de classement automatique des surfaces non polies

A prestudy indicated superior accuracy and convergence properties of apseudo-spectral method compared to a spline-based method implemented byCòrdoba et al. in 2005 when solving the α-patches problem. In this thesis wefurther investigate the numerical properties of the pseudo-spectral method and makeit more robust by implementing the Nonequispaced Fast Fourier Transform. Wepresent a more detailed overview and analysis of the pseudo-spectral method and theα-patches problem in general and conclude that the pseudo-spectral method issuperior in regards to accuracy in periodic settings.

La mesure du débit sanguin tissulaire par effet doppler optique est une idée séduisante. L'utilisation d'une source laser, par la cohérence spatiale et géométrique qu'elle offre, en simplifie la réalisation pratique. La vitesse des différentes composantes, notamment les hématies, n'est pas uniforme. Il en résulte donc une distribution spectrale image de cette répartition. De plus, l'environnement du faisceau laser étant constitué par de la matière vivante, de nombreux paramètres influencent les résultats. Dans un premier temps, nous décrivons l'évolution des doppler-lasers, et nous exposons les problèmes qu'ils soulèvent. Ceci nous amène à considérer ensuite, que seule une étude fine du spectre peut nous conduire à un appareil fiable et réellement utilisable en routine. Nous présentons ici un doppler-laser à traitement numérique. La distribution spectrale est calculée par un processeur de signaux numérique (dsp) grâce à un algorithme de transformée de Fourier rapide. Nous donnons les paramètres caractéristiques qui nous paraissent optimaux, et relevons les difficultés qui subsistent avant de pouvoir réaliser un système performant

Le gliome est le type le plus agressif et mortel de tumeur cérébrale. Ces tumeurs se caractérisent par la présence conjointe de phénotypes solides (de bas grade, moins invasif, hautement vascularisé) et diffus (haut grade, très envahissant et diffus) des glioblastomes multiformes. Les collagènes sont des composants majeurs de la MEC des cellules tumorales des gliomes, et sont également présents dans la membrane basale des vaisseaux sanguins, mais avec une composition différente entre vasculatures saine et tumorale. L'abondance et la typologie des collagènes dans la MEC des cellules tumorales et la vasculature représentent donc un marqueur potentiel de diagnostic pour la gradation des tumeurs gliales. Nous avons développé la spectro-imagerie infrarouge à transformée de Fourier pour déterminer les modifications morphologiques et moléculaires apparaissant dans les formes solides et diffuses de gliomes, ainsi que dans les vasculatures saine et tumorale. Nous avons d'abord mis en évidence les vasculatures saine et tumorale en utilisant des nanoparticules injectées dans le système sanguin. Ensuite, nous avons appliqué des méthodes de reconstruction spectrale pour distinguer les tissus sains vs. ceux des formes solide et diffuse de tumeurs sur la base de leurs contenus en collagène de la MEC. Enfin, nous avons déterminé les changements de types du collagène au cours de la progression tumorale, validant ainsi la notion que l’analyse de ces contenus est potentiellement un marqueur diagnostic pour la gradation des gliomes
The glioma is the most aggressive and lethal type of brain tumor. Such tumor is characterized both by solid (low grade, less invasive, highly vascularized) and diffuse (high grade, very invasive and diffuse) phenotypes in high-grades. Collagens are major components of ECM in glioma tumor cells, and are also present in basement membrane of blood vessels in vasculature, but with different composition between healthy and tumor capillaries. The abundance and typology of collagens in tumor cell ECM and vasculature is thus a potential diagnostic marker for grading glioma tumors. We developed Fourier transform infrared (FTIR) spectro-imaging as a functional technique to determine the morphological and molecular changes occurring in solid and diffuse form of tumor tissues as well as in healthy and tumor vasculatures. We first highlighted healthy and tumor vasculatures using nanoparticles injected in blood system. Then, we applied curve-fitting methods to distinguish between healthy tissue vs. solid and diffuse tumor tissues on the basis of the collagen contents found in ECM. Finally, we determined collagen typology changes during tumor progression, thus validating that collagen contents analysis is potentially a diagnostic marker for glioma grading

