Das Ziel dieser Arbeit ist, drei Werke aus verschiedenen Epochen der deutschen Literaturgeschichte zu analysieren: Der Sandmann (1816), von ETA Hoffmann, Der Sandmann (1992), von Bodo Kirchhoff und Wolfgang Herrndorfs Sand (2011). Die Beziehungen zwischen ihnen können auf drei Ebenen festgestellt werden: auf der Narratologischen, auf der thematisch/metaphorischen Ebene und auf der der Identität. Die erste Ebene bezieht sich auf die Gemeinsamkeiten aus einer strukturellen Sichtweise als Metafiktion, Multiperspektivität und wechselnde Stimmen, die die Elemente des unzuverlässigen Effekts des Erzählers erzeugen. Auf der thematisch/metaphorische Ebene kann das Visuelle dem Sand-Element zugeschrieben werden, sowohl als konstitutives Element der Wüste, in der Luftspiegelungen geschehen, als auch als Sand-Korn in den Augen, was zu der Metapher der verzerrten oder erfundenen Visionen konvergiert. Zum Dritten bezieht sich die Identitätsebene vor allem auf die Konstruktion von Identität durch die Sicht der Anderen, die in den Büchern einem Zusammenbruch des Ichs gleichkommt, indem das Ich sich destabilisiert und kollabiert. Die Protagonisten dieser Werke repräsentieren vor allem den Menschen als ein unwiderrufliches Subjekt des Werdens. / Esta dissertação tem como propósito analisar três obras de diferentes momentos na história literária alemã: O homem de areia (1816) de E.T.A Hoffmann, O homem de areia (1992) de Bodo Kirchhoff e Areia (2011) de Wolfgang Herrndorf. O relacionamento entre elas se dá em três níveis distintos: narratológico, temático/metafórico e identitário. O primeiro refere-se aos pontos em comum do ponto de vista estrutural, como a metaficção, a multiperspectividade e a alternância de vozes, que são elementos generativos do efeito inconfiável dos narradores. No plano temático/ metafórico, podem se arrolar a questão visual atribuída ao elemento da areia que, tanto como elemento constitutivo do deserto, onde miragens acontecem, quanto como um grão intruso nos olhos, converge para a metáfora da visão distorcida ou inventada. Por último, o nível identitário refere-se, especialmente, à construção da identidade a partir do olhar do outro, o que nos livros ocorre como um colapso, em que o eu se desestabiliza, resultando assim na sucumbência. Os protagonistas destas obras representam, sobretudo, o homem como sujeito irrevogável do devir.

Das Ziel dieser Arbeit ist, drei Werke aus verschiedenen Epochen der deutschen Literaturgeschichte zu analysieren: Der Sandmann (1816), von ETA Hoffmann, Der Sandmann (1992), von Bodo Kirchhoff und Wolfgang Herrndorfs Sand (2011). Die Beziehungen zwischen ihnen können auf drei Ebenen festgestellt werden: auf der Narratologischen, auf der thematisch/metaphorischen Ebene und auf der der Identität. Die erste Ebene bezieht sich auf die Gemeinsamkeiten aus einer strukturellen Sichtweise als Metafiktion, Multiperspektivität und wechselnde Stimmen, die die Elemente des unzuverlässigen Effekts des Erzählers erzeugen. Auf der thematisch/metaphorische Ebene kann das Visuelle dem Sand-Element zugeschrieben werden, sowohl als konstitutives Element der Wüste, in der Luftspiegelungen geschehen, als auch als Sand-Korn in den Augen, was zu der Metapher der verzerrten oder erfundenen Visionen konvergiert. Zum Dritten bezieht sich die Identitätsebene vor allem auf die Konstruktion von Identität durch die Sicht der Anderen, die in den Büchern einem Zusammenbruch des Ichs gleichkommt, indem das Ich sich destabilisiert und kollabiert. Die Protagonisten dieser Werke repräsentieren vor allem den Menschen als ein unwiderrufliches Subjekt des Werdens. / Esta dissertação tem como propósito analisar três obras de diferentes momentos na história literária alemã: O homem de areia (1816) de E.T.A Hoffmann, O homem de areia (1992) de Bodo Kirchhoff e Areia (2011) de Wolfgang Herrndorf. O relacionamento entre elas se dá em três níveis distintos: narratológico, temático/metafórico e identitário. O primeiro refere-se aos pontos em comum do ponto de vista estrutural, como a metaficção, a multiperspectividade e a alternância de vozes, que são elementos generativos do efeito inconfiável dos narradores. No plano temático/ metafórico, podem se arrolar a questão visual atribuída ao elemento da areia que, tanto como elemento constitutivo do deserto, onde miragens acontecem, quanto como um grão intruso nos olhos, converge para a metáfora da visão distorcida ou inventada. Por último, o nível identitário refere-se, especialmente, à construção da identidade a partir do olhar do outro, o que nos livros ocorre como um colapso, em que o eu se desestabiliza, resultando assim na sucumbência. Os protagonistas destas obras representam, sobretudo, o homem como sujeito irrevogável do devir.

