Higher-dimensional Hamiltonian systems usually exhibit a mixed phase space in which regular and chaotic motion coexist. While regular trajectories are confined to regular tori, chaotic trajectories can be transported through a web of so called resonance channels which disrupt the regular structures. The focus of this thesis are time-discrete 4D symplectic maps which represent the lowest dimensional system for which the chaotic transport can circumvent regular tori. While the dynamics of 2D maps are well established, many fundamental questions are open for maps of dimension four and higher due to this property. In particular, the mechanism of the power-law trapping is unknown for these maps. In this thesis, the organization and hierarchy of the regular structures of 4D maps is uncovered and the slow chaotic transport close to these structures is examined. Specifically, this transport is shown to be organized by a set of overlapping resonance channels. The transport across these channels is found to be governed by partial transport barriers. For the transport along a channel a stochastic process including a drift is conjectured. Based on each of these two types of chaotic transport a possible mechanism for the power-law trapping in higher-dimensional systems is proposed.

O objetivo deste trabalho foi avaliar vozes saudáveis e com alterações patológicas aplicando análise de Padrões Visuais de Dinâmica Vocal (PVDV) em conjunto com análise acústica e análise perceptivo-auditiva. Foram avaliadas 91 vozes da vogal sustentada /a/ do português do Brasil, de sujeitos de ambos os gêneros com idades entre 21 e 88 anos. As vozes foram gravadas com taxa de amostragem de 22.050 Hz, 16 bits, mono canal e formato WAV. Foram obtidos valores de jitter, shimmer e freqüência fundamental. Para análise perceptivo-auditiva foram avaliadas rugosidade, soprosidade, tensão e instabilidade. Para descrever a dinâmica dos sinais de voz dos PVDV foi utilizada a técnica de reconstrução de espaço de fase e foram analisados qualitativamente os parâmetros de loops, regularidade e convergência de traçados. Foram aplicados testes estatísticos paramétricos e não paramétricos. Os resultados demonstram que jitter apresenta uma correlação negativa com loop, regularidade e convergência dos traçados; e que shimmer tem correlação negativa com convergência e loops. As características de rugosidade e soprosidade estão correlacionadas negativamente com os três parâmetros dinâmicos. A análise qualitativa dos PVDV é uma técnica promissora, por considerar os componentes caótico e determinístico da voz. É sugerido que não substitui as técnicas existentes, embora possa aperfeiçoar e complementar os métodos usados por profissionais fonoaudiólogos e otorrinolaringologistas. / The aim of this research was to analyze healthy and pathologic voices using Vocal Dynamic Visual Patterns (VDVP) in combination with acoustical and perceptual analysis. Ninety one voice signals of sustained vowel /a/ from Brazilian Portuguese, from male and female patients, were analyzed using acoustical analysis, perceptual analysis and Vocal Dynamic Visual Patterns (VDVP) analysis. All voice samples were quantized in amplitude with 16 bits and recorded in mono-channel WAV format. The sampling frequency was 22050 Hz. Acoustical values for jitter, shimmer and fundamental frequency were obtained. Roughness, breathiness, strain and irregularity were analyzed for perceptual analysis. Phase space reconstruction technique was performed in order to describe the voice signal nonlinear characteristics by Vocal Dynamic Visual Patterns. Results showed negative correlation for jitter and the 3 dynamic parameters, as well as, for shimmer with convergence and loops. Roughness and breathiness were negative correlated with dynamical parameters. Vocal Dynamic Visual Pattern analysis is a promising technique for voice evaluation; including voice chaotic and deterministic components. It is suggested that visual pattern analysis do not replace the existing voice analysis techniques, although it complements and improves the voice evaluation methods available for speech therapist and laryngologists.

