Sparse spectral methods on disk-slices, trapeziums and spherical caps

This thesis develops sparse spectral methods for solving partial differential equations (PDEs) on various multidimensional domains, with a specific focus on the disk-slice and trapezium in 2D, and the spherical cap in 3D. For the latter, the PDEs are surface PDEs involving Laplace-Beltrami operators, spherical gradients and other spherical operators. We begin with an introduction to sparse spectral methods via viewing spherical harmonics as multidimensional orthogonal polynomials in x, y, and z. We explain how differential operators can be applied as banded-block-banded matrix operators to coefficient vectors for a function’s expansion. Further, we demonstrate how vector spherical harmonics in x, y, and z can be used as an orthogonal basis for vector-valued functions, yielding similar banded-block-banded gradient and divergence operators. We move on to presenting a new framework for choosing a suitable orthogonal polynomial basis for more general 2D domains defined via an algebraic curve as a boundary. This work builds on the observation that sparsity is guaranteed due to this definition of the boundary, and that the entries of partial differential operators can be determined using formulae in terms of (non-classical) univariate orthogonal polynomials. Triangles and the full disk are then special cases of our framework, which we formalise for the disk-slice and trapezium. Piecing together the techniques used thus far, we present a new orthogonal polynomial basis and sparse spectral method for the spherical cap, complete with the same observation of the guaranteed sparsity of operators. The motivation is for one to use spherical caps bands as in a spectral element method for the sphere, with many applications in meteorology and astrophysics – in particular, as a potential replacement of the spherical harmonics approach currently in use at ECMWF, which is predicted to become too costly due to a parallel scalability bottleneck arising from the global spectral transform.Open Acces

Measurements, Models, Systems and Design

531 s.

Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-3)

Papers from the Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES) are presented. The papers discuss current research in the general field of inverse, semi-inverse, and direct design and optimization in engineering sciences. The rapid growth of this relatively new field is due to the availability of faster and larger computing machines

A cumulative index to the 1973 issues of Aeronautical engineering: A special bibliography

This publication is a cumulative index to the abstracts contained in NASA SP-7037 (28) through NASA SP-7037 (39) of Aeronautical Engineering: A Special Bibliography. NASA SP-7037 and its supplements have been compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). This cumulative index includes subject, personal author, corporate source, contract, and report number indexes

