Дисертації з теми "Anisotroping"

Ce travail de thèse porte sur le développement d'un modèle pour la turbulence anisotrope et inhomogène au moyen d'une approche statistique spectrale. La variable de base de ce nouveau modèle est le spectre du tenseur de Reynolds, quantité qui dépend des variables d'espace et du temps, mais aussi du module du vecteur d'onde. Ce travail s'appuie sur les fondements théoriques posés par A. Laporta (1995) pour le développement autour de l'homogénéité des équations des corrélations en deux points et sur les travaux de S. Parpais (1996) pour la modélisation des termes les plus complexes mis à jour dans ce type de démarche. Dans cette thèse, un modèle exploitable numériquement dans des géométries complexes a été proposé. Il faut noter que ce modèle repose sur des hypothèses quasi-normales amorties pour représenter les flux d'énergie vers les petites échelles et ne nécessite donc pas, comme les modèles de turbulence usuels, l'utilisation d'une équation de transport pour la dissipation de l’énergie cinétique turbulente. Les informations spectrales fournies par le modèle ont été utilisées pour analyser finement la turbulence. Nous avons ainsi pu caractériser dans des écoulements tels que celui autour d'un profil d'aile en incidence certaines situations de déséquilibre de la turbulence. Ce déséquilibre s'exprime en particulier au niveau des spectres de l’énergie cinétique turbulente par un écart à la théorie de Kolmogorov (1941) et à une distribution d'énergie selon les nombres d'onde k proportionnelle à k-5/ 3 (dans la zone inertielle). L'analyse spectrale permet aussi de proposer des quantités en un point pertinentes pour mettre en évidence ces états de déséquilibre, ouvrant ainsi de nouvelles voies de modélisation
Spectral modelling for anisotropic and inhomogeneous turbulence This work concerns the development of a model for anisotropic and inhomogeneous turbulence by means of a spectral statistical approach. The basic unknown of this new model is the spectrum of the Reynolds stress tensor, a quantity which depends on space and time variables as well as on the wave vector module. The theoretical base of this work was provided by A. Laporta (1 995), who expanded about homogeneity the equations for the two point velocity correlations, and on the work of S. Parpais (1996) for the modelling part of the complex terms involved in this kind of approach. In this thesis, a numerical model was proposed that can be used in complex geometries. It should be noted that this model is based on quasi-normal assumptions intended to represent the energy cascade towards the small scales and therefore does not require, like usual turbulence models, the use of a transport equation for the dissipation of the turbulent kinetic energy. The spectral information provided by this new model was used to scrutinize some properties of turbulence. The model allows to characterize situations of turbulence desequilibrium in flows such as that around an airfoil with incidence. The spectral desequilibrium is characterized by comparisons with the Kolmogorov (1941) theory leading to a distribution of energy proportional to k-5/ 3, for wave numbers k in the inertial range. The spectral analysis enables to propose relevant one-point quantities to highlight these non-equilibrium states, thus opening new modelling frontiers

Pour les écoulements turbulents d’intérêt pratique, la turbulence interagit avec le confinement et les forces externes, ce qui cause inhomogénéité et anisotropie statistiques. Isoler leur contribution à des statistiques ciblées est indispensable pour comprendre les différents phénomènes physiques. Le but de cette thèse a donc été d’acquérir une meilleure connaissance de l’anisotropie en fonction de la direction et de l’échelle dans un ensemble de contextes idéalisés et réalistes. On a utilisé une caractérisation statistique dans l’espace spectral ainsi que dans l’espace de séparation. La caractérisation dans l’espace spectral concerne les statistiques anisotropes de turbulence sous forme de spectres directionnels d’énergie, polarisation et hélicité. La caractérisation dans l’espace de séparation s’appuie sur les moments des incréments de vitesse à deux points du deuxième et troisième ordre, et sur les corrélations de vitesse à deux points. Tout d’abord, on a étudié l’effet du forçage spectral de grandes échelles. Les schémas de forçage considérés sont le schéma de forçage de type Euler, non hélicitaire et hélicitaire, et le schéma ABC. On a montré que les deux forçages ont un inconvénient, dans le sens que, si le nombre de modes suffisamment excités est petit, de l’anisotropie se produit même aux petites échelles. Dans le cas du forçage Euler, cela dépend de la gamme de nombres d’onde forcés ainsi que de leur hélicité. Le forçage