O objetivo deste trabalho foi avaliar vozes saudáveis e com alterações patológicas aplicando análise de Padrões Visuais de Dinâmica Vocal (PVDV) em conjunto com análise acústica e análise perceptivo-auditiva. Foram avaliadas 91 vozes da vogal sustentada /a/ do português do Brasil, de sujeitos de ambos os gêneros com idades entre 21 e 88 anos. As vozes foram gravadas com taxa de amostragem de 22.050 Hz, 16 bits, mono canal e formato WAV. Foram obtidos valores de jitter, shimmer e freqüência fundamental. Para análise perceptivo-auditiva foram avaliadas rugosidade, soprosidade, tensão e instabilidade. Para descrever a dinâmica dos sinais de voz dos PVDV foi utilizada a técnica de reconstrução de espaço de fase e foram analisados qualitativamente os parâmetros de loops, regularidade e convergência de traçados. Foram aplicados testes estatísticos paramétricos e não paramétricos. Os resultados demonstram que jitter apresenta uma correlação negativa com loop, regularidade e convergência dos traçados; e que shimmer tem correlação negativa com convergência e loops. As características de rugosidade e soprosidade estão correlacionadas negativamente com os três parâmetros dinâmicos. A análise qualitativa dos PVDV é uma técnica promissora, por considerar os componentes caótico e determinístico da voz. É sugerido que não substitui as técnicas existentes, embora possa aperfeiçoar e complementar os métodos usados por profissionais fonoaudiólogos e otorrinolaringologistas. / The aim of this research was to analyze healthy and pathologic voices using Vocal Dynamic Visual Patterns (VDVP) in combination with acoustical and perceptual analysis. Ninety one voice signals of sustained vowel /a/ from Brazilian Portuguese, from male and female patients, were analyzed using acoustical analysis, perceptual analysis and Vocal Dynamic Visual Patterns (VDVP) analysis. All voice samples were quantized in amplitude with 16 bits and recorded in mono-channel WAV format. The sampling frequency was 22050 Hz. Acoustical values for jitter, shimmer and fundamental frequency were obtained. Roughness, breathiness, strain and irregularity were analyzed for perceptual analysis. Phase space reconstruction technique was performed in order to describe the voice signal nonlinear characteristics by Vocal Dynamic Visual Patterns. Results showed negative correlation for jitter and the 3 dynamic parameters, as well as, for shimmer with convergence and loops. Roughness and breathiness were negative correlated with dynamical parameters. Vocal Dynamic Visual Pattern analysis is a promising technique for voice evaluation; including voice chaotic and deterministic components. It is suggested that visual pattern analysis do not replace the existing voice analysis techniques, although it complements and improves the voice evaluation methods available for speech therapist and laryngologists.

Diversos estudos foram realizados para detecção de patologias na laringe. Essas patologias causam alteração na frequência, amplitude e formato de onda do sinal de voz e podem ser estudadas através dos parâmetros convencionais de análise como jitter e shimmer, ou sob o enfoque da dinâmica não linear. Essas técnicas são não invasivas e servem de apoio ao especialista da área de fonoaudiologia para o diagnóstico de patologias nas pregas vocais. As técnicas de análise acústica baseiam-se no formato de onda vocal no domínio do tempo e domínio da frequência, enquanto que a técnica de análise não linear utilizada nesse trabalho baseia-se no atrator reconstruído do sinal de voz. O objetivo dessa tese é diferenciar vozes normais e patológicas e entre patologias usando a técnica de análise não linear conhecida como Seção de Poincaré. Foram analisados 48 sinais de vozes humanas, divididos em 3 grupos (16 normais, 16 com nódulo e 16 com edema de Reinke). Em seguida foram selecionados 3 trechos de 500 ms nos intervalos 0.5s-1.0s, 2.0s-2.5s e 4.0s-4.5s chamado de primeiro critério e um trecho 500ms no trecho de maior variação de pitch, chamado de segundo critério. Em seguida, o atrator foi reconstruído em 3 dimensões, determinado o atrator médio, e de cada ponto do atrator médio foi extraída a seção de Poincaré. De cada seção de Poincaré foi calculada a dispersão dos pontos do atrator no plano através da média e desvio padrão das dispersão dos pontos da seção de Poincaré em relação ao ponto médio da seção. A validação da ferramenta desenvolvida para essa tese foi realizada utilizando um sinal senoidal inserindo jitter gradativamente, onde verificou-se uma variação proporcional da média da dispersão. Os resultados obtidos mostraram que não foi possível diferenciar patologias mas foi possível classificar vozes normais das patológicas. O melhor intervalo para classificar as vozes normais das patológicas utilizando o primeiro critério foi entre 0.5s-1.0s pois nesse intervalo todas as vozes normais foram classificadas corretamente. No entanto, 6 vozes patológicas foram classificadas como normais com 2 vozes patológicas na fronteira que separa as vozes normais das patológicas. O segundo critério classificou todas as vozes normais corretamente e apenas uma voz patológica foi classificada como patológica. Concluiu-se que a ferramenta proposta utilizando o segundo critério mostrou-se superior em relação ao primeiro critério para diferenciar vozes normais das patológicas. / Several studies have been performed to detect pathologies of the larynx. These pathologies cause changes in the frequency, amplitude, and waveform of the voice signal. They can be studied by means of conventional analysis parameters such as jitter and shimmer, or from nonlinear dynamics concepts. These techniques are noninvasive and can help the speech therapist to better diagnose the pathologies in the vocal folds. The acoustic analysis techniques are based on the voice waveform in the time and frequency domains, while the non-linear analysis techniques are based on the attractor reconstructed from the speech signal.The aim of this thesis is to differentiate normal and pathological voices using a nonlinear analysis technique named Poincaré section. We analyzed 48 human voice signals divided into 3 groups (16 normal, 16 nodule and 16 Reinke\'s edema). Then, we analyzed 3 stretches of 500ms in the intervals 0.5s-1.0s, 2.0s-2.5s e 4.0-4.5s, denominated first criteria, and a stretch of 500ms in a higher variation in pitch, denominated second criteria. The attractor was then reconstructed in three dimensions, the average attractor was determined, and at each point of the average attractor, a Poincaré section was extracted. From each Poincaré section, the dispersion of the points of the attractor was calculated in the plane by means of the statistical average and standard deviation related to the medium point of the section. The validation of the tool developed for this thesis was achieved by inserting jitter gradually in a sinusoidal wave, where there was a proportional variation of average\'s dispersion was observed. The results obtained for this set of voices showed that the average and standard deviation of dispersion of the points in the Poincaré section differentiate the groups of voices, but not the pathological groups. The Statistical tests of Anova and Tukey were used to analyze the 3 groups and all group pairings, two by two, with a statistical significance of 5%. The best interval to classify normal voices from pathological voices by means of the first criteria was between 0.5s-1.0s, given the fact that in this interval, all normal voices were correctly classified. However, 6 pathological voices were classified as normal voices, with 2 voices border lining the frontier between normal voices from pathological voices. The second criteria classified all normal voices correctly, with only one pathological voice incorrectly classified. In conclusion, the second criteria tool proposed by this thesis was proven superior to differentiate normal voices from pathological ones.