Single- and multi-microphone speech dereverberation using spectral enhancement

In speech communication systems, such as voice-controlled systems, hands-free mobile telephones, and hearing aids, the received microphone signals are degraded by room reverberation, background noise, and other interferences. This signal degradation may lead to total unintelligibility of the speech and decreases the performance of automatic speech recognition systems. In the context of this work reverberation is the process of multi-path propagation of an acoustic sound from its source to one or more microphones. The received microphone signal generally consists of a direct sound, reflections that arrive shortly after the direct sound (commonly called early reverberation), and reflections that arrive after the early reverberation (commonly called late reverberation). Reverberant speech can be described as sounding distant with noticeable echo and colouration. These detrimental perceptual effects are primarily caused by late reverberation, and generally increase with increasing distance between the source and microphone. Conversely, early reverberations tend to improve the intelligibility of speech. In combination with the direct sound it is sometimes referred to as the early speech component. Reduction of the detrimental effects of reflections is evidently of considerable practical importance, and is the focus of this dissertation. More specifically the dissertation deals with dereverberation techniques, i.e., signal processing techniques to reduce the detrimental effects of reflections. In the dissertation, novel single- and multimicrophone speech dereverberation algorithms are developed that aim at the suppression of late reverberation, i.e., at estimation of the early speech component. This is done via so-called spectral enhancement techniques that require a specific measure of the late reverberant signal. This measure, called spectral variance, can be estimated directly from the received (possibly noisy) reverberant signal(s) using a statistical reverberation model and a limited amount of a priori knowledge about the acoustic channel(s) between the source and the microphone(s). In our work an existing single-channel statistical reverberation model serves as a starting point. The model is characterized by one parameter that depends on the acoustic characteristics of the environment. We show that the spectral variance estimator that is based on this model, can only be used when the source-microphone distance is larger than the so-called critical distance. This is, crudely speaking, the distance where the direct sound power is equal to the total reflective power. A generalization of the statistical reverberation model in which the direct sound is incorporated is developed. This model requires one additional parameter that is related to the ratio between the direct sound energy and the sound energy of all reflections. The generalized model is used to derive a novel spectral variance estimator. When the novel estimator is used for dereverberation rather than the existing estimator, and the source-microphone distance is smaller than the critical distance, the dereverberation performance is significantly increased. Single-microphone systems only exploit the temporal and spectral diversity of the received signal. Reverberation, of course, also induces spatial diversity. To additionally exploit this diversity, multiple microphones must be used, and their outputs must be combined by a suitable spatial processor such as the so-called delay and sum beamformer. It is not a priori evident whether spectral enhancement is best done before or after the spatial processor. For this reason we investigate both possibilities, as well as a merge of the spatial processor and the spectral enhancement technique. An advantage of the latter option is that the spectral variance estimator can be further improved. Our experiments show that the use of multiple microphones affords a significant improvement of the perceptual speech quality. The applicability of the theory developed in this dissertation is demonstrated using a hands-free communication system. Since hands-free systems are often used in a noisy and reverberant environment, the received microphone signal does not only contain the desired signal but also interferences such as room reverberation that is caused by the desired source, background noise, and a far-end echo signal that results from a sound that is produced by the loudspeaker. Usually an acoustic echo canceller is used to cancel the far-end echo. Additionally a post-processor is used to suppress background noise and residual echo, i.e., echo which could not be cancelled by the echo canceller. In this work a novel structure and post-processor for an acoustic echo canceller are developed. The post-processor suppresses late reverberation caused by the desired source, residual echo, and background noise. The late reverberation and late residual echo are estimated using the generalized statistical reverberation model. Experimental results convincingly demonstrate the benefits of the proposed system for suppressing late reverberation, residual echo and background noise. The proposed structure and post-processor have a low computational complexity, a highly modular structure, can be seamlessly integrated into existing hands-free communication systems, and affords a significant increase of the listening comfort and speech intelligibility

Gyrokinetic particle-in-cell global simulations of ion-temperature-gradient and collisionless-trapped-electron-mode turbulence in tokamaks

