27 research outputs found

    Selected Topics in Gravity, Field Theory and Quantum Mechanics

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    Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories

    Dynamical Tidal Response of Kerr Black Holes from Scattering Amplitudes

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    We match scattering amplitudes in point particle effective field theory (EFT) and general relativity to extract low frequency dynamical tidal responses of rotating (Kerr) black holes to all orders in spin. In the conservative sector, we study local worldline couplings that correspond to the time-derivative expansion of the black hole tidal response function. These are dynamical (frequency-dependent) generalizations of the static Love numbers. We identify and extract couplings of three types of subleading local worldline operators: the curvature time derivative terms, the spin - curvature time derivative couplings, and quadrupole - octupole mixing operators that arise due to the violation of spherical symmetry. The first two subleading couplings are non-zero and exhibit a classical renormalization group running; we explicitly present their scheme-independent beta functions. The conservative mixing terms, however, vanish as a consequence of vanishing static Love numbers. In the non-conservative sector, we match the dissipation numbers at next-to-leading and next-to-next-to leading orders in frequency. In passing, we identify terms in the general relativity absorption probabilities that originate from tails and short-scale logarithmic corrections to the lowest order dissipation contributions.Comment: 50 pages, 3 figures; comments are welcom

    Étude de la propagation acoustique en milieu complexe par des réseaux de neurones profonds

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    Abstract : Predicting the propagation of aerocoustic noise is a challenging task in the presence of complex mean flows and geometry installation effects. The design of future quiet propul- sion systems requires tools that are able to perform many accurate evaluations with a low computational cost. Analytical models or hybrid numerical approaches have tradition- ally been employed for that purpose. However, such methods are typically constrained by simplifying hypotheses that are not easily relaxed. Thus, the main objective of this thesis is to develop and validate novel methods for the fast and accurate prediction of aeroacoustic propagation in complex mean flows and geometries. For that, data-driven deep convolutional neural networks acting as auto-regressive spatio-temporal predictors are considered. These surrogates are trained on high-fidelity data, generated by direct aeroacoustic numerical solvers. Such datasets are able to model complex flow phenomena, along with complex geometrical parameters. The neural network is designed to substitute the high-fidelity solver at a much lower computational cost once the training is finished, while predicting the time-domain acoustic propagation with sufficient accuracy. Three test cases of growing complexity are employed to test the approach, where the learned surrogate is compared to analytical and numerical solutions. The first one corresponds to the two-dimensional propagation of Gaussian pulses in closed domains, which allows understanding the fundamental behavior of the employed convolution neural networks. Second, the approach is extended in order to consider a variety of boundary conditions, from non-reflecting to curved reflecting obstacles, including the reflection and scattering of waves at obstacles. This allows the prediction of acoustic propagation in configurations closer to industrial problems. Finally, the effects of complex mean flows is investigated through a dataset of acoustic waves propagating inside sheared flows. These applications highlight the flexibility of the employed data-driven methods using convolutional neural networks. They allow a significant acceleration of the acoustic predictions, while keeping an adequate accuracy and being also able to correctly predict the acoustic propagation outside the range of the training data. For that, prior knowledge about the wave propa- gation physics is included during and after the neural network training phase, allowing an increased control over the error performed by the surrogate. Among this prior knowledge, the conservation of physics quantities and the correct treatment of boundary conditions are identified as key parameters that improve the surrogate predictions.Prédire la propagation du bruit aéroacoustique est une tâche difficile en présence d’écoulements moyens complexes et d’effets géométriques d’installation. La conception des futurs systèmes de propulsion silencieux appelle au développement d’outils capables d’effectuer de nombreuses évaluations avec une faible erreur et un faible coût de calcul. Traditionnellement, des modèles analytiques ou des approches numériques hybrides ont été utilisés à cette fin. Cependant, ces méthodes sont généralement contraintes par des hypothèses simplificatrices qui ne sont pas facilement assouplies. Ainsi, l’objectif principal de cette thèse est de développer et de valider de nouvelles méthodes pour la prédiction rapide et précise de la propagation aéroacoustique dans des écoulements moyens et des géométries complexes. Pour cela, des réseaux de neurones profonds à convolution, entraînés sur des données, et agissant comme prédicteurs spatio-temporels sont considérés. Ces modèles par substitution sont entraînés sur des données de haute fidélité, générées par des solveurs numériques aérocoustiques directs. De telles bases de données sont capables de modéliser des phénomènes d’écoulement, ainsi que des paramètres géométriques complexes. Le réseau de neurones est conçu pour remplacer le solveur haute fidélité à un coût de calcul beaucoup plus faible une fois la phase d’entraînement terminée, tout en prédisant la propagation acoustique dans le domaine temporel avec une précision suffisante. Trois cas de test, de complexité croissante, sont utilisés pour tester l’approche, où le substitut appris est comparé à des solutions analytiques et numériques. Le premier cas correspond à la propagation acoustique bidimensionnelle dans des domaines fermés, où des sources impulsionnelles Gaussiennes sont considérées. Ceci permet de comprendre le comportement fondamental des réseaux de neurones à convolution étudiés. Deuxièmement, l’approche est étendue afin de prendre en compte une variété de conditions aux limites, notamment des conditions aux limites non réfléchissantes et des obstacles réfléchissants de géométrie arbitraire, modélisant la réflexion et la diffusion des ondes acoustiques sur ces obstacles. Cela permet de prédire la propagation acoustique dans des configurations plus proches des problématiques industrielles. Enfin, les effets des écoulements moyens complexes sont étudiés à travers une base de données d’ondes acoustiques qui se propagent à l’intérieur d’écoulements cisaillés. Ces applications mettent en évidence la flexibilité des méthodes basées sur les données, utilisant des réseaux de neurones à convolution. Ils permettent une accélération significative des prédictions acoustiques, tout en gardant une précision adéquate et en étant également capables de prédire correctement la propagation acoustique en dehors de la gamme de paramètres des données d’apprentissage. Pour cela, des connaissances préalables sur la physique de propagation des ondes sont incluses pendant et après la phase d’apprentissage du réseau de neurones, permettant un contrôle accru sur l’erreur effectuée par le substitut. Parmi ces connaissances préalables, la conservation des grandeurs physiques et le traitement correct des conditions aux limites sont identifiés comme des paramètres clés qui améliorent les prédictions du modèle proposé

