Diss. Techn. Hochschule Darmstadt. / Literaturverz.

Entre 1855 e 1862 o físico e fisiologista Hermann von Helmholtz dedicou-se primariamente a questões relativas à física e fisiologia acústicas, e à aplicação dos resultados obtidos à epistemologia da música e à estética musical. Ainda que tais investigações tenham sido desenvolvidas por período restrito, seus principais frutos cuja apresentação mais completa se encontra na obra de 1863 Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (que traduziríamos por A doutrina das sensações tonais como uma base fisiológica para a teoria da música) tiveram impacto imediato e duradouro sobre a musicologia ocidental. Em um primeiro momento, o presente trabalho objetiva analisar os antecedentes filosófico-científicos que orientaram tal empreitada, bem como a metodologia empregada na mesma; isso a fim de podermos, em um segundo momento, abordar criticamente a forma como Helmholtz aplica seus resultados ao âmbito da estética musical. Afinal, ao fixar deterministicamente causas físicas e fisiológicas para noções eurocêntricas de musicalidade, não estaria Helmholtz operando certa naturalização dos sistemas de organização tonal imperantes em sua conjuntura histórico-cultural em detrimento de sistemas oriundos de outros períodos e culturas, amiúde dotados de critérios distintos de ordenação sonora? O trabalho proposto ganha em complexidade na medida em que a musicologia de Helmholtz, particularmente em sua dimensão epistemológica, não se mostra inteiramente insensível a riscos dessa espécie. Assim, figura entre nossos objetivos avaliarmos em que medida tal musicologia, de grande rigor científico, é capaz de coexistir com sistemas musicais que escapem às diretrizes estéticas que busca naturalizar. Seríamos mesmo racionalmente compelidos a adotar, como parece tacitamente sugerir a obra de Helmholtz, uma espécie de hierarquia valorativa no que toca aos sistemas musicais de diferentes períodos e culturas? Dentre tais sistemas, seriam alguns verdadeiramente mais aptos que os demais em plasmar uma suposta musicalidade universal? Acreditamos que, por meio de investigação renovada do nó epistêmico presente na percepção musical na qual se veem entretecidas considerações de natureza física, fisiológica, psicológica e filosófica , algumas distinções possam ser esboçadas entre fatores determinantes necessários (físicos e fisiológicos e, portanto, transculturais) e contingentes (biográfico-culturais) da mesma, e o problema devidamente atacado. / In the second half of the nineteenth century, German physicist and physiologist Hermann von Helmholtz devoted himself to the investigation of questions pertaining to physical and physiological acoustics, and to the application of the results of said research to the epistemology of music and musical aesthetics. While such endeavors represent a relatively brief part of his career, the chief innovations they brought forth the most thorough presentation of which may be found in On the Sensations of Tone as a Physiological Basis for the Theory of Music (originally published in 1863) have had a lasting impact on the whole of Western musicology. An analysis of the philosophical and scientific foundations and methodological principles his investigations rested upon occupies the opening chapters of the present work. Subsequent chapters present, in addition, a critical assessment of the scientists problematic attempt to extend the reach of his results to the sphere of musical aesthetics. The following two questions are central to our efforts: by establishing material and physiological traits as an ultimate, deterministic ground for the criteria for sound classification and ordering prevalent in nineteenth-century European art music, was Helmholtz not arguing for the naturalization of the musical systems prevalent in his own historical and cultural juncture? And, should this indeed be the case, would such a naturalization not be accomplished to the detriment of musical systems employed in other cultures and/or historical periods, often based on distinct modes of classification and ordering? Ultimately, then, the central aim of the present work is to evaluate and discuss to what an extent the rigorous scientific component of a musicology such as Helmholtzs is able to coexist with musical systems that obey aesthetic principles other than the ones said musicology espouses. Are we indeed rationally compelled to adopt a value-based hierarchy in regards to the systems of different cultures and/or historical periods, as the scientists work appears to suggest? Are certain musical systems indeed more apt than others to actualize human musicality? We believe an investigation of the epistemic knot which characterizes musical perception a phenomenon in which physical, physiological, psychological and philosophical strands are intricately intertwined may allow us to advance a few preliminary distinctions between its necessary (physical and physiological, which is to say transcultural) and its contingent (cultural and biographical) determinants, and thus properly attack the problem.