The goal of thermonuclear fusion research is to provide power plants, that will be able to produce one gigawatt of electricity. Among the different ways to achieve fusion, the tokamak, based on magnetic confinement, is the most promising one. A gas is heated up to hundreds of millions of degrees and becomes a plasma, which is maintained – or confined – in a toroidal vessel by helical magnetic field lines. Then, deuterium and tritium are injected and fuse to create an α particle and an energetic neutron. In order to have a favorable power balance, the power produced by fusion reactions must exceed the power needed to heat the plasma and the power losses. This can be cast in a very simple expression which stipulates that the product of the density, the temperature and the energy confinement time must exceed some given value. Unfortunately, present-days tokamaks are not able to reach this condition, mostly due to plasma turbulence. The latter phenomenon enhances the heat losses and degrades the energy confinement time, which cannot be predicted by analytical theories such as the so-called neoclassical theory in which the heat losses are caused by Coulomb collisions. Therefore, numerical simulations are being developed to model plasma turbulence, mainly caused by the Ion and Electron Temperature-Gradient and the Trapped-Electron-Mode instabilities. The plasma is described by a distribution function which evolves according to the Vlasov equation. The electromagnetic fields created by the particles are self-consistently obtained through Maxwell's equations. The resulting Vlasov-Maxwell system is greatly simplified by using the gyrokinetic theory, which consists, through an appropriate ordering, of eliminating the fast gyromotion (compared to the typical frequency of instabilities). Nevertheless, it is still extremely difficult to solve this system numerically due to the large range of time and spatial scales to be resolved. In this thesis, the Vlasov-Maxwell system is solved in the electrostatic and collisionless limit with the Particle-In-Cell (PIC) ORB5 code in global tokamak geometry. This Monte-Carlo approach suffers from statistical noise which unavoidably degrades the quality of the simulation. Consequently, the first part of this work has been devoted to the optimization of the code with a view to reduce the numerical noise. The code has been rewritten in a new coordinate system which takes advantage of the anisotropy of turbulence, which is mostly aligned with the magnetic field lines. The overall result of the optimization is that for a given accuracy, the CPU time has been decreased by a factor two thousand, the total memory has been decreased by a factor ten and the numerical noise has been reduced by a factor two hundred. In addition, the scaling of the code with respect to plasma size is presently optimal, suggesting that ORB5 could compute heat transport for future fusion devices such as ITER. The second part of this thesis presents the validation of the code with numerical convergence tests, linear (including dispersion relations) and nonlinear benchmarks. Furthermore, the code has been applied to important issues in gyrokinetic theory. It is shown for the first time that a 5D global delta-f PIC code can achieve a thermodynamic steady state on the condition that some dissipation is present. This is a fundamental result as the main criticism against delta-f PIC codes is their inability to deal with long time simulations. Next, the role of the parallel nonlinearity is studied and it is demonstrated in this work that this term has no real influence on turbulence, provided the numerical noise is sufficiently low. This result should put an end to the controversy that recently occurred, in which gyrokinetic simulations using different numerical approaches yielded contradictory results. Finally, thanks to the optimization of the code, the gyrokinetic model has been extended to include the kinetic response of trapped-electrons, in place to the usual adiabatic (Boltzmann) approximation. For the first time, global TEM nonlinear simulations are presented, and the role of the zonal flow on heat transport is analyzed. This study will help in acquiring some knowledge on the less-known TEM turbulence (as compared to ITG). In conclusion, this thesis is one of the main steps of the development of ORB5, which is now a state-of-the-art gyrokinetic code for collisionless ITG and TEM turbulence, and has brought several contributions to the understanding of these phenomena