ABC, pour lequel le niveau d’hélicité injectée ne peut pas être contrôlé, n’excite que six modes et donc il produit toujours de l’anisotropie et à toutes les échelles résolues. Ensuite, on a analysé l’anisotropie en fonction de l’échelle et de la direction pour la turbulence homogène en rotation. Chose étonnante, l’anisotropie se produit à toutes les échelles même si la rotation est faible. En particulier, on a identifié deux gammes d’échelles anisotropes qualitativement différentes. Aux grandes échelles, l’anisotropie directionnelle est plus grande et décroît avec le nombre d’onde. Aux petites échelles, elle est beaucoup plus faible—mais encore significative—et croit lentement avec le nombre d’onde jusqu’aux échelles dissipatives. Une autre conclusion intéressante et originale de cette partie du travail concerne le rôle de l’échelle de Zeman et son lien avec l’anisotropie aux différentes échelles de l’écoulement. D’après des travaux précédents, l’échelle de Zeman devrait être l’échelle de longueur caractéristique qui sépare les échelles affectées par la rotation par les échelles isotropes. Après une plus ample investigation, en utilisant simulations à différents paramètres, on a découvert que l’échelle de séparation entre grande et faible anisotropie est plutôt l’échelle de longueur caractéristique pour laquelle les effets de rotation et de dissipation s’équilibrent. Ce résultat, toutefois, n’est pas en contradiction avec l’argument de Zeman sur le rétablissement de l’isotropie dans la limite asymptotique de viscosité nulle, comme l’échelle de séparation s’annule à nombre de Reynolds infini, et donc seulement la gamme d’anisotropie décroissante devrait persister et les échelles beaucoup plus petite que celle de Zeman pourraient récupérer l’isotropie. Enfin, on a considéré l’écoulement de von Kármán entre deux disques équipés de pales en contre-rotation dans une cavité cylindrique. On a répété l’analyse dans l’espace de séparation dans plusieurs petites sous-régions, afin d’enquêter les analogies possibles entre la dynamique de l’écoulement et celle de la turbulence homogène en rotation. On a découvert que, dans les régions du domaine où l’écoulement a un taux de rotation moyen plus grand, les distributions des statistiques dans l’espace de séparation montrent certaines des caractéristiques typiques de la turbulence en rotation
In turbulent flows of practical interest, turbulence interacts with confinement and external forces, leading to statistical inhomogeneity and anisotropy. Isolating their contributions to some targeted statistics is indispensable for understanding the underlying physical phenomena. The aim of this thesis has therefore been to gain further insight into direction- and scale-dependent anisotropy in a set of idealized and realistic contexts. Both spectral space and separation space statistical characterizations have been employed. The spectral characterization concerns the anisotropic statistics of turbulence under the form of directional energy, polarization and helicity spectra. The separation space characterization is built on two-point second- and third-order velocity increment moments, and two-point velocity correlations. First, we studied the effect of large-scale spectral forcing. The considered forcing methods are the non-helical and the helical Euler scheme, and the ABC-scheme. We showed that both forcings have a drawback in that, if the number of sufficiently excited modes is too low, anisotropy is bound to arise even at small scales. In the case of Euler forcing, this depends on both the range of forcing wavenumbers and its helicity contents. The ABC forcing, for which the amount of injected helicity cannot be controlled, excites only six modes and therefore always generates anisotropy at all resolved scales. Our second step was to analyze the scale- and direction-dependent anisotropy of homogeneous rotating turbulence. Surprisingly, anisotropy arises at all scales even at low rotation rate. In particular, we identified two anisotropic ranges with different features. In the large scales, directional anisotropy is larger and decreases with wavenumber. At smaller scales, it is much weaker—although still significant—and slowly increases with wavenumber all the way to the dissipative scales. Another interesting and original conclusion of this part of the work concerns the role of the Zeman scale and its link with the flow scale-dependent anisotropy. The Zeman scale was previously argued to be the characteristic lengthscale separating rotation-affected scales 2 from isotropic ones. Upon closer investigation using several simulations at different parameters, we found that the separating scale between large and weak anisotropy is rather the characteristic lengthscale at which rotation and dissipation effects