L'interaction entre le vent solaire (VS) et la magnétosphère (MSP) terrestre se fait par l'intermédiaire de la magnétopause (MP). Le VS éjecté du Soleil, voyage transportant avec lui le champ magnétique interplanétaire (CMI). Ce dernier interagit avec le champ géomagnétique provoquant le phénomène de reconnexion magnétique (RM). La RM permet l'entrée d'une grande quantité de particules du VS dans la MSP. Si le CMI est dirigé vers le nord, la RM peut avoir lieu à haute latitude, mais n'est pas assez efficace pour justifier la quantité de plasma typique du VS, observée par les satellites à l'intérieur de la MSP. En outre, dans les cas où le CMI est dirigé vers le nord, la formation d'une couche de mélange est observée à basse latitude. Les tourbillons de Kelvin-Hemholtz (KH) fournissent un mécanisme efficace pour la formation d'une couche de mélange à la MP. Les simulations numériques montrent que l'évolution temporelle de l'instabilité de KH dépend fortement des profils initiales à grande échelle. La comparaison des données spatiales et des simulations numériques est donc d'une importance fondamentale dans ce contexte. Les principaux résultats obtenus au cours de ce travail sont la caractérisation de la turbulence à l'intérieur des tourbillons de KH, ainsi que des événements de RM à petite échelle; la sélection d'un événement où nous avons une combinaison des données des satellites avant et après KHI se développe; l'observation d'un décalage entre les profils de densité et de vitesse et constat que ce décalage initial entraîne une évolution différente de la simulations numériques qui est en accord avec les observations satellites. / Solar Wind (SW) and the Earth's magnetosphere interaction is mediated by the magnetopause. The SW carries with it the Interplanetary Magnetic Field (IMF) which interacts with northwards geomagnetic field lines causing magnetic reconnection (MR) events that make SW particles to be tranferred into the Earth's magnetosphere. If the IMF is directed northward, MR takes place at high latitude, but it is not efficient enough to justify the amount of SW plasma observed by satellites inside the magnetosphere. During northwards conditions one observe the formation of a wide boundary layer (BL) at the low latitude. This BL is thought to be driven by the the Kelvin-Helmholtz instability (KHI) , originating from the velocity shear between SW and the almost static near-Earth plasma. Numerical simulations (NS) have shown that the long time evolution of the KHI depends strongly on the initial large scale field profiles used as initial conditions. In order to make a further step towards the comprehension of this complex system, it is imperative to combine satellite data and NS. The idea here is to initialize NS by using in-situ observations of the main field profiles since only a correct initialization can reproduce the correct dynamics. The main results achieved in this work are: characterize the turbulence inside KH vortices and the small scale MR; select one event where there is a combination of a satellite measurements before and after KH develops, find that density and velocity profiles are shifted by a distance comparable to their shear lengths and that this initial shift cause a different evolution of the KHI leading to a final state in agreement with satellites observations.