Neste trabalho, o objetivo geral é investigar os processos sinóticos, dinâmicos e termodinâmicos de dois ciclones subtropicais ocorridos no Atlântico Sul. Utilizou-se um algoritmo de rastreamento de máximos de vorticidade ciclônica e o algoritmo Cyclone Phase Space (CPS), que permite classificar o ciclo de vida dos ciclones. Desenvolveu-se um processo de automatização destes algoritmos, que possibilitou a análise dos diagramas de fase de todos os ciclones ocorridos no Atlântico Subtropical durante 2008, 2009 e março de 2010. As condições sinóticas para dois eventos foram analisadas desde o período prévio à formação até o decaimento dos sistemas, e as equações do balanço de vorticidade e de calor foram utilizadas para investigar os processos dinâmicos e termodinâmicos. Embora com fraca intensidade em termos de pressão central, os ciclones tiveram impacto importante nas condições de tempo sobre suas regiões de atuação, e os ventos máximos superaram 15 m/s em 925 hPa por várias horas. Ambos os ciclones apresentaram, ao menos em algum tempo de sua fase subtropical, um pico de advecção horizontal quente em altos níveis, enquanto a advecção horizontal quente em baixos níveis apresentou fraca intensidade. Nos estágios de fase híbrida, o termo diabático foi responsável pelas tendências de aquecimento em baixos níveis. Já durante a fase de transição extratropical ocorrida em um dos ciclones, o sentido dos fluxos turbulentos em superfície se inverteu e o termo diabático passou a contribuir para tendências de resfriamento em baixos níveis. Em altos níveis, foram encontradas regiões em que altos valores positivos do termo diabático da equação da termodinâmica correspondem a regiões de intenso resíduo negativo da equação da vorticidade. Nestas regiões, os processos convectivos podem explicar os imbalanços de vorticidade. Nas demais regiões e níveis em que esta relação não ocorreu, sugere-se que a convecção influencia as variações locais de vorticidade de uma forma mais distribuída na coluna atmosférica, assim como a divergência associada aos movimentos verticais pode ocorrer de forma distribuída ao longo da troposfera. / This work aims to investigate the synoptic and dynamic processes of a sample of subtropical cyclones that occurred near the east coast of South America. A cyclonic vorticity maximum tracking algorithm and the Cyclone Phase Space (CPS) algorithm are used to track and to classify the life cycle evolution of the cyclones. By automating these algorithms, it was possible to perform the analysis of the phase diagrams of all the cyclones occurred in the Subtropical Atlantic during 2008, 2009 and March 2010. The synoptic conditions for two events were analyzed from the period prior to the genesis until the decay of the systems, and the heat and vorticity balance equations were used to investigate the thermodynamic and dynamic processes. Although with low intensity in terms of central pressure, the cyclones had a major impact on the weather conditions in their regions of occurrence, and the 925 hPa maximum sustained winds exceeded 15 m/s for several hours. Both selected cyclones, at least at a time of its subtropical phase, had a peak of warm horizontal advection at higher levels, whilst the warm horizontal advection at lower levels showed weak intensity. In the hybrid stages of both cyclones, the diabatic term was responsible for warming trends at low levels. However, during the extratropical transition in one of the cyclones, the direction of the near-surface turbulent fluxes reversed and the diabatic term began to contribute to cooling trends at low levels. In the upper troposphere, it was found that in some regions that featured large positive values of the thermodynamic equation diabatic term, there was also a significant negative residual of the vorticity equation. In these regions, the convective processes can explain the observed vorticity imbalances. For other regions and levels, at which there was no direct relationship between the residual fields, it is suggested here that convection influences the local variations of vorticity in a more distributed way in the atmospheric column, as well as the divergence associated with the vertical velocities can be more distributed throughout the troposphere, without being concentrated at only some levels.