This thesis presents new numerical methods for solving differential equations with periodicity. Spectral methods for solving linear and nonlinear ODEs, linear ODE eigenvalue problems and linear time-dependent PDEs on a periodic interval are reviewed, and a novel approach for computing multiplication matrices is presented. Choreographies, periodic solutions of the n-body problem that share a common orbit, are computed for the first time to high accuracy using an algorithm based on approximation by trigonometric polynomials and optimization techniques with exact gradient and exact Hessian matrix. New choreographies in spaces of constant curvature are found. Exponential integrators for solving periodic semilinear stiff PDEs in 1D, 2D and 3D periodic domains are reviewed, and 30 exponential integrators are compared on 11 PDEs. It is shown that the complicated fifth-, sixth- and seventh-order methods do not really outperform one of the simplest exponential integrators, the fourth-order ETDRK4 scheme of Cox and Matthews. Finally, algorithms for solving semilinear stiff PDEs on the sphere with spectral accuracy in space and fourth-order accuracy in time are proposed. These are based on a new variant of the double Fourier sphere method in coefficient space and standard implicit-explicit time-stepping schemes. A comparison is made against exponential integrators and it is found that implicit-explicit schemes perform better. The algorithms described in each chapter of this thesis have been implemented in MATLAB and made available as part of Chebfun.

La mécanique des fluides numérique a permis d'optimiser de nombreux systèmes dont, notamment, les moteurs d'avions. Dans l'industrie aéronautique, les calculs numériques d'écoulements sont principalement limités à des approches stationnaires de par le coût prohibitif des simulations instationnaires. Néanmoins, les écoulements qui se développent dans les machines tournantes, à savoir les principaux composants d'un moteur d'avion, sont majoritairement périodiques en temps. En partant de cette hypothèse de périodicité temporelle, des approches dites spectrales en temps ont vus le jour il y a plus de quinze ans. Elles restent principalement limitées à des écoulements mono-fréquentiels, à savoir composés d'une seule fréquence de base et de ses harmoniques. Récemment, une méthode d'équilibrage harmonique multi-fréquentielle a été développée et implémentée dans le code de calcul elsA, élargissant le champ des applications possibles. En particulier, l'étude de l'aéroélasticité des machines tournantes multi-étagées devient alors envisageable.Cette thèse se propose d'appliquer la méthode d'équilibrage harmonique multi-fréquentielle pour étudier l'aéroélasticité d'une configuration nouvelle de moteur d'avion: les doublets d'hélices contra-rotatives. La méthode est tout d'abord validée analytiquement et numériquement sur des cas tests linéaires et non-linéaires avec succès. Deux problèmes sont soulevés pour l'utilisation d'une telle méthode sur des configurations aéroélastiques arbitraires: le conditionnement du terme source et la convergence de la méthode. Des approches originales ont été développées afin d'améliorer le conditionnement et de fournir une estimation a priori du nombre d'harmoniques nécessaire pour obtenir un certain niveau de convergence. La méthode d'équilibrage harmonique est ensuite validée sur un cas standard d'aéroélasticité des machines tournantes et montre des résultats très proches de ceux expérimentaux. L'applicabilité de la méthode est finalement démontrée pour la simulation de l'aéroélasticité des doublets d'hélices contra-rotatives
Computational Fluid Dynamics (CFD) has allowed the optimization of many configurations among which aircraft engines. In the aeronautical industry, CFD is mostly restricted to steady approaches due to the high computational cost of unsteady simulations. Nevertheless, the flow field across the rotating parts of aircraft engines, namely turbomachinery blades, is essentially periodic in time. Years ago, Fourier-based time methods have been developed to take advantage of this time periodicity. However, they are, for the most part, restricted to mono-frequential flow fields. This means that only a single base-frequency and its harmonics can be considered. Recently, a multi-frequential Fourier-based time method, namely the multi-frequential Harmonic Balance (HB), has been developed and implemented into the elsA CFD code, enabling new kinds of applications as, for instance, the aeroelasticity of multi-stage turbomachinery.The present PhD thesis aims at applying the HB approach to the aeroelasticity of a new type of aircraft engine: the contra-rotating open rotor. The method is first validated on analytical, linear and non-linear numerical test problems. Two issues are raised, which prevent the use of such an approach on arbitrary aeroelastic configurations: the conditioning of the multi-frequential HB source term and the convergence of the method. Original methodologies are developed to improve the condition number of the simulations and to provide a priori estimates of the number of harmonics required to achieve a given convergence level. The HB method is then validated on a standard configuration for turbomachinery aeroelasticity. The results are shown to be in fair agreement with the experimental data. The applicability of the method is finally demonstrated for aeroelastic simulations of contra-rotating open rotors