Cette thèse porte sur la méthode du gradient topologique appliquée au traitement d'images. Principalement, on s'intéresse à la détection d'objets assimilés, soit à des contours si l'intensité de l'image à travers la structure comporte un saut, soit à une structure fine (filaments et points en 2D) s'il n'y a pas de saut à travers la structure. On commence par généraliser la méthode du gradient topologique déjà utilisée en détection de contours pour des images dégradées par du bruit gaussien, à des modèles non linéaires adaptés à des images contaminées par un processus poissonnien ou du bruit de speckle et par différents types de flous. On présente également un modèle de restauration par diffusion anisotrope utilisant le gradient topologique pour un domaine fissuré. Un autre modèle basé sur une EDP elliptique linéaire utilisant un opérateur anisotrope préservant les contours est proposé. Ensuite, on présente et étudie un modèle de détection de structures fines utilisant la méthode du gradient topologique. Ce modèle repose sur l'étude de la sensibilité topologique d'une fonction coût utilisant les dérivées secondes d'une régularisation de l'image solution d'une EDP d'ordre 4 de type Kirchhoff. En particulier on explicite les gradients topologiques pour des domaines 2D fissurés ou perforés, et des domaines 3D fissurés. Plusieurs applications pour des images 2D et 3D, floutées et contaminées par du bruit gaussien, montrent la robustesse et la rapidité de la méthode. Enfin on généralise notre approche pour la détection de contours et de structures fines par l'étude de la sensibilité topologique d'une fonction coût utilisant les dérivées m−ième d'une régularisation de l'image dégradée, solution d'une EDP d'ordre 2m. / This thesis deals with the topological gradient method applied in imaging. Particularly, we are interested in object detection. Objects can be assimilated either to edges if the intensity across the structure has a jump, or to fine structures (filaments and points in 2D) if there is no jump of intensity across the structure. We generalize the topological gradient method already used in edge detection for images contaminated by Gaussian noise, to quasi-linear models adapted to Poissonian or speckled images possibly blurred. As a by-product, a restoration model based on an anisotropic diffusion using the topological gradient is presented. We also present a model based on an elliptical linear PDE using an anisotropic differential operator preserving edges. After that, we study a variational model based on the topological gradient to detect fine structures. It consists in the study of the topological sensitivity of a cost function involving second order derivatives of a regularized version of the image solution of a PDE of Kirchhoff type. We compute the topological gradients associated to perforated and cracked 2D domains and to cracked 3D domains. Many applications performed on 2D and 3D blurred and Gaussian noisy images, show the robustness and the fastness of the method. An anisotropic restoration model preserving filaments in 2D is also given. Finally, we generalize our approach by the study of the topological sensitivity of a cost function involving the m − th derivatives of a regularization of the image solution of a 2m order PDE.