Cette thèse a pour objet les corrections perturbatives de CDQ pour la production de quatre jets dans l'annihilation des électrons et positrons. Les corrections à une boucle pour le sous-processus $e^+ e^- \rightarrow q \bar{q} Q \bar{Q}$ sont calculées avec de nouvelles méthodes qui comprennent la décomposition de couleur, la méthode des spineur d'hélicité, et une décomposition inspirée par la supersymmétrie. Nous avons également profité des contraintes découlants de l'unitarité et des limites colinéaires pour restreindre la forme analytique des amplitudes. Dans une deuxième phase, j'ai écrit un programme numérique qui combine des contributions dues aux corrections radiatives des sous-processus $e^+ e^- \rightarrow q \bar{q} Q \bar{Q}$ et $e^+ e^- \rightarrow q g g \bar{q}$ et dues aux corrections d'émission réelle. Le programme utilise le formalisme des dipoles pour annuler les divergences infra-rouge. L'analyse numérique contient des résultats sur la section efficace totale, le paramètre $D$ et la variable d'élargissement d'un jet.

Cette thèse décrit quelques développements dans les techniques de calcul des amplitudes de diffusion en théorie supersymétrique de champ de jauge . L'accent est mis sur les relations de récurrence on-shell et sur l'utilisation de méthodes d'unitarité pour des calculs de boucle. En particulier, la récurrence on-shell est liée aux règles BCFW pour calculer les amplitudes de jauge au niveau des arbres. Les combinaisons de techniques de coupe d'unitarité et la récurrence sont utilisées pour calculer les amplitudes de boucle, et finalement, à partir des amplitudes, pour obtenir la fonction de corrélation énergie-énergie en théorie de super-Yang-Mills N = 4 à l'aide de la représentation de Mellin-Barnes. Dans le dernier chapitre, nous tentons de trouver un contour convergent pour les intégrales de Mellin Barnes en multi-dimension obtenu par une certaine approximation d'un contour de phase stationnaire.