balance. This result, however, does not contradict Zeman’s argument about isotropy recovery in the asymptotic limit of vanishing viscosity, since the separating scale vanishes at infinite Reynolds number, and therefore only the decreasing anisotropy range should persist and scales much smaller than the Zeman one may recover isotropy. Finally, we considered the von Kármán flow between two counter-rotating bladed disks in a cylindrical cavity. We repeated the separation space analysis in different small sub-regions, in order to question the possible analogies in the flow dynamics with that of homogeneous rotating turbulence. We found that, in the regions of the domain where the mean flow has a larger average rotation rate, the distributions of the statistics in separation space display some of the features typical of rotating turbulence

Dans le cadre de l’étude des phénomènes magnétiques et de la spintronique qui sont présents aux échelles nanoscopiques nous avons étudié différents aspects des structures asymétriques de Pt/Co/AlOx. L’un des objectifs de cette thèse est le contrôle de l’oxydation et des propriétés magnétiques de ces multicouches. Nous avons combiné les mesures de structures (réflexion de Rayon-X), transports (Effet Hall anormal), et magnétiques (VSM-SQUID) afin de déterminer les rôles des effets magnétiques et d’interfaces. Un objectif était d’analyser le rôle de quelques monocouches (MCs) de CoO (qui peut se former lors de la sur oxydation de l’Al) sur les propriétés de la multicouche. Nous avons utilisé une technique de déposition avec un gradient d’épaisseur pour contrôler l’oxydation à l’échelle nanométrique. Nous avons établis que quelques monocouches (MCs) de CoO a un impact sur l’anisotropie de a multicouche. Pour approfondir l’effet de la couche de CoO, nous avons construit des bicouches ultrafines de Co(0.6nm)/CoO(0.6nm). Nous avons effectué des mesures refroidi sur champ sur ce système et trouvé un fort effet de couplage d'échange. Ces résultats indiquent que la couche CoO garde une forte anisotropie même en dans la limite des monocouches et permet de réfuter certains modèles sur l’effet d’échange bias et indique que les couches, couramment négligé, de CoO doivent être prises en considération dans le bilan énergétiques du système. Nous avons construits un appareil de mesure perpendiculaire de la magnétorésistance tunnel anisotrope (TAMR) à partir de la structure Pt/Co/AlOx. La TAMR est un effet de spintronique relativement récent dans lequel la rotation d’aimantation dans une électrode magnétique (combiné avec un couplage spin-orbite) peut entrainer un changement de la probabilité de l’effet tunnel, ce qui se manifeste comme un effet de magnétorésistance. Nous avons démontré qu’un contrôle précis de l’état d’oxydation est essentiel pour l’effet TAMR. La forte anisotropie magnétique induite nous permet d’atteindre des valeurs de TAMR plus grande comparée à celle des structures Pt/Co/AlOx
In the context of studying magnetic and spintronics phenomena occurring at the nanoscale, we investigated several aspects of Pt/Co/AlOx asymmetric structures. One of the objectives of this thesis was the control of the oxidation and the tailoring of the magnetic properties of these multilayers. We combined structural (X-Ray Reflectivity), transport (Anomalous Hall Effect) and magnetic measurements (VSM-SQUID), to study the interplay of magnetic and interfacial effects. One objective was to analyze the role that few monolayers (MLs) of CoO (which can form when overoxidizing the Al layer), could have on the properties of the stack. We used a wedge deposition techniques to control the oxidation on a subnanometer scale. We established that few MLs of CoO largely affect the total anisotropy of the stack. To further investigate the impact of the CoO, we engineered ultrathin Co(0.6nm)/CoO(0.6nm) bilayers. We performed field cooled measurements on this system and we found a large exchange bias anisotropy. These results indicate that the CoO keeps a large anisotropy even in the ML regime, help to rule out some of the models proposed to explain the exchange bias effect and imply that the usually neglected CoO presence must be considered in the energy balance of the system. We build perpendicular Tunneling Anisotropic MagnetoResistance (TAMR) devices based on the Pt/Co/AlOx structure. The TAMR is a relatively new spintronics effect in which the rotation of the magnetization in a single magnetic electrode (combined with the Spin-Orbit Coupling) can cause a change of the tunnel probability, which manifests as a magnetoresistance effect. We demonstrated that a careful control of the interface oxidation is crucial for the TAMR effect. The large induced magnetic anisotropy allowed us to achieve enhanced TAMR values compared to similar Pt/Co/AlOx structures