Après une présentation des notations usuelles de la théorie des graphes, on étudie l'ensemble des fonctions harmoniques sur les graphes, c'est à dire des fonctions dont le laplacien est nul. Ces fonctions forment un espace vectoriel et sur un graphe uniformément localement fini, on montre que cet espace vectoriel est soit de dimension un, soit de dimension infinie. Lorsque le graphe comporte une infinité de cycles, ce résultat tombe en défaut et on exhibe des exemples qui montrent qu'il existe un graphe sur lequel les harmoniques forment un espace vectoriel de dimension n, pour tout n. Un exemple de graphe périodique est également traité. Ensuite, toujours pour le laplacien, on étudie plus précisément sur les arbres uniformément localement finis les valeurs propres dont l'espace propre est de dimension infini. Dans ce cas, il est montré que l'espace propre contient un sous-espace isomorphe à l'ensemble des suites réelles bornées. Une inégalité concernant le spectre est donnée dans le cas spécial où les arêtes sont de longueur un. Des exemples montrent que ces inclusions sont optimales. Dans le chapitre suivant, on étudie le comportement asymptotique des valeurs propres pour des opérateurs elliptiques d'ordre 2 quelconques sous des conditions de Kirchhoff dynamiques. Après réécriture du problème sous la forme d'un opérateur de Sturm-Liouville, on écrit le problème de façon matricielle. Puis on trouve une équation caractéristique dont les zéros correspondent aux valeurs propres. On en déduit une formule pour l'asymptotique des valeurs propres. Dans le dernier chapitre, on étudie la stabilité de solutions stationnaires pour certains problèmes de réaction-diffusion où le terme de non linéarité est polynomial. / After a quick presentation of usual notations for the graph theory, we study the set of harmonic functions on graphs, that is, the functions whose laplacian is zero. These functions form a vectorial space. On a uniformly locally finite tree, we shaw that this space has dimension one or infinity. When the graph has an infinite number of cycles, this result change and we describe some examples showing that there exists a graph on which the harmonic functions form a vectorial space of dimension n, for all n. We also treat the case of a particular periodic graph. Then, we study more precisely the eigenvalues of infinite dimension. In this case, the eigenspace contains a subspace isomorphic to the set of bounded sequences. An inequality concerning the spectral is given when edges length is equal to one. Examples show that these inclusions are optimal. We also study the asymptotic behavior of eigenvalues for elliptic operators under dynamical Kirchhoff node conditions. We write the problem as a Sturm-Liouville operator and we transform it in a matrix problem. Then we find a characteristic equation whose zeroes correspond to eigenvalues. We deduce a formula for the asymptotic behavior. In the last chapter, we study the stability of stationary solutions for some reaction-diffusion problem whose the non-linear term is polynomial.