Les travaux présentés dans ce manuscrit sont consacrés à l’étude des effets des collisions dans les spectres infrarouges de CH₃I qui est une source importante de l’iode qui est un catalyseur de la destruction d’ozone. Une bonne modélisation de son spectre d’absorption est donc essentielle pour les mesures de concentration atmosphérique. Dans les bases de données internationales, la bande ν6 n’est pas mentionnée en raison du manque de paramètres spectroscopiques. Étant très intense et localisée dans la fenêtre atmosphérique de 11 μm, la bande ν6, pourrait servir à une future détection IR de CH₃I, par des instruments sondant dans l’IR, comme l’instrument IASI-NG en cours de préparation. Mais auparavant, il est nécessaire de fournir les paramètres spectroscopiques de CH₃I, grâce à la spectroscopie de laboratoire. C’est dans ce contexte que notre travail s’est inscrit. Le manuscrit comporte cinq parties. La première partie concerne les propriétés spectroscopiques de la molécule CH₃I. La deuxième partie est dédiée à l’appareillage, avec la description du spectromètre IRTF Bruker IFS125HR. Dans la troisième partie, nous exposons les résultats des intensités et des auto-élargissements de raies qui sont extrait à partir des spectres enregistré. La quatrième partie présente les résultats obtenus sur les coefficients d’élargissement et le déplacement collisionnel par N₂ et O₂. La dernier partie est consacrée à l’interprétation des mesures des élargissements collisionnels, obtenus précédemment à l’aide des calculs théoriques. La dépendance de ces paramètres en fonction des nombres quantiques J et K a été étudiée
The work presented in this manuscript is devoted to the study of the effects of collisions in the infrared spectra of CH₃I, which is an important source of iodine, which is a catalyst for ozone destruction. Good modelling of its absorption spectrum is therefore essential for atmospheric concentration measurements. In international databases, the band ν6 is not mentioned due to the lack of spectroscopic parameters. Being very intense and localized in the atmospheric window of 11 μm, the ν6 band could be used for future IR detection of CH₃I, by instruments probing in the IR, such as the IASI-NG instrument under preparation. But first, it is necessary to provide the spectroscopic parameters of CH₃I, using laboratory spectroscopy. It is in this context that our work has been carried out. The manuscript consists of five parts. The first part concerns the spectroscopic properties of the CH3I molecule. The second part is dedicated to the apparatus, with a description of the Bruker IFS125HR FTIR spectrometer. In the third part, we present the results of the line intensities and self-broadening coefficients that are extracted from the recorded spectra. The fourth part presents the results obtained on N₂, O₂ broadening and shift coefficients. The last part is devoted to the interpretation of the collisional widening measurements, previously obtained using theoretical calculations. The dependence of these parameters on the quantum numbers J and K has been studied