Émission quantique spontanée : modifications induites par l’environnement

The control of the spontaneous emission of quantum emitters is of fundamental importance for the development of future quantum technologies, like quantum cryptography or quantum computing. Such applications rely on the manipulation of atoms, molecules, or "artificial" atoms, as elementary sources of light, and on the exploitation of the quantum nature of the emitted light, single photons. With the recent developments in nanofabrication techniques and nanotechnologies, the modification of the dynamics of the spontaneous emission by the environment is being investigated at the level of a few emitters, allowing for unprecedented control and manipulation of the spontaneous emission. In parallel to the experimental efforts, theoretical understanding of the fundamental interaction mechanisms between quantum emitters and their environment also becomes more and more essential.In this thesis, we tackle three different paradigms of the spontaneous emission phenomenon, all dealing with modifications of the spontaneous emission induced the environment. Firstly, we tackle the problem of monitored spontaneous emission, that is how the processus of emission is modified when the emitting system is being frequently monitored by an external observer, and which is closely related to the problem of measurementin quantum mechanics. Secondly, we consider the interaction between quantum emitters and optical resonances supported by nearby nanostructures. Finally, we study the remote interaction between quantum emitters and surfaces engraved with nanostructures which are designed and arranged in specific patterns, so-called metasurfaces.We present and deal with different formalisms to model such different situations, interfacing different fields of physics like quantum optics and nanophotonics. In each of these situations, we illustrate with realistic theoretical predictions how the spontaneous emission is modified: in the first case, how the lifetime of the quantum emitter is altered,in the second case how the frequency of the emitted photon is altered, and in the last situation how the environment may induce quantum coherence in the emitter. For each case, for provide with experimental proposals for future confirmations of these predictions, to bring a better understanding and control over these fundamental processes.Le contrôle de l’émission spontanée d’émetteurs quantiques est d’une importance capitale dans le développement des futures technologies quantiques telles que la cryptographie ou l’ordinateur quantiques. La base de ces applications consiste en la manipulation d’atomes, de molécules ou d’atomes « artificiels » comme sources élémentaires de lumière, et en l’exploitation de la nature quantique de la lumière émise, constituée de photonsuniques. Grâce au développement récent des techniques de nanofabrication et des nanotechnologies, la modification de l’émission spontanée par l’environnement est en train d’être explorée au niveau de quelques émetteurs seulement, ce qui ouvre la voie vers un contrôle et une manipulation de l’émission spontanée sans précédent. En parallèle des efforts expérimentaux, une compréhension théorique des mécanismes d’interactionfondamentaux entre émetteurs quantiques et leur environnement devient également indispensable.Dans cette thèse, nous considérons l’émission spontanée dans trois paradigmes différents traitant de la modification de ce processus due à l’environnement. Dans le premier, nous considèrons le problème du « monitorage » de l’émission spontanée, c’est-à-dire le fait qu’un observateur extérieur puisse modifier le processus d’émission par des mesures fréquentes de l’état du système, ce qui est étroitement relié au problème de la mesure en mécanique quantique. Dans un deuxième temps, nous considérons l’interaction d’émetteurs quantiques avec des résonances optiques supportées par des structures nanométriques placées à proximité. Enfin, nous traitons de l’interaction lointaine entre des émetteurs et des surfaces gravées avec des nanostructures fabriquées et positionnéesselon un motif particulier, appelées métasurfaces. Nous présentons et utilisons plusieurs formalismes pour modéliser ces différentes situations, qui interfacent divers domaines de la physique comme l’optique quantique et la nanophotonique. Nous illustrons chaque situation par des prédictions théoriques réalistes sur la manière dont l’émission spontanée est modifiée : dans le premier cas, par une altération de la durée de vie de l’émetteur, dans le second, par une altération de la fréquence du photon qui est émis, et, dans la dernière situation, comment l’environnement peut induire à longue distance une cohérence quantique chez l’émetteur. Pour chacune de ces prédictions, nous faisons des propositions expérimentales pour de futures confirmations de ces effets, afin d’améliorer notre compréhension et le contrôle de ces processus fondamentaux d’interaction lumière-matière

Particle Physics Reference Library

This third open access volume of the handbook series deals with accelerator physics, design, technology and operations, as well as with beam optics, dynamics and diagnostics. A joint CERN-Springer initiative, the “Particle Physics Reference Library” provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A,B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open acces

Computational Modelling of Concrete and Concrete Structures

Computational Modelling of Concrete and Concrete Structures contains the contributions to the EURO-C 2022 conference (Vienna, Austria, 23-26 May 2022). The papers review and discuss research advancements and assess the applicability and robustness of methods and models for the analysis and design of concrete, fibre-reinforced and prestressed concrete structures, as well as masonry structures. Recent developments include methods of machine learning, novel discretisation methods, probabilistic models, and consideration of a growing number of micro-structural aspects in multi-scale and multi-physics settings. In addition, trends towards the material scale with new fibres and 3D printable concretes, and life-cycle oriented models for ageing and durability of existing and new concrete infrastructure are clearly visible. Overall computational robustness of numerical predictions and mathematical rigour have further increased, accompanied by careful model validation based on respective experimental programmes. The book will serve as an important reference for both academics and professionals, stimulating new research directions in the field of computational modelling of concrete and its application to the analysis of concrete structures. EURO-C 2022 is the eighth edition of the EURO-C conference series after Innsbruck 1994, Bad Gastein 1998, St. Johann im Pongau 2003, Mayrhofen 2006, Schladming 2010, St. Anton am Arlberg 2014, and Bad Hofgastein 2018. The overarching focus of the conferences is on computational methods and numerical models for the analysis of concrete and concrete structures