Anisotropies essentially affect magnetism in thin ferromagnetic films of few atomic layers. On the one hand they can stabilize long range order in these systems, on the other hand they strongly influence the orientation of magnetization. The intrinsic causes of anisotropies in these systems are the spin-orbit coupling of the electrons and the long-range magnetic dipole interaction. While the dipole interaction always favors an orientation of magnetization in the plane of the film, spin-orbit coupling can favor different orientations of magnetization on the surface and in the inner layers of the film. This can lead to a competition between anisotropies, which in turn leads to a spin reorientation transition with varying film thickness. This transition can be of varying order, i. e. be continuous or discontinuous. Experiments also find a spin reorientation transition with varying temperature, which until now was not well understood. In the framework of a classical Heisenberg model this transition is investigate d by means of different theoretical methods in the course of this thesis. At zero temperature the system can be dealt with analytically and criteria for the spin reorientation transition and its order are found. Furthermore it is investigated whether the long-range dipole interaction results in a domain ground state. These investigations are extended to finite temperatures by means of a molecular field theory and results are compared to Monte Carlo simulations. It is shown that in contrast to other works the temperature driven spin reorientation transition in the monolayer is discontinuous also in the simulations, whereas in general it is continuous for the bilayer. Consequently the molecular field theory and the Monte Carlo simulations agree qualitatively. Exemplary for thicker films the influence of an external magnetic field is investigated in the bilayer, furthermore the effective anisotropies Kn(T) of the phenomenological Landau theory are calculated numerically for the microscopic model. Analytic expres sions for the dependence of the anisotropies Kn(T) on the parameters of the model are obtained by the means of perturbation theory, which lead to a deeper understanding of the spin reorientation transition. Accordingly to this the origin for the spin reorientation transition lies in the differing temperature dependence of the dipolar and spin-orbit parts of the Kn(T). Additionally the magnetization in the surface of the film decreases more rapidly with increasing temperature. As a consequence the influence of the surface anisotropy decreases with increasing temperature. This effects a similar result as increasing the film thickness and leads to the transition. Finally the model is extended to continuous film thicknesses, since in experiment the spin reorientation transition depends crucially on film thickness. The results of this extended model are compared to experiment and give good agreement.

En partant d'une problématique industrielle correspondant à la naissance de fissures lors de l'excavation d'un tunnel dans un matériau argileux, nous proposons de nous intéresser à un sujet plus large qui est celui de la nucléation d'une fissure de dimension macroscopique. Ainsi, des résultats généraux et théoriques sont établis tout au long de ce mémoire. Ces derniers sont toutefois utilisés pour proposer une interprétation aux faciès de fissuration observés lors de l'excavation de galeries de stockage à grandeur profondeur. Dans un premier temps, un modèle géométrique idéalisé pour des fissures est justifié. Cette étude préalable permet à la fois d'acter la nature fermée des fissures susceptibles de nucléer ainsi que d'utiliser le critère mixte en statuant sur le bienfondé d'une étude bidimensionnelle équivalente. En précisant la notion de longueur de nucléation stable et en s'inspirant des outils classiques de la mécanique linéaire de la rupture, nous établissons dans un second temps notre propre critère de nucléation. Pour ce faire, nous proposons, grâce à des modélisations micromécaniques, de revisiter l'approche thermodynamique usuelle dans un cadre adiabatique afin d'être davantage en accord avec la brutalité du phénomène étudié. Par la suite, nous mettons aux points différentes méthodes permettant d'utiliser le critère suggéré. Enfin, le critère est mis en œuvre dans le cadre de la problématique industrielle initiale pour essayer de donner une justification à l'anisotropie des géométries des fissures observées, et ce, en prenant en compte les différentes directions de forage de l'ouvrage. Dans un deuxième temps, nous proposons de nous intéresser, de manière plus prospective, aux problématiques liées aux modèles locaux d'endommagement. Une attention particulière est accordée à la notion de stabilité des états d'équilibre. Ainsi, une adaptation du critère de Hill est proposée et des différences quantitatives sont soulignées lorsqu'un cadre adiabatique, nous paraissant plus justifié, est pris en compte. Enfin, le problème de la localisation de l'endommagement dans un problème unidimensionnel est abordé