Wave propagation is a phenomenon resulting from high transient loadings where the duration of the load is in µ seconds range. In aerospace and space craft industries it is important to gain knowledge about the high frequency characteristics as it aids in structural health monitoring, wave transmission/attenuation for vibration and noise level reduction. The wave propagation problem can be approached by the conventional Finite Element Method(FEM); but at higher frequencies, the wavelengths being small, the size of the finite element is reduced to capture the response behavior accurately and thus increasing the number of equations to be solved, leading to high computational costs. On the other hand such problems are handled in the frequency domain using Fourier transforms and one such method is the Spectral Finite Element Method(SFEM). This method is introduced first by Doyle ,for isotropic case and later popularized in developing specific purpose elements for structural diagnostics for inhomogeneous materials, by Gopalakrishnan. The general approach in this method is that the partial differential wave equations are reduced to a set of ordinary differential equations(ODEs) by transforming these equations to another space(transformed domain, say Fourier domain). The reduced ODEs are usually solved exactly, the solution of which gives the dynamic shape functions. The interpolating functions used here are exact solution of the governing differential equations and hence, the exact elemental dynamic stiffness matrix is derived. Thus, in the absence of any discontinuities, one element is sufficient to model 1-D waveguide of any length. This elemental stiffness matrix can be assembled to obtain the global matrix as in FEM, but in the transformed space. Thus after obtaining the solution, the original domain responses are obtained using the inverse transform. Both the above mentioned manuscripts present the Fourier transform based spectral finite element (FSFE), which has the inherent aliasing problem that is persistent in the application of the Fourier series/Fourier transforms. This is alleviated by using an additional throw-off element and/or introducing slight damping in to the system. More recently wave let transform based spectral finite element(WSFE) has been formulated which alleviated the aliasing problem; but has a limitation in obtaining the frequency characteristics, like the group speeds are accurate only up-to certain fraction of the Nyquist(central frequency). Currently in this thesis Laplace transform based spectral finite elements(LSFE) are developed for sandwich members. The advantages and limitations of the use of different transforms in the spectral finite element framework is presented in detail in Chapter-1. Sandwich structures are used in the space craft industry due to higher stiffness to weight ratio. Many issues considered in the design and analysis of sandwich structures are discussed in the well known books(by Zenkert, Beitzer). Typically the main load bearing structures are modeled as beam sand plates. Plate structures with kh<1 is analysed based on the Kirch off plate theory/Classical Plate Theory(CPT) and when the bending wavelength is small compared to the plate thickness, the effect of shear deformation and rotary inertia needs to be included where, k is the wave number and h is the thickness of the plate. Many works regarding the wave propagation in sandwich structures has been published in the past literature for wave propagation in infinite sandwich structure and giving the complete description of dispersion relation with no restriction on frequency and wavelength. More recently exact analytical solution or simply supported sandwich plate has been derived. Also it is seen by comparison of dispersion curves obtained with exact (3D formulation of theory of elasticity) and simplified theories (2D formulation as generalization of Timoshenko theory) made on infinite domain and concluded that the simplified theory can be reliably used to assess the waveguide properties of sandwich plate in the frequency range of interest. In order to approach the problems with finite domain and their implementation in the use of general purpose code; finite degrees of freedom is enforced. The concept of displacement based theories provides the flexibility in assuming different kinematic deformations to approach these problems. Many of the displacement based theories incorporate the Equivalent Single Layer(ESL) approach and these can capture the global behavior with relative ease. Chapter-2 presents the Laplace spectral finite element for thick beams based on the First order Shear Deformation Theory (FSDT). Here the effect of different choices of the real part of the Laplace variable is demonstrated. It is shown that the real part of the Laplace variable acts as a numerical damping factor. The spectrum and dispersion relations are obtained and the use of these relations are demonstrated by an example. Here, for sandwich members based on FSDT, an appropriate choice of the correction factor ,which arises due to the inconsistency between the kinematic hypothesis and the desired accuracy is presented. Finally the response obtained by the use of the element is validated with experimental results. For high shock loading cases, the core flexibility induces local effects which are very predominant and this can lead to debonding of face sheets. The ESL theories mentioned above cannot capture these effects due to the computation of equivalent through the thickness section properties. Thus, higher order theories such as the layer-wise theories are required to capture the local behaviour. One such theory for sandwich panels is the Higher order Sandwich Plate theory (HSaPT). Here, the in-plane stress in the core has been neglected; but gives a good approximation for sandwich construction with soft cores. Including the axial inertial terms of the core will not yield constant shear stress distribution through the height of the core and hence more recently the Extended Higher order Sandwich Plate theory (EHSaPT) is proposed. The LSFE based on this theory has been formulated and is presented in Chapter-4. Detailed 3D orthotropic properties of typical sandwich construction is considered and the core compressibility effect of local behavior due to high shock loading is clearly brought out. As detailed local behavior is sought the degrees of freedom per element is high and the specific need for such theory as compared with the ESL theories is discussed. Chapter-4 presents the spectral finite element for plates based on FSDT. Here, multi-transform method is used to solve the partial differential equations of the plate. The effect of shear deformation is brought out in the spectrum and dispersion relations plots. Response results obtained by the formulated element is compared and validated with many different experimental results. Generally structures are built-up by connecting many different sub-structures. These connecting members, called joints play a very important role in the wave transmission/attenuation. Usually these joints are modeled as rigid joints; but in reality these are flexible and exhibits non-linear characteristics and offer high damping to the energy flow in the connected structures. Chapter-5 presents the attenuation and transmission of wave energy using the power flow approach for rigid joints for different configurations. Later, flexible spectral joint model is developed and the transmission/attenuation across the flexible joints is studied. The thesis ends with conclusion and highlighting futures cope based on the developments reported in this thesis.

