Conditions transparentes pour la diffraction d'ondes en milieu élastique anisotrope

This thesis is motivated by the numerical simulation of Non Destructive Testing by ultrasonic waves. It aims at designing a method to compute by Finite Element (EF) the diffraction of elastic waves in time-harmonic regime by a bounded defect in an anisotropic plate. The goal is to take into account an infinite plate and to restrict the FE calculations to a bounded area. This point is difficult due to the anisotropy and, in particular, methods such as perfectly matched layers fail.In this thesis, we have mainly considered two-dimensional cases that enabled us to implement the main ingredients of a method designed for the three-dimensional case of the plate. The first part deals with the diffraction problem in an infinite strip. The classical approach consists in writing transparent conditions by matching on a boundary the displacement and the axial stress using a modal expansion in the safe part of the plate, and the FE representation in the perturbed area. We have shown the interest of imposing these matching conditions on two separated boundaries, by introducing an overlap between the modal domain and the FE domain. Thus, we can take advantage of the bi-orthogonality relations valid for general anisotropy, and also improve the rate of convergence of iterative methods of resolution. In the second part, that represents the main part of the thesis, we discuss the diffraction problem in an anisotropic medium infinite in the two directions.The key idea is that we can express the solution (via the Fourier transform) in a half-plane given its trace on the boundary. Therefore, the approach consists in coupling several analytical representations of the solution in half-planes surrounding the defect (at least 3) with the FE representation. The difficulty is to ensure that all these representations match, in particular in the infinite intersections of the half-planes. It leads to a formulation which couples, via integral operators, the solution in a bounded domain including the defect, and its traces on the edge of the half-planes. The approximation releases a truncation and a discretization both in space and Fourier variables.For each of these two parts, the methods have been implemented and validated with a C++ code developed during the thesis, first in the scalar acoustic case, and then in the elastic case. Cette thèse est motivée par la simulation numérique du Contrôle Non Destructif par ultrasons. Elle vise à concevoir une méthode de calcul par éléments finis (EF) de la diffraction d’ondes élastiques harmoniques en temps par un défaut borné dans une plaque anisotrope infinie. L'objectif est de tenir compte du caractère non borné de la plaque tout en restreignant les calculs EF à une zone bornée autour du défaut. Ce point est difficile en raison de l'anisotropie, et, en particulier, les méthodes de type couches absorbantes parfaitement adaptées sont inopérantes. Dans cette thèse, nous avons considéré principalement des cas bidimensionnels plus simples qui nous ont permis de mettre en place les ingrédients essentiels d'une méthode destinée au cas tridimensionnel de la plaque. La première partie traite du problème de diffraction dans une bande infinie. L'approche classique consiste à écrire des conditions transparentes en raccordant sur une frontière le déplacement et la contrainte axiale exprimés à l'aide des modes de la plaque dans les parties saines d'une part, et des EF dans la zone perturbée d'autre part. Nous avons mis en évidence l'intérêt d'écrire ces raccords sur deux frontières séparées en introduisant un recouvrement entre le domaine modal et EF. Nous pouvons ainsi exploiter les relations de bi-orthogonalité valables pour une anisotropie arbitraire, et également accélérer la convergence des méthodes itératives de résolution. Dans la seconde partie, qui constitue le cœur de la thèse, nous avons étudié le problème de diffraction dans un milieu anisotrope infini dans les deux directions. L'idée clé est que l'on peut exprimer (via la transformée de Fourier) la solution dans un demi-plan en fonction de sa trace sur son bord. Ainsi, l'approche consiste à coupler plusieurs représentations analytiques de la solution dans des demi-plans entourant le défaut (au moins 3) avec la représentation EF. La difficulté est d'assurer la compatibilité de ces représentations, en particulier dans les intersections infinies des demi-plans. Cela nous conduit à une reformulation couplant, via des opérateurs intégraux, à la fois la solution dans un domaine borné contenant le défaut, et ses traces sur les bords des demi-plans. Numériquement, une troncature et une discrétisation dans les variables d'espace et de Fourier sont nécessaires.Pour chacune de ces deux parties, les méthodes ont été implémentées et validées à l'aide d'un code C++ développé pendant la thèse, d'abord dans le cas scalaire acoustique plus simple, puis dans le cas de l'élasticité

Australian Dixidae [Dipt.]

Previously nothing was known of the representatives of this family in Australia except a record of Skuse saying that he knew three species belonging to the genus Dixa in New South Wales; they remained, however, undescribed, and I have been unable to find the specimens in his collection, preserved pro parte in the Australian Museum in Sydney and pro parte in the Macleay Museum in Sydney University. During a short stay in New South Wales and Victoria and one summer spent in Tasmania, I found five species of Dixa, and recently Mr. A. J. Nicholson discovered another in New South Wales, which he kindly gave me for study, for which loan I am much obliged to him. These Australian species indubitably belong to the genus Dixa, as they differ very little from the forms of the rest of the world; like them, they are differentiated from each other by mere details of colouration, relative length of antenna, peculiarities of venation such as the position of r-m and relative length of fork of R2,3 and chiefly by the structure of the hypopygium. André Léon Tonnoir (9 April 1885 - 30 January 1940), was a Belgian entomologist

Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides

International audienceWe consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite straight isotropic elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with or without an overlap between the domains. Specific transmission conditions are used, so that only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using the Fraser bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized, in particular for the extension to the anisotropic case. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time

The Halfspace Matching Method : a new method to solve scattering problem in infinite media