Starting from an industrial issue that is cracks onset when excavating a tunnel, this work aims at giving new insights into a more general problematic which is the initiation of macroscopic cracks. Thus, general and theoretical results are established. Nevertheless, they are applied in order to give some explanations to the excavation-induced fractures observed around the deep geological repository. To begin with, an idealised geometrical model is detailed and justified. Thanks to this preliminary work, we establish that the cracks that should be taken into account are closed ones. In addition we show that it's possible for small cracks length to work on an equivalent bidimensionnal problem. This last result allows us to apply the mixed criteria. After giving the definition of a stable crack initiation length we define our own criteria to predict cracks onset. In order to do so and in order to be more in adequacy with the caracter brutal of a crack initiation, we offer through a micromecanic modelisation to deploy the usual thermodynamic approach in an adiabatic context. Different methods to compute the key quantity which is the incremental energy released rate are then built. Finally, the criteria is applied to give some justifications to the anisotropic geometry of the excavation-induced fractures. In a second part of this work, we focuse on the problematics tied to the local damage models. For instance, the notion of stability for an equilibrium state is discussed. Hill's stability critera is adapted to damage problems. Once again, it seems that an adiabatic context is more suited and the differences implied are emphasized. To conclude, we offer to investigate the localisation issue in one dimensionnal problems

GaMnAs est un semi-conducteur ferromagnétique dilué où l’interaction d’échange est induite par des porteurs délocalisés. Ces derniers sont souvent décrits par des états de Bloch dans la bande de valence, malgré une controverse sur l’influence d’une mini-bande d’impuretés Mn. Une connaissance plus précise de la structure de bandes reste nécessaire pour déterminer à la fois la position du niveau de Fermi et la nature exacte des anisotropies magnétiques, encore mal connues. Nous avons étudié l’anisotropie de magnétorésistance en régime tunnel (TAMR) de diodes Zener-Esaki p++-GaMnAs/n+-GaAs, reliée aux anisotropies de la structure de bandes de GaMnAs. Le transport tunnel inter-bandes permet de réaliser la spectroscopie électrique de la TAMR, résolue en énergie ou en impulsion. La comparaison de la dépendance en énergie des anisotropies cubique et uniaxiales montrent que le niveau de Fermi se trouve loin du haut de la bande de valence, et non piégé dans la minibande, et que les bandes de trous ont des contributions opposées à la TAMR, en accord qualitatif avec des calculs k. P. De plus, la dépendance en énergie de l’anisotropie uniaxiale planaire précise son lien avec la mini-bande d’impuretés Mn. La spectroscopie résolue en impulsion révèle aussi les effets de structure de bandes et de filtrage des états de Bloch, mais ne permet pas de déterminer les courbes de dispersion (transport multi-bandes et à 3D). Des résultats préliminaires offrent des perspectives d’études sur la spectroscopie de TAMR réalisée par effet tunnel résonant via un niveau d’énergie d’un puits quantique, mais aussi sur l’utilisation de la TAMR comme sonde du nanomagnétisme de plots individuels de GaMnAs
Ferromagnetism in highly-doped diluted magnetic semiconductor GaMnAs is mediated by delocalized carriers. Those are often described as Bloch states in the valence band of GaMnAs in presence of an exchange interaction. Nevertheless, the exact role of the Mn-impurity band overlapping the valence band is still under debate. A better knowledge of the exact band structure is still necessary to determine the actual Fermi level position, as well as to fully understand the true nature of bands anisotropies (valence bands, imurity band). We investigate the tunneling anisotropic magnetoresistance (TAMR) in ferromagnetic tunnel diodes p++-GaMnAs/n+-GaAs. Inter-band tunneling allows us to carry out the electrical spectroscopy of the TAMR, both in energy or impulse space. The comparison in the energy dependence of the cubic and uni-axial anisotropies suggests that the Fermi level is not pinned in the impurity band but lies deep into the valence band. The results further reveal the opposite contributions of different valence bands to TAMR, in qualitative agreement with k. P calculations, as well as an additional contribution to the in-plane uniaxial anisotropy due to the impurity band. Besides, spectroscopy in momentum space shows an enhancement of TAMR due to Bloch’s states impulse filtering. Nevertheless, multi-bands tunnel spectroscopy of delocalized states in 3D space does not allow to determine the curves of dispersion. Preliminary results on the electrical spectroscopy of TAMR using resonant tunnelling through energy levels of a quantum well are also shown, as well as others on the use of TAMR to study nanomagnetism of an individual GaMnAs nanodot