For some alloys martensitic transformation is responsible for the so-called shape memory effect and pseudoelasticity. These properties are used in a wide range of industry applications. Each of these materials is transformed to the shape it was manufactured in when heated to its critical temperature (austenite phase) no matter how seriously it was deformed at lower temperatures (martensite phase). Looking at the microstructure, one can observe significant change of crystalographic lattice depending on temperature and deformation. This the- sis focuses on modelling the evolution of microstructure during deformation for materials in the martensite phase. In this case, the creation of multiple variants of martensite is observed, divided by interfaces where a part of energy is stored. This behaviour can be described by the phase-field model. The numerical im- plementation of this model using the standard finite element method requires large computational costs. The aim of this thesis is to implement this model in MATLAB using a spectral method based on the fast Fourier transform, which is suitable for solving problems on a periodic domain. It is interesting to com- pare the computation using spectral method on a conventional PC with the computation written in FEniCS computed on a cluster. However, the...

碩士
國立中央大學
地球物理研究所
92
In this study we use TSMIP strong-motion station records to analyze the site effects of stations in taiwan.We choose earthquake events from 1998/08 to 2000/12 and restricts the earthquake parameter in depth < 50 Km and recorded station over than 100.We analyze these records in two ways:1.whole taiwan effects and 2.each TSMIP divided region.And we finally divide all TSMIP station into four groups:1.Fourier amplitude spectrum ratio larger than 1 at frequency less than 1 Hz;2.Fourier amplitude spectrum ratio larger than 1 between frequency 1hz to 10 hz;3.Fourier amplitude spectrum ratio larger than 1 at frequency larger than 10 hz;4.Fourier amplitude spectrum ratio value was approach 1 in every frequency sequence.

The spectral analysis of heart rate variability is a tool that gained more and more clinical importance in the latest years. It can be used in order to access autonomic function on the cardiovascular system through the evaluation of the different frequency bands of the HRV. So far different mathematical approaches have been used towards this aim, often with contradictory results. Therefore, the need for standardization of the methods seems more and more important. In this thesis 2 non-parametric, Fourier-based methods and two parametric based on autoregressive modeling were used in order to extract the power spectral density of patients with epilepsy. Their results were statistically compared to age matched controls. The analysis have shown that when a parametric method is used, a careful model order selection method must be used, and when this is accomplished, the power spectrum could more efficient highlight differences between controls and patients. The results between non-parametric and parametric methods were different, therefore these methods cannot be considered interchangeable. The analysis methodolgy established in this first part of the study has been used to analyse HRV signals from patients before and after deep brain stimulation.
Η φασματική ανάλυση της Μεταβλητότητας της Καρδιακής Συχνότητας (ΜΚΣ) χρησιμοποείται όλο και περισσότερο σε κλινικές μελέτες τα τελευταία χρόνια. Και αυτό γιατί μπορεί να δώσει πληροφορίες σχετικά με την λειτουργία του αυτόνομου νευρικού συστήματος πάνω στην καρδιά αναλύοντας το συχνοτικό περιεχόμενο των ΜΚΣ σημάτων σε διακριτές ζώνες συχνοτήτων. Μέχρι τώρα διαφορετικές μαθηματικές μέθοδοι έδωσαν διαφορετικά, συχνα αντικρουόμενα αποτελέσματα. Έτσι η ανάγκη λεπτομερής περιγραφής των μεθόδων φαίνεται όλο και περισσοτερο επιτακτική. Σε αυτή τη διπλωματική εργασία, δυο μη παραμετρικές μέθοδοι και δύο παραμετρικές βασισμένες σε μοντέλα αυτοπαλινδρόμησης (autoregressive modeling) εφαρμόστηκαν προκειμένου να υπολογιστεί το φάσμα ασθενών με χρόνια επιληψία. Τα αποτελέσματα συγκρίθηκαν με υγιείς εθελοντές ίδιου ηλικιακού προφίλ. Η ανάλυση έδειξε ότι όταν χρησιμοποιουνται παραμετρικές μέθοδοι, η επιλογή της τάξης του μοντέλου πρέπει να γίνεται με προσοχή και όταν αυτό γίνει, το φάσμα μπορεί να αναδείξει πιο αποτελεσματικά διαφορές μεταξύ ασθενών και υγειών εθελοντών. Τα αποτελέσματα μεταξύ παραμετρικών και μη παραμετρικών μεθόδων αποδείχθηκαν διαφορετικα, και κατά συνέπεια οι δύο αυτές κατηγορίες ανάλυσης δεν μπορούν να θεωρηθούν ίδιες. Η μεθοδολογία που αναπτύχθηκε στο πρώτο αυτό μέρος της εργασίας χρησιμοποιήθηκε για να αναλύσει σήματα ΜΚΣ από ασθενείς με Πάρκινσον πριν και μετά εν τω βάθει ερεθισμό (Deep brain simulation).

