Les modèles intégrables sont des modèles physiques pour lesquels certaines quantités peuvent être calculées de manière exacte, sans recours aux méthodes de perturbations. Ces modèles très particuliers suscitent un intérêt croissant en physique théorique. Les applications directes en physique de la matière condensée et les liens subtils plus récemment mis en évidence avec certaines théories de jauge supersymétriques ont motivé depuis des décennies l’élaboration d’outils mathématiques complexes. Parmi eux, l’ansatz de Bethe a joué un rôle central, et permis la diagonalisation de nombreux modèles de natures très différentes. Le premier chapitre de cette thèse est consacré à une introduction aux deux approches de l’ansatz de Bethe, dites ”en coordonnée” et ”algébrique”, dans le cadre de la chaîne de spin de Heisenberg et d’un modèle stochastique généralisant à un spin continu le modèle du Totally Asymmetric Simple Exclusion Process. Le deuxième chapitre de cette thèse présente l’ansatz algébrique modifié pour la chaîne XXX périodique. Cet ansatz modifié est proposé pour résoudre le cas de la chaîne ouverte, pour laquelle l’ansatz classique n’est plus efficace. Le produit scalaire des états de Bethe modifiés ainsi obtenus est étudié. Le troisième chapitre concerne la résolution de l’identité, et le problème fonctionnel inverse. Une expression pour les états de spin en terme des états de Bethe est présentée pour le q-TASEP, et une expression de la résolution de l’identité en terme des états de Bethe pour la chaîne de spin XXZ infinie est démontrée, faisant intervenir dans les deux cas la contribution des états liés. Enfin, le quatrième chapitre concerne les représentions en déterminant dans l’ansatz de Bethe. Une expression pour les éléments de matrice de l’opérateur Nombre de Particule pour le gaz de Bose avec interaction delta en terme d’un déterminent est démontrée, et des représentations intégrales pour les déterminants d’Izergin-Korepin et de Slavnov sont investiguées, établissant ainsi un nouveau lien formel direct entre ces deux représentations en déterminant. / Integrable models are physical models for which some quantities can be exactly obtained, without use of perturbation theory. Those very special models are source of an increasing interest in theoretical physics. The direct applications in condensed matter physics and the subtle links evidenced more recently with some supersymmetric gauges theories motivated the development of complex mathematical tools. Among these, Bethe ansatz played an important role, and provides an efficient approach for diagonalizing a lot of models of various nature. The first chapter of this thesis is devoted to the introduction to the two approaches of the Bethe ansatz, said “coordinate” and “algebraic”, in the context of the XXX Heisenberg spin chain and a continuous spin generalization of the Totally Asymmetric Simple Exclusion Process, the so called Zero-range Chipping model with factorized steady state (ZCM). The second chapter is devoted to the Modified Algebraic Bethe Ansatz in the context of the periodic XXX chain. This modified ansatz is proposed for solving the spectral problem of the open spin chain, for which the usual ansatz fails. The scalar product of the obtained modified Bethe states is studied. The third chapter concerns the resolution of the identity and the inverse functional problem. An expression for the spin states in terms of Bethe states est presented for the ZCM, and an expression for the resolution of the identity in term of Bethe states for the infinite XXZ chain is proved, involving in both cases the contribution of bound states. At last, the fourth chapter concerns determinant representations in the Bethe ansatz. An expression for the “matrix elements of the particle number operator” for the delta-Bose gas in terms of a determinant is proved, and some integral representations for the Izergin-Korepin and Slavnov determinants are investigated, then establishing a new formal link between these two determinant representations.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20656号 / 理博第4321号 / 新制||理||1621(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々木 節, 教授 田中 貴浩, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24410号 / 理博第4909号 / 新制||理||1701(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 福間 將文, 教授 橋本 幸士, 准教授 吉岡 興一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