L’objectif de ce travail est le développement de dispositifs de contrôle de la diffusion des ondes acoustiques à l’aide de surfaces hétérogènes, pour des applications à l’acoustique urbaine. Pour remplir cet objectif, deux méthodes sont employées. La première à l’aide d’une métasurface, la direction d’une onde réfléchie est contrôlée. La seconde étude concerne l’influence d’un traitement inhomogène aux parois d’un guide ouvert sur les effets conjoints ou compétitifs d’absorption, de confinement et de rayonnement de l’onde. Nous montrons expérimentalement la possibilité de dissimuler un objet disposé sur un mur pour une onde acoustique audible. Pour y parvenir, une métasurface composée de différents résonateurs de Helmholtz est conçue et est réalisée de façon à être la plus fine possible. Ces travaux sont réalisés dans le domaine fréquentiel mais également dans le domaine temporel, ce qui permet de mettre en avant le caractère large bande de la métasurface. Il est démontré numériquement et expérimentalement que la direction des ondes réfléchies peut être contrôlée. Enfin la dernière partie est consacrée à l’influence d’une paroi hétérogène sur la propagation d’une onde acoustique à l’intérieur d’une rue. Une rue pouvant être assimilée à un guide d’onde ouvert engendre donc des modes de propagation complexes, dus aux pertes par rayonnement. La présence d’un matériau poreux sur les parois d’un guide vient perturber fortement la localisation spatiale des modes, ce qui les rend plus ou moins fuyants. / The aim of this thesis is to develop a scheme for controling the propagation of acoustic waves using heteregenous surfaces. Its results can be applied in the field of urban acoustic. The thesis is composed of two sections, each of them employing a different method. The first section focuses on controling the direction of a reflected wave, using a metasurface. The second concentrates on the influence of an inconsistent treatment to the side of an open waveguide on the wave joint and competitive effects of absorption, confinement and radiation. Part one provides experimental evidence that it is possible to conceal an object placed on a wall from an audible acoustic wave. To prove it, the thinest possible metasurface was constructed with Helmholtz resonators. The experimental results were compared to a numerical study realized with finite elements. This work was made in both temporal and frequency domains, allowing to point out the wide frequency characteristics of the metasurface. The numerical and experimental results show that the direction of a reflected wave can, indeed, be controled. Part two analyse the impact of a heterogeneous wall on the spreadinf of an acoustic wave in a street. Due to radiation losses, the street produces complex ways of propagation. The presence of a porous material on a waveguide‘ side deeply disrupt the spatial location of these waves, making them more or less fleeting. In particular, depending on the position of the material in the street, certain waves will be more confined to the inside of the street, radiating less towards the open external environment. They are consequently, less cushioned.

<p>A method is developed for solving the two dimensional Helmholtz equation in a ductwith varying cross-section region bounded by a curved top and flat bottom, having oneregion inside. To compute the propagation of sound waves in a curved duct with a curvedinternal interface is difficult problem. One method is to transform the wave equation intoa solvable form and making the curved interface plane. To this end a local orthogonaltransformation is developed for the varying cross-sectional duct having one medium inside.This transformation is first used to make the curved top of the waveguide flat andto transform the Helmholtz equation into an initial value problem. Later on the local orthogonaltransformation is developed for a waveguide having two media inside with flattop, a flat bottom and a curved interface. This local orthogonal transformation is used toflatten the interface and also to transform the Helmholtz equation into a simple, solvableordinary differential equation. In this paper we present operator formulation for the partwith flat bottom and curved top including a curved interface. In the ordinary differentialequation with operators in coefficients, obtained after the transformation, all the operationsrelated to the transverse variable are treated as operators while the derivative withrespect to the range variable is kept.</p>

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L'entraînement sans surveillance efficace et inférence dans les modèles génératifs profonds reste un problème difficile. Une approche assez simple, la machine de Helmholtz, consiste à entraîner du haut vers le bas un modèle génératif dirigé qui sera utilisé plus tard pour l'inférence approximative. Des résultats récents suggèrent que de meilleurs modèles génératifs peuvent être obtenus par de meilleures procédures d'inférence approximatives. Au lieu d'améliorer la procédure d'inférence, nous proposons ici un nouveau modèle, la machine de Helmholtz bidirectionnelle, qui garantit qu'on peut calculer efficacement les distributions de haut-vers-bas et de bas-vers-haut. Nous y parvenons en interprétant à les modèles haut-vers-bas et bas-vers-haut en tant que distributions d'inférence approximative, puis ensuite en définissant la distribution du modèle comme étant la moyenne géométrique de ces deux distributions. Nous dérivons une borne inférieure pour la vraisemblance de ce modèle, et nous démontrons que l'optimisation de cette borne se comporte en régulisateur. Ce régularisateur sera tel que la distance de Bhattacharyya sera minisée entre les distributions approximatives haut-vers-bas et bas-vers-haut. Cette approche produit des résultats de pointe en terme de modèles génératifs qui favorisent les réseaux significativement plus profonds. Elle permet aussi une inférence approximative amérliorée par plusieurs ordres de grandeur. De plus, nous introduisons un modèle génératif profond basé sur les modèles BiHM pour l'entraînement semi-supervisé. / Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better generative models can be obtained with better approximate inference procedures. Instead of improving the inference procedure, we here propose a new model, the bidirectional Helmholtz machine, which guarantees that the top-down and bottom-up distributions can efficiently invert each other. We achieve this by interpreting both the top-down and the bottom-up directed models as approximate inference distributions and by defining the model distribution to be the geometric mean of these two. We present a lower-bound for the likelihood of this model and we show that optimizing this bound regularizes the model so that the Bhattacharyya distance between the bottom-up and top-down approximate distributions is minimized. This approach results in state of the art generative models which prefer significantly deeper architectures while it allows for orders of magnitude more efficient approximate inference. Moreover, we introduce a deep generative model for semi-supervised learning problems based on BiHM models.