abstract: High-order methods are known for their accuracy and computational performance when applied to solving partial differential equations and have widespread use in representing images compactly. Nonetheless, high-order methods have difficulty representing functions containing discontinuities or functions having slow spectral decay in the chosen basis. Certain sensing techniques such as MRI and SAR provide data in terms of Fourier coefficients, and thus prescribe a natural high-order basis. The field of compressed sensing has introduced a set of techniques based on $\ell^1$ regularization that promote sparsity and facilitate working with functions having discontinuities. In this dissertation, high-order methods and $\ell^1$ regularization are used to address three problems: reconstructing piecewise smooth functions from sparse and and noisy Fourier data, recovering edge locations in piecewise smooth functions from sparse and noisy Fourier data, and reducing time-stepping constraints when numerically solving certain time-dependent hyperbolic partial differential equations.
Dissertation/Thesis
Doctoral Dissertation Applied Mathematics 2016

A primarily software based Fourier Deep Level Transient Spectroscope (FDLTS) is built. The raw capacitance transient is acquired and digitized using capacitance meter HP4280A whereas the signal analysis is done using a customized software module. The software module calculates both the conventional DLTS spectrum and the Fourier DLTS spectrum. This home-made FDLTS set up was compared to a commercial conventional box-car DLTS system (Sula Technology's DLTS) as well as to a commercial Fourier DLTS system (Bio-rad) and it was found to be either equivalent to the commercial systems or even better in some respects. In one case, Fourier analysis using the home-made setup, led to the detection of a trap completely undetected by the commercial conventional DLTS. The FDLTS system together with the commercial conventional DLTS were used to study possible gold contamination in an industrial process. The study was accomplished by comparing conventional and Fourier DLTS spectra and corresponding calculated trap properties using Schottky barrier diodes fabricated on the suspect wafers and an intentionally gold diffused reference sample wafer. During the investigation minority carrier emission in DLTS using Schottky barrier diodes was observed. The study revealed the presence of some possible gold-like contamination which trapped minority carriers (i.e. electrons) in p type silicon.
Graduation date: 2003

Title: Numerical modeling of unstable fluid flow past heated bodies Author: Jan Pech Department: Mathematical Institute of Charles University Supervisor: prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: Presented work brings new results to numerical computations of flow influenced by temperature changes. Constructed numerical algorithm takes into account variable coefficients of the differential operators in the system of in- compressible Navier-Stokes equations coupled with thermal heat equation. The spatial discretisation of the problem targets to application of high order method, the spectral element method. Phenomenons connected with high order approxi- mations are discussed on a number of examples and comparisons with methods of lower order, which are more common. Results were achieved for two fluids with opposite response to heating, air and water. The observed quantity is par- ticularly a frequency of vortex shedding, the Strouhal number, as dependent on temperature and Reynolds number. The calculated values were compared with experimental results and exhibit a good coincidence. Numerical analysis of sep- aration angle in flow around heated circular cylinder may give a new impulse to verification of accuracy and reliability of the developed method. Keywords:...