International audienceWe are interested in acoustic wave propagation in time harmonic regime in a two-dimensional medium which is a local perturbation of an infinite isotropic or anisotropic homogeneous medium. We investigate the question of finding artificial boundary conditions to reduce the numerical computations to a neighborhood of this perturbation. Our objective is to derive a method which can extend to the anisotropic elastic problem for which classical approaches fail. The idea consists in coupling several semi-analytical representations of the solution in halfspaces surrounding the defect with a Finite Element computation of the solution around the defect. As representations of the same function, they have to match in the infinite intersections of the halfspaces. It leads to a formulation which couples, via integral operators, the solution in a bounded domain including the defect and its traces on the edge of the halfspaces. A stability property is shown for this new formulation

Morphology of powerful suction organs from blepharicerid larvae living in raging torrents

BackgroundSuction organs provide powerful yet dynamic attachments for many aquatic animals, including octopus, squid, remora, and clingfish. While the functional morphology of suction organs from some cephalopods and fishes has been investigated in detail, there are only few studies on such attachment devices in insects. Here we characterise the morphology and ultrastructure of the suction attachment organs of net-winged midge larvae (genus Liponeura; Diptera: Blephariceridae) – aquatic insects that live on rocks in rapid alpine waterways where flow speeds can reach 3 m s− 1 – using scanning electron microscopy, confocal laser scanning microscopy, and X-ray computed micro-tomography (micro-CT). Furthermore, we study the function of these organs in vivo using interference reflection microscopy.ResultsWe identified structural adaptations important for the function of the suction attachment organs in L. cinerascens and L. cordata. First, a dense array of spine-like microtrichia covering each suction disc comes into contact with the substrate upon attachment, analogous to hairy structures on suction organs from octopus, clingfish, and remora fish. These spine-like microtrichia may contribute to the seal and provide increased shear force resistance in high-drag environments. Second, specialised rim microtrichia at the suction disc periphery were found to form a continuous ring in close contact and may serve as a seal on a variety of surfaces. Third, a V-shaped cut on the suction disc (“V-notch“) is actively opened via two cuticular apodemes inserting on its flanks. The apodemes are attached to dedicated V-notch opening muscles, thereby providing a unique detachment mechanism. The complex cuticular design of the suction organs, along with specialised muscles that attach to them, allows blepharicerid larvae to generate powerful attachments which can withstand strong hydrodynamic forces and quickly detach for locomotion.ConclusionThe suction organs from Liponeura are underwater attachment devices specialised for resisting extremely fast flows. Structural adaptations from these suction organs could translate into future bioinspired attachment systems that perform well on a wide range of surfaces

Scanning tunneling spectroscopy study of epitaxial graphene on superconducting rhenium

Obtenir une interface transparente entre le graphène et un supraconducteur s'est révélé être difficile et pourtant essentiel pour induire des corrélations supraconductrices dans le graphène par effet de proximité. Cette thèse présente une étude par spectroscopie tunnel (STS) à très basse température (50 mK) d'un système nouveau qui réalise ce bon couplage électronique en faisant croitre du graphène par épitaxie sur du rhénium supraconducteur. La fabrication et sélection des films minces de rhénium de haute qualité cristalline sont brièvement expliquées, suivies par le procédé de croissance CVD du graphène sur divers métaux et en particulier sur du rhénium. Les images topographiques obtenues par STM révèlent un moiré qui résulte de la différence de paramètre de maille entre le graphène et le rhénium. Nous identifions ce système à une monocouche de graphène en forte interaction avec le substrat, résultat corroboré par des calculs DFT. Des analyses STS dans une gamme d'énergie de plusieurs centaines de meV montrent une modulation spatiale de la densité d'états (DOS) à l'échelle du moiré, indiquant différentes forces de couplage entre les ‘collines' et les ‘vallées' du moiré. Les propriétés supraconductrices de l'échantillon en volume sont sondées par des mesures de transport, desquelles nous extrayons la température de transition Tc~2K et la longueur de cohérence supraconductrice ξ=18nm. Le gap supraconducteur est extrait de la DOS mesurée par STS à 50 mK (Δ=330µeV) et trouvé homogène à l'échelle du moiré. L'état mixte supraconducteur est étudié sous champ magnétique et un réseau de vortex d'Abrikosov est mis à jour. Enfin, une étude sur diverses morphologies de surface présente un effet de proximité supraconducteur latéral anormal, en contradiction avec les modèles existants.Obtaining a transparent interface between graphene and a superconductor has proved to be very challenging and yet essential to induce superconducting correlations in graphene via the so-called proximity effect. This thesis presents a scanning tunneling spectroscopy (STS) study at very low temperature (50 mK) of a novel system achieving such a good electronic contact by the growth of epitaxial graphene on superconducting rhenium. The fabrication and selection of high-crystallographic quality rhenium thin films are briefly explained, followed by the CVD growth process of graphene on various metal substrates and in particular rhenium. STM topographic images reveal a moiré pattern due to the lattice mismatch between graphene and rhenium. We identify this system to a graphene monolayer in strong interaction with the underlying substrate, as corroborated by DFT calculations. STS analyses in the hundreds-meV energy range show a spatial modulation of the density of states (DOS) at the moiré scale, indicating different coupling strengths between ‘hills' and ‘valleys' regions. The bulk superconducting properties are probed by transport measurements, from which we extract the transition temperature Tc~2K and a superconducting coherence length ξ=18nm. The superconducting gap is extracted from the DOS at 50 mK (Δ=330µeV) and found homogeneous at the moiré scale. The superconducting mixed state is studied under magnetic field and an Abrikosov vortex-lattice is uncovered. Finally, a study on various surface morphologies exhibits an anomalous lateral superconducting proximity effect in contradiction with the existing models