Transportation is the main source of environmental noise in Europe, with an estimated 125 million people affected by excessive noise levels from road traffic, causing a burden of noise related diseases and having a substantial economic impact on society. In order to reduce exposure to high levels of traffic noise, two approaches are the topic of extensive research: preventing sound from propagating from roads and railways using for example noise barriers, and reducing the sources of noise themselves. The second solution, which addresses directly the cause of the problem, requires improved design methods, with a more systematic resort to multi-functional design. Addressing cross-functions simultaneously reduces the number of design iterations and the high cost of prototyping. The work presented in this thesis aims at developing methods that can be used to design quieter vehicle concepts within a multi-functional approach, and is articulated around two main axis of research, aerodynamic sound generation and sound propagation. The first axis aims at performing an aeroacoustic analysis to predict aerodynamic sound sources. A hybrid method is used on the example of a type of submerged air inlet called a NACA duct, where the near-field flow is solved through detached eddy simulation (DES) and where the far-field acoustics is computed using the Ffowcs Williams and Hawkings integral. Results for the flow for various operating conditions are presented and validated against experimental data from the literature, with very good agreement. Far-field acoustic results are shown, exhibiting levels and components that are strongly dependent on the operating conditions. This analysis gives a framework for future aeroacoustic analysis in the project, and sets the path for the development of air inlets with improved aerodynamic and aeroacoustic characteristics. The second axis focuses on the propagation of sound from a given source, moving in an urban environment. An approximate boundary method is presented, which relies on the Kirchhoff approximation applied to the Kirchhoff-Helmholtz integral equation. Using this approximation speeds up the computational time compared to using a regular boundary element method. The resulting expression is extended to account for multiple scattering through consecutive updates of the surface pressures, and for moving sources through the introduction of a retarded time and of a Doppler shift. Validation tests for this method are presented, from simple scatterers to a more realistic configuration, showing good agreement with analytical, experimental and simulated work. / Fordon är den främsta källan till bullerexponering i Europa med uppskattningsvis 125 miljoner människor som är utsatta för höga ljudnivåer från vägtrafik, vilket kan orsaka bullerrelaterade häsloproblem samt har en betydande ekonomisk effekt på samhället. För att minska exponeringen för höga ljudnivåer från fordon, finns det två angreppssätt som båda idag är ämne för omfattande forskning: att förhindra ljudutbredning från vägar och järnvägar (till exempel med hjälp av bullerskydd), samt att minska ljudnivån från olika bullerkällor. Den sistnämnda, som direkt riktar sig till problemets orsak, kräver förbättrade designmetoder med mer systematisk användning av multifunktionell design. Att hantera flera funktioner hos fordonet samtidigt minskar antalet designiterationer och den höga kostnaden för prototyper. Arbetet som presenteras i denna avhandling syftar till att utveckla metoder som kan användas för att utforma tystare fordonskoncept inom ramen för en multifunktionell strategi och fokuserar på två spår i forskningen: aerodynamisk ljudalstring och ljudutbredning från rörliga källor. Det första spåret i forskningen syftar till att utföra en aeroakustisk undersökning för att modellera aerodynamiska ljudkällor. En hybridmetod tillämpas på ett typ av nedsänkt luftintag, kallat NACA-intag, där källområdet i strömningen löses genom detached eddy simulation (DES) och akustiken i fjärrfältet beräknas enligt Ffowcs Williams och Hawkings integral. Resultat för strömningen för olika driftförhållanden presenteras och valideras mot experimentella data från litteraturen, med mycket god överensstämmelse. Resultat för det akustika fjärrfältet visas, vilket uppvisar nivåer och komponenter som är starkt beroende av driftförhållandena. Denna analys ger en ram för kommande analyser av aeroakustik inom projektet och visar vägen för utvecklingen av luftintag med förbättrade aerodynamiska och aeroakustika egenskaper. Det andra spåret i forskningsprojektet är inriktat på ljudets utbredning från en given källa som rör sig i en urban miljö. En approximativ randvärdesmetod presenteras som bygger på Kirchhoff approximation tillämpad på Kirchhoff-Helmholtz integralekvation. Med hjälp av denna approximation minskas beräkningstiden jämfort med vanlig boundary element method (BEM). Modellen utvecklas sedan för att kunna hantera flera reflektioner genom att det akustiska trycket på ytorna uppdateras för varje reflektion samt för att kunna hantera rörliga källor genom att introducera tidsfördröjningar och Dopplerförskjutning. Validering för denna modell presenteras, från enkla spridare till en mer realistisk urban konfiguration, som visar god överensstämmelse med analytiskt, experimentellt och simulerat data. / <p>QC 20151002</p>