[pt] Este trabalho tem por objetivo um estudo da viabilidade de se fazer varreduras com uma antena gregoriana off-set com deslocamentos apenas do alimentador. São localizadas as regiões focais para a antena receptora de modo a posicionar o alimentador de uma maneira simples. Também são apresentados os diagramas de radiação correspondentes a estes deslocamentos calculados segundo a Teoria Escalar da Difração; e as limitações de varreduras para a antena particular que serviu para testar a eficiência do método. / [en] This work is related to the study of the pattern of Gregorian off-set antennas, by displacement of the feeder. The position of the feeder is obtained, in a simple way, by determining the focal regions of the antennas, working in reception. The radiation patterns corresponding to different position of the feeder are also presented. Such patterns are calculated according to the scalar theory of diffraction. The useful range of scanning, for a given antenna, used to check the efficiency of the method, is determined.

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This work presents the new Synthesized Cell Texture (SCT) algorithm for visualizing related multiple scalar value fields within the same 3D space. The SCT method is particularly well suited to scalar quantities that could be represented in the physical domain as size fractionated particles, such as in the study of sedimentation, atmospheric aerosols, or precipitation. There are two components to this contribution. First a Scaling and Distribution (SAD) algorithm provides a means of specifying a multi-scalar field in terms of a maximum cell resolution (or density of represented values). This information is used to scale the multi-scalar field values for each 3D cell to the maximum values found throughout the data set, and then randomly distributes those values as particles varying in number, size, color, and opacity within a 2D cell slice. This approach facilitates viewing of closely spaced layers commonly found in sigma-coordinate grids. The SAD algorithm can be applied regardless of how the particles are rendered. The second contribution provides the Synthesized Cell Texture (SCT) algorithm to render the multi-scalar values. In this approach, a texture is synthesized from the location information computed by the SAD algorithm, which is then applied to each cell as a 2D slice within the volume. The SCT method trades off computation time (to synthesize the texture) and texture memory against the number of geometric primitives that must be sent through the graphics pipeline of the host system. Analysis results from a user study prove the effectiveness of the algorithm as a browsing method for multiple related scalar fields. The interactive rendering performance of the SCT method is compared with two common basic particle representations: flat-shaded color-mapped OpenGL points and quadrilaterals. Frame rate statistics show the SCT method to be up to 44 times faster, depending on the volume to be displayed and the host system. The SCT method has been successfully applied to oceanographic sedimentation data, and can be applied to other problem domains as well. Future enhancements include the extension to time-varying data and parallelization of the texture synthesis component to reduce startup time.

<p>In many scientific, medical and defense applications of image/video compression, an <em>l</em>_∞error bound is required. However, pure <em>l</em>_∞-optimized image coding, colloquially known as near-lossless image coding, is prone to structured errors such as contours and speckles if the bit rate is not sufficiently high; moreover, previous <em>l</em>_∞-based image coding methods suffer from poor rate control. In contrast, the <em>l</em>₂ error metric aims for average fidelity and hence preserves the subtlety of smooth waveforms better than the <em>l</em>_∞ error metric and it offers fine granularity in rate control; but pure <em>l</em>₂-based image coding methods (e.g., JPEG 2000) cannot bound individual errors as <em>l</em>_∞-based methods can. This thesis presents a new compression approach to retain the benefits and circumvent the pitfalls of the two error metrics.</p> / Master of Applied Science (MASc)