    Instability and acoustics of compressible exponential boundary layer flows

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    In this thesis, inviscid instability and acoustics of compressible exponential boundary layer flows are investigated. Based on the linearised Euler equations (LEEs) and the normal-mode approach, the acoustic wave equation of parallel shear flows, the generalised Pridmore-Brown equation (PBE), is derived. For a boundary layer flow mimicked by an exponential velocity profile, an exact solution to the corresponding PBE is given in terms of the confluent Heun function (CHF). In the stability analyses, the eigenvalue equation for the stability problem based on the exact solution to the PBE is derived, and temporal stability and spatial stability are investigated respectively. For this, asymptotic analyses of the eigenvalue equation are first performed, and analytical solutions for limiting cases are obtained. Then, solutions to the eigenvalue equation are computed, which allow a comprehensive picture of the stability behaviour of the exponential boundary layer. In particular, the first three acoustic modes are computed as a function of the Mach number, the streamwise wavenumber, and the frequency. Unstable modes are found, where the first acoustic mode is always the most unstable one of all acoustic modes. Besides, an acoustic boundary layer thickness (ABLT) is defined, which essentially quantifies how far eigenfunctions reach into the area afar from the boundary layer. Meanwhile, wave angles, which describe the direction of the phase velocity, and eigenfunctions of acoustic modes are displayed. In the end, links between eigenvalues in the temporal stability and spatial stability problems are established. In the study of acoustics of boundary layer flows, the exact solution to the PBE is again employed to derive the reflection coefficient as a function of the Mach number, the streamwise wavenumber, and the incident angle of acoustic waves, and it is computed in wide parameter ranges. It is shown that the over-reflection of acoustic waves arises in boundary layer flows, i.e. the reflected amplitude of acoustic waves is greater than that of incident waves. The phenomenon is validated to be closely related to the critical layer, at which there is an optimal energy exchange from the base flow through the critical layer into the acoustic wave. Meanwhile, a special acoustic phenomenon, the resonant over-reflection, is observed and proved to be caused by the resonant frequency of unstable modes in the temporal stability problem. In addition, the resonant over-reflection also appears at resonant frequencies caused by higher unstable modes, but their over-reflection coefficients are always smaller than that caused by the first unstable mode. In the last part of the present work, the over-reflection of acoustic waves in a supersonic inviscid compressible boundary layer flow is validated by direct numerical simulations (DNS). A wave packet containing plane waves with constant wavelengths and amplitudes is superimposed with the free stream, and the incidence and reflection processes of the wave packet are simulated. In the simulations, the dispersion of the wave packet is observed due to strong shear effects near the wall. Amplification of the amplitude of the reflected waves is determined when the reflected wave eventually returns to the free stream. In particular, there is an exceptionally large over-reflection coefficient when the frequency of the incident wave is close to the resonant frequency, which indicates an occurrence of the resonant over-reflection