A method is developed for solving the two dimensional Helmholtz equation in a ductwith varying cross-section region bounded by a curved top and flat bottom, having oneregion inside. To compute the propagation of sound waves in a curved duct with a curvedinternal interface is difficult problem. One method is to transform the wave equation intoa solvable form and making the curved interface plane. To this end a local orthogonaltransformation is developed for the varying cross-sectional duct having one medium inside.This transformation is first used to make the curved top of the waveguide flat andto transform the Helmholtz equation into an initial value problem. Later on the local orthogonaltransformation is developed for a waveguide having two media inside with flattop, a flat bottom and a curved interface. This local orthogonal transformation is used toflatten the interface and also to transform the Helmholtz equation into a simple, solvableordinary differential equation. In this paper we present operator formulation for the partwith flat bottom and curved top including a curved interface. In the ordinary differentialequation with operators in coefficients, obtained after the transformation, all the operationsrelated to the transverse variable are treated as operators while the derivative withrespect to the range variable is kept.

In the modern world, because of increasing oil prices and the need to control greenhouse gas emission, a new interest in the production of electric cars is coming about. One of the products is a charging point for electric cars, at which electric cars can be recharged by a plug in cable. Usually people are required to pay for the electricity after recharging the electric cars. Today, the payment is handled by using SMS or through the parking system. There is now an opportunity, in cooperation with AES (the company with which we are working), to equip the pole with GPRS, and this requires development and maintenance of the antenna. The project will include data analysis of the problem, measurements and calculations. In this work, we are computing energy flow of the wave due to the location of the antenna inside the box. We need to do four steps. First, we take a set of points (determined by the computational mesh) that have the same distance from the antenna in the domain. Second, we calculate the angles between the ground and the points in the set. Third, we do an angle-energy plot, to analyse which angle can give the maximum energy. And last, we need to compare the maximum energy value of different position of the antenna. We are going to solve the problem in Matlab, based on the Maxwell equation and the Helmholtz equation, which is not time-dependent.

We consider computation of resonances in open systems and acoustic scattering problems. These problems are posed on an unbounded domain and domain truncation is required for the numerical computation. In this paper, a perfectly matched layer (PML) technique is proposed for computation of solutions to the unbounded domain problems. For resonance problems, resonance functions are characterized as improper eigenfunction (non-zero solutions of the eigenvalue problem which are not square integrable) of the Helmholtz equation on an unbounded domain. We shall see that the application of the spherical PML converts the resonance problem to a standard eigenvalue problem on the infinite domain. Then, the goal will be to approximate the eigenvalues first by replacing the infinite domain by a finite computational domain with a convenient boundary condition and second by applying finite elements to the truncated problem. As approximation of eigenvalues of problems on a bounded domain is classical [12], we will focus on the convergence of eigenvalues of the (continuous) PML truncated problem to those of the infinite PML problem. Also, it will be shown that the domain truncation does not produce spurious eigenvalues provided that the size of computational domain is sufficiently large. The spherical PML technique has been successfully applied for approximation of scattered waves [13]. We develop an analysis for the case of a Cartesian PML application to the acoustic scattering problem, i.e., solvability of infinite and truncated Cartesian PML scattering problems and convergence of the truncated Cartesian PML problem to the solution of the original solution in the physical region as the size of computational domain increases.