Jet noise has been a growing concern in recent years due to the costs associated with hearing loss of United States service members. Jet noise is also becoming more of a concern due to the rise of civilian complaints regarding the noise of jets near civilian and military air stations. One source of noise generation is from packets of air called eddies, which move with a convection velocity Uc. The current work seeks to expand upon the understanding of jet noise by collecting data using Time-resolved Doppler global velocimetry (TR-DGV) from regions of the jet known to produce high levels of acoustic radiation. Past experiments in studying convection velocity are reviewed based on the technique for obtaining the velocities. To add to these experiments, the current work analyzes data obtained using TR-DGV applied to a perfectly expanded Mach 1.65 flow with total temperature ratio (TTR) equal to 1. Additional measurements were obtained on a Mach 1.5 nozzle operated at a slightly over expanded condition and at TTR = 2. The cold jet flow is compared to the past experiments on unheated jets and demonstrates good agreement with respect to normalized convection velocities based on the jet exit speed. The data is then compared to past experiments conducted on the same nozzle at heated conditions. Shadowgraph imaging is used as a qualitative tool to locate shock cells within the jet plume. TR-DGV data from near the lipline (r = 0.5D) is axially aligned with the shadowgraph images to demonstrate that the shock structure within the potential core causes detectable variations in the scalar convective velocity. Additionally, it is shown that in the heated and unheated Mach 1.65 jet and the over expanded heated Mach 1.48 jet that the convection velocity does increase beyond the potential core. The Mach 1.48 jet is also compared to mean velocities obtained using Particle Image Velocimetry and found that the convective and mean velocities were only similar in some regions of the jet. A discussion is provided on suggestions of future work on where to obtain data within the jet plume and how to collect the data using current capabilities. Suggestions are also provided for improving data quality in future experiments, as well as ideas for future investigations into convection velocity along the length of the jet plume using TR-DGV. / Master of Science / Jet noise has been a growing concern in recent year due to the costs associated with hearing loss of United States service members. Additionally, many civilians complain about the noise of aircraft flying both out of military facilities and commercial airports. One source of noise generation is from packets of air called eddies which move with a convection velocity. Researchers have identified that by affecting the convection velocities of these eddies, there is a larger benefit than other traditional methods such as engine chevrons. The current work summarizes techniques used to investigate convective velocity as well as to provide evidence for other unconfirmed theories. This study focuses on using a laser-based technique to obtain data within the flow of an unheated supersonic jet. An unheated jet is studied to allow for easy comparison to other experiments that have used different diagnostic techniques. Additionally, this case is studied to complete a set of experiments that were previously conducted on the same nozzle so that there is a true base-line or “control” case for future work. Later in this paper, analysis will be done to show how shocks within the jet affect the convective velocity. A combination of both quantitative and qualitative efforts are performed to accomplish this. Additionally, it will be shown that after the potential core of the jet breaks down, there is an increase in the local convective velocity in this region immediately after the potential core. Finally, a brief summary will be given and suggestions for future work will be presented.

In this thesis, we investigate the thermodynamics of the de Sitter static patch in order to extract information which can constrain microscopic models of de Sitter quantum gravity. We begin by reviewing previous works which demonstrate how to make sense of the seemingly ill-defined static patch density of states through the introduction of Harish-Chandra group characters, or equivalently through renormalization with respect to a reference problem in Rindler space. A thermal partition function can then be constructed and expressed in terms of a sum over quasinormal mode frequencies. We recap how, in the scalar case, this partition function is equivalent to a 1-loop sphere path integral, as expected from the Gibbons-Hawking proposal, and provides macroscopic data which microscopic models must be consistent with. We next present novel results dealing with scalar Green functions in de Sitter. After constructing various static patch correlators and showing how they can be obtained from their sphere counterparts, we relate the spectral Green function to the Harish-Chandra characters that we came across before, tying them to observables directly accessible within the static patch. We comment on how this result will allow us to generalize thermodynamic considerations to interacting theoriesand therefore place stronger consistency constraints on microscopic models. We finally generalize our analysis to spinning fields, for which thermal partition functions differ from Euclidean path integrals by edge corrections. We reveal new findings which trace the source of these discrepancies to those quasinormal modes which do not correspond to regular Euclidean solutions, explicitly demonstrating this through several examples. Our results highlight the differences between Lorentzian and Euclidean approaches to de Sitter thermodynamics, and hint at new avenues to pursue in the hopes of providing more consistency constraints.