In the thesis explicit dual parabolic-elliptic models are constructed for the Konenkov flexural edge wave and the Stoneley-type flexural interfacial wave in case of thin linearly elastic plates. These waves do not appear in an explicit form in the original equations of motion within the framework of the classical Kirchhoff plate theory. The thesis is aimed to highlight the contribution of the edge and interfacial waves into the overall displacement field by deriving specialised equations oriented to aforementioned waves only. The proposed models consist of a parabolic equation governing the wave propagation along a plate edge or plate junction along with an elliptic equation over the interior describing decay in depth. In this case the parabolicity of the one-dimensional edge and interfacial equations supports flexural wave dispersion. The methodology presented in the thesis reveals a dual nature of edge and interfacial plate waves contrasting them to bulk-type wave propagating in thin elastic structures. The thesis tackles a number of important examples of the edge and interfacial wave propagation. First, it addresses the propagation of Konenkov flexural wave in an elastic isotropic plate under prescribed edge loading. For the latter, parabolic-elliptic explicit models were constructed and thoroughly investigated. A similar problem for a semi-infinite orthotropic plate resulted in a more general dual parabolic-elliptic model. Finally, an anal- ogous model was derived and analysed for two isotropic semi-infinite Kirchhoff plates under perfect contact conditions.

Corrosion often occurs in the inner aluminum lining of the HB-53 helicopter external fuel tank, resulting in fuel leaks. This project centers on developing an in-situ ultrasonic inspection technique to detect corroded areas inside the fuel tank. Due to the complexity of the composite structure of the tank, the ultrasonic inspection is carried out from inside the tank using a monostatic backscattering technique. The backscattered field contains information related to the insonified surface properties (surface roughness scales). Numerical predictions are implemented with a simplified model of backscattered intensity (Ogilvy, 1991). Experimental results are obtained on artificially corroded plates, and on the actual fuel tank of the HB-53 helicopter. Signal processing techniques (Envelope Correlation and Inverse Technique) are used to detect corroded surfaces with data obtained with a focused 10 MHz pulsed transducer.

As improving the performance of turbofan designs becomes increasingly difficult, manufacturers are looking to new technologies for the next generation of jet engines. An 'open rotor' replaces the fan of the turbofan with a set of external rotors. This has the potential to offer a significant improvement in propulsive efficiency, but the design for low noise is a key challenge. Hence, high fidelity noise prediction methods are needed to accurately predict and compare the noise of different designs. This thesis focuses on one set of methods based on the Ffowcs Williams-Hawkings (\fwh) equation. This equation is considered to be the most realistic description of aeroacoustic noise generation, as it is a direct rearrangement of the Navier-Stokes equations. The \fwh\ equation is difficult to solve for realistic test cases such as an open rotor, and is susceptible to several types of error. This thesis categorises these errors as ``input'', ``neglection'' and ``discretisation'' errors. Discretisation errors arise from the need to integrate a discretised source field for the total noise, neglection errors result from needing to ignore part of the source field for practical reasons, and input errors relate to any errors caused by inaccurate input to the solver. The fundamental motivation of this thesis is to advance the understanding of neglection and discretisation errors and how they can be mitigated, in order to develop best practice solvers and methodologies for application to open rotors. Dimensional analysis is combined with analytical flow solutions to develop a process for isolating and quantifying discretisation errors. This process is used to study a wide range of solver methodologies and select a best practice solver methodology for open rotor noise prediction. This first-of-a-kind study produces a solver methodology that reduces discretisation errors by an order of magnitude compared to an industry standard solver. Previous research into neglection errors has shown that avoiding density perturbations in acoustic source terms can be beneficial. This thesis uses a generic aeroacoustic analogy to provide a new, physically intuitive method of incorporating a surface discontinuity that enables density perturbations to be avoided in a far more elegant manner than previous research. The above method improvements are investigated using a modern open rotor rig test case. The results demonstrate that discretisation and neglection errors can be severe in realistic cases and the potential of the method improvements to significantly mitigate them.

A Matlab numerical model for scattering simulation was proposed based on the solution derived from the Beckmann-Kirchhoff scalar theory of scattering of electromagnetic waves from rough surfaces. A series of various synthetic surface samples were obtained using the open source software Gwyddion on which numerical simulations of scattering were carried out. The validity of this numerical model was tested and compared with experimental results.

We describe a preconditioner for the Kirchhoff plate equation for use of Bogner-Fox-Schmidt finite elements based on a hierarchical technique.