    Numerical Methods for Aeroacoustic Analysis of Turbomachines

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    Numerical simulations are important tools for developing new aircraft that can meet future needs. When numerical simulations are used to compute aircraft noise, a two-step procedure is often employed. In the first step, the noise sources are determined using, e.g., computational fluid dynamics. In the second step, noise propagation between the sources and the observers is then computed, often by solving an acoustic analogy. In this thesis, a range of numerical methods that are useful when turbomachinery tonal noise is computed based on such a two-step procedure are considered. For the first step, the time-domain Harmonic Balance method proposed by Hall et al. is used. To improve the accuracy of this method, the impact of time sampling on aliasing is investigated for both the single frequency and the multiple frequency problem. A new oversampling strategy for the multiple frequency problem is also developed for this purpose. Another challenge associated with the Harmonic Balance method is numerical instabilities. This problem is investigated using a von Neumann stability analysis. Based on knowledge gained from this analysis, a novel preconditioner that stabilizes an explicit Harmonic Balance solver is then developed. To minimize reflections of waves against boundaries of the computational domain, a generic formulation of the exact, nonlocal, nonreflecting boundary condition introduced by Giles is also derived and implemented to work with the Harmonic Balance method. For the second step, the convective Ffowcs Williams - Hawkings equation for permeable surfaces proposed by Najafi-Yazidi\ua0et al. is used. A detailed derivation of this equation is first presented. The solution to this equation for the case when the surface is stationary relative to the observer is then derived. Finally, a tool for computing duct modes based on a normal mode analysis of the linearized Euler equations is presented. In summary, the work reported in this thesis provides a detailed analysis of the aforementioned methods, that should be valuable for people who are interested in adopting them. It also provides some improvements, which can help to further improve the results obtained with these methods

    Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections

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    Gravitational waves emitted from the coalescence of neutron star binaries open a new window to probe matter and fundamental physics in unexplored, extreme regimes. To extract information about the supranuclear matter inside neutron stars and the properties of the compact binary systems, robust theoretical prescriptions are required. We give an overview about general features of the dynamics and the gravitational wave signal during the binary neutron star coalescence. We briefly describe existing analytical and numerical approaches to investigate the highly dynamical, strong-field region during the merger. We review existing waveform approximants and discuss properties and possible advantages and shortcomings of individual waveform models, and their application for real gravitational-wave data analysis.Comment: invited review for General Relativity and Gravitation; any comment or suggestion is welcom

    Hamiltonian regularisation of the unidimensional barotropic Euler equations

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    Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been introduced by Clamond and Dutykh. This system is Galilean invariant, linearly non-dispersive and conserves formally an H1H^1-like energy. In this paper, we generalise this regularisation for the barotropic Euler system preserving the same properties. We prove the local (in time) well-posedness of the regularised barotropic Euler system and a periodic generalised two-component Hunter-Saxton system. We also show for both systems that if singularities appear in finite time, they are necessary in the first derivatives

    Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles

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    We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic-sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties.Comment: 43 pages; 2 figures; To be published in Advances in Mathematics (2019