Für das Verständnis einer Vielzahl von Problemen von der Himmelsmechanik bis hin zur Beschreibung von Molekülen spielen Systeme mit mehr als zwei Freiheitsgraden eine entscheidende Rolle. Aufgrund der Dimensionalität gestaltet sich ein Verständnis dieser Systeme jedoch deutlich schwieriger als bei Systemen mit zwei oder weniger Freiheitsgraden. Die vorliegende Arbeit soll zum besseren Verständnis der klassischen und quantenmechanischen Eigenschaften getriebener Systeme mit zwei Freiheitsgraden beitragen. Hierzu werden dreidimensionale Schnitte durch den Phasenraum von 4D Abbildungen betrachtet. Anhand dreier Beispiele, deren Phasenräume zunehmend kompliziert sind, werden diese 3D Schnitte vorgestellt und untersucht. In einer sich anschließenden quantenmechanischen Untersuchung gehen wir auf zwei wichtige Aspekte ein. Zum einen untersuchen wir die quantenmechanischen Signaturen des klassischen "Arnold Webs". Es wird darauf eingegangen, wie die Quantenmechanik dieses Netz im semiklassischen Limes auflösen kann. Darüberhinaus widmen wir uns dem wichtigen Aspekt quantenmechanischer Kopplungen klassisch getrennter Phasenraumgebiete anhand der Untersuchung dynamischer Tunnelraten. Für diese wenden wir sowohl den in der Literatur bekannten "fictitious integrable system approach" als auch die Theorie des resonanz-unterstützen Tunnelns auf 4D Abbildungen an. / Systems with more than two degrees of freedom are of fundamental importance for the understanding of problems ranging from celestial mechanics to molecules. Due to the dimensionality the classical phase-space structure of such systems is more difficult to understand than for systems with two or fewer degrees of freedom. This thesis aims for a better insight into the classical as well as the quantum mechanics of 4D mappings representing driven systems with two degrees of freedom. In order to analyze such systems, we introduce 3D sections through the 4D phase space which reveal the regular and chaotic structures. We introduce these concepts by means of three example mappings of increasing complexity. After a classical analysis the systems are investigated quantum mechanically. We focus especially on two important aspects: First, we address quantum mechanical consequences of the classical Arnold web and demonstrate how quantum mechanics can resolve this web in the semiclassical limit. Second, we investigate the quantum mechanical tunneling couplings between regular and chaotic regions in phase space. We determine regular-to-chaotic tunneling rates numerically and extend the fictitious integrable system approach to higher dimensions for their prediction. Finally, we study resonance-assisted tunneling in 4D maps.

Tunneling is one of the most prominent features of quantum mechanics. While the tunneling process in one-dimensional integrable systems is well understood, its quantitative prediction for systems with mixed phase space is a long-standing open challenge. In such systems regions of regular and chaotic dynamics coexist in phase space, which are classically separated but quantum mechanically coupled by the process of dynamical tunneling. We derive a prediction of dynamical tunneling rates which describe the decay of states localized inside the regular region towards the so-called chaotic sea. This approach uses a fictitious integrable system which mimics the dynamics inside the regular domain and extends it into the chaotic region. Excellent agreement with numerical data is found for kicked systems, billiards, and optical microcavities, if nonlinear resonances are negligible. Semiclassically, however, such nonlinear resonance chains dominate the tunneling process. Hence, we combine our approach with an improved resonance-assisted tunneling theory and derive a unified prediction which is valid from the quantum to the semiclassical regime. We obtain results which show a drastically improved accuracy of several orders of magnitude compared to previous studies. / Der Tunnelprozess ist einer der bedeutensten Effekte in der Quantenmechanik. Während das Tunneln in eindimensionalen integrablen Systemen gut verstanden ist, gestaltet sich dessen Beschreibung für Systeme mit gemischtem Phasenraum weitaus schwieriger. Solche Systeme besitzen Gebiete regulärer und chaotischer Bewegung, die klassisch getrennt sind, aber quantenmechanisch durch den Prozess des dynamischen Tunnelns gekoppelt werden. In dieser Arbeit wird eine theoretische Vorhersage für dynamische Tunnelraten abgeleitet, die den Zerfall von Zuständen, die im regulären Gebiet lokalisiert sind, in die sogenannte chaotische See beschreibt. Dazu wird ein fiktives integrables System konstruiert, das im regulären Bereich eine nahezu gleiche Dynamik aufweist und diese Dynamik in das chaotische Gebiet fortsetzt. Die Theorie zeigt eine ausgezeichnete Übereinstimmung mit numerischen Daten für gekickte Systeme, Billards und optische Mikrokavitäten, falls nichtlineare Resonanzketten vernachlässigbar sind. Semiklassisch jedoch bestimmen diese nichtlinearen Resonanzketten den Tunnelprozess. Daher kombinieren wir unseren Zugang mit einer verbesserten Theorie des Resonanz-unterstützten Tunnelns und erhalten eine Vorhersage,die vom Quanten- bis in den semiklassischen Bereich gültig ist. Ihre Resultate zeigen eine Genauigkeit, die verglichen mit früheren Theorien um mehrere Größenordnungen verbessert wurde.

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