    On the numerical simulation of compressible flows

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    In this thesis, numerical tools to simulate compressible flows in a wide range of situations are presented. It is intended to represent a step forward in the scientific research of the numerical simulation of compressible flows, with special emphasis on turbulent flows with shock wave-boundary-layer and vortex interactions. From an academic point of view, this thesis represents years of study and research by the author. It is intended to reflect the knowledge and skills acquired throughout the years that at the end demonstrate the author’s capability of conducting a scientific research, from the beginning to the end, present valuable genuine results, and potentially explore the possibility of real world applications with tangible social and economic benefits. Some of the applications that can take advantage of this thesis are: marine and offshore engineering, combustion in engines or weather forecast, aerodynamics (automotive and aerospace industry), biomedical applications and many others. Nevertheless, the present work is framed in the field of compressible aerodynamics and gas combustion with a clear target: aerial transportation and engine technology. The presented tools allow for studies on sonic boom, drag, noise and emissions reduction by means of geometrical design and flow control techniques on subsonic, transonic and supersonic aerodynamic elements such as wings, airframes or engines. Results of such studies can derive in new and ecologically more respectful, quieter vehicles with less fuel consumption and structural weight reduction. We start discussing the motivation for this thesis in chapter one, which is placed into the upcoming second generation of supersonic aircraft that surely will be flying the skies in no more than 20 years. Then, compressible flows are defined and the equations of motion and their mathematical properties are presented. Navier Stokes equations arise from conservation laws, and the hyperbolic properties of the Euler equations will be used to develop numerical schemes. Chapter two is focused on the numerical simulation with Finite Volumes techniques of the compressible Navier-Stokes equations. Numerical schemes commonly found in the literature are presented, and a unique hybrid-scheme is developed that is able to accurately predict turbulent flows in all the compressible regimens (subsonic, transonic and supersonic). The scheme is applied on the flow around a NACA0012 airfoil at several Mach numbers, showing its ability to be used as a design tool in order to reduce drag or sonic boom, for example. At subsonic regimens, results show excellent agreement with reference data, which allowed the study of the same case at transonic conditions. We were able to observe the buffet phenomenon on the airfoil, which consists of shock-waves forming and disappearing, causing a dramatic loss of aerodynamic performance in a highly unsteady process. To perform a numerical simulation, however, boundary conditions are also required in addition to numerical schemes. A new set of boundary conditions is introduced in chapter three. They are developed for three-dimensional turbulent flows with or without shocks. They are tested in order to assess its suitability. Results show good performance for three-dimensional turbulent flows with additional advantages with respect traditional boundary conditions formulations. Unfortunately, compressible flows usually require high amounts of computational power to its simulation. High speeds and low viscosity result in very thin boundary layers and small turbulent structures. The grid required in order to capture this flow structures accurately often results in unfeasible simulations. This fact motivates the use of turbulent models and wall models in order to overcome this restriction. Turbulent models are discussed in chapter four. The Reynolds-Averaged Navier Stokes (RANS) approach is compared with Large-Eddy Simulation (LES) with and without wall modeling (WMLES). A transonic diffuser is simulated in order to evaluate its performance. Results showed the ability of RANS methods to capture shock-wave positions accurately, but failing in the detached part of the flow. LES, on the other hand, was not able to reproduce shock-waves positions accurately due to the lack of precision on the shock wave-boundary-layer interaction (SBLI). The use of a wall model, nevertheless, allowed to overcome this issue, resulting in an accurate method to capture shock-waves and also flow separation. More research on WMLES is encouraged for future studies on SBLIs, since they allow three-dimensional unsteady studies with feasible levels of computational requirements. With all these tools, we are able to solve at this point any problem concerned with the aerodynamic design of high-speed vehicles which were identified in previous paragraphs. Finally, multi-component flows are discussed in chapter five. Our hybrid scheme is upgraded to deal with multi-component gases and tested in several cases. We demonstrate that with a redefinition of the discontinuity sensor multi-components flows can be solved with low levels of diffusion while being stable in the presence of high scalar gradients. Because of the work of this thesis, a complete numerical approach to the numerical simulation of compressible turbulent multi-component flows with or without discontinuities in a wide range of Reynolds and Mach numbers is proposed and validated. Direct applications can be found in civil aviation (subsonic and supersonic) and engine operation.En aquesta tesis es presenten tècniques numèriques per a la simulació de compressibles en una gran varietat de situacions. L’objectiu és el de donar un pas endavant en la investigació científica de la simulació numèrica de fluids compressibles, amb especial èmfasi en fluxos turbulents amb interaccions entre ones de xoc, capa límit y vòrtex. Algunes de les aplicacions que es poden beneficiar d’aquesta investigació són: enginyeria marítima, combustió en motors, predicció meteorològica, aerodinàmica en la industria automotriu y aeronàutica, aplicacions biomèdiques y moltes altres. Tot i així, aquest treball s’emmarca en el camp de l’aerodinàmica compressible y la combustió de gasos amb un clar objectiu: el transport aeri i la tecnologia de motors. Les ferramentes presentades permeten l’estudi del sònic boom, resistència aerodinàmica, soroll y reducció d’emissions mitjançant el disseny geomètric i tècniques de control de flux en elements aerodinàmics tals com ales o motors en règims subsònics, transsònics i supersònics. Els resultats de tals estudis poden donar lloc a nous vehicles més ecològics, respectuosos amb el medi ambient, més silenciosos, amb menor peso estructural i menys consum de combustible.Postprint (published version
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