The questions I ask myself are generally all along the lines of "so where did all this structure come from?". I hoped that work in the CMB and its cosmological implications would give me insight into this. It is an adventure that is still young. I began my PhD with an investigation of some formal aspects of Ehlers-Ellis Relativistic Kinetic Theory in mind { the implications of the truncation conditions found in the exact theory. I ended up trying to calculate CMB anisotropies as an application of this beautiful and somewhat purist formalism. The Ehler-Ellis (1+3) Lagrangian approach to General Relativity (GR) and Relativistic Kinetic Theory (RKT) are apparently not well known nor well used and have only recently begun to show advantages over the more usual ADM and Bardeen perturbative approaches to astrophysical cosmology when combined with the Ellis Bruni perturbation theory.

My work Anisotropic Streaming is written for the University of Iowa Symphonic Orchestra. It is approximately 16 minutes in length. The inspiration of the piece was the cosmic background radiation remaining from the Big Bang. In 1964, it was discovered that space was filled with a faint amount of radiation; a relic from the time when slight temperature variance allowed for the coalescence of particles. These particle collections soon had varying masses and therefore varying gravitational pulls, which in turn created the stars and galaxies. Since the universe expanded while the temperature variances allowed for this particle accumulation, the background radiation is patterned in a manner that is anisotropic: a nearly uniform arrangement of the radiation that appears different depending on the observer's orientation. As a formal tool, this phenomenon has suggested a compositional process focused on transition and contextualization. The concept of anisotropy manifests itself in my composition in a number of ways. The first of three sections "collects" individual pitches until those frequencies are no longer perceptible - the listener's mind fuses the pitches into a single yet complex sonority. This fusion is encouraged further by the arrangement of pitches mimicking the overtone series. The second section features a very active and thick texture combining to make a single mass of sound. The texture gradually removes layers to reveal the individual short melodies that make up the mass. The third section rearranges these short melodies, making the high melodies low and the low melodies high. Each melody grows one note longer on each iteration, until each are so long they begin to fuse into a single, complex sonority. In these ways, I attempt to create the same kind of sound but through a shifting perspective, exposing sound's anisotropic construction. Formally, the piece divides into three sections, each a composite sound at different levels of synchronicity and perspective. The sections are further subdivided into two parts, the first being transitional and the second being a more static exhibition of the section's conceptual purpose. The pitch material in expositional areas is based on the mathematical overtone series (rounded to the nearest semitone). Pitch material in transitional phrases collects into aggregates, generally derived from a frequency modulation, amplitude modulation, or distortion by common fate. These pitches are not necessarily relegated to their registral frequencies, allowing for some octave equivalence. The first section, an exposition of separate elements creating a whole sonority, begins with the accumulation of material in the middle, high, then low register. As events become more synchronized, these three disparate elements become parts of an Eb1 sonority through additive synthesis. After a brief transitional section of aggregate sonorities in a symmetrical rhythm, the fundamental switches to G1 as a pizzicato cloud texture replaces the higher overtones. The additive G1 sonority occurs repeatedly, getting more frequent towards the end of the section. Using common overtones, overtones of the G1 sonority are sustained and the harmony is displaced by Eb1. The second section is a discovery of separate elements that exist within a sound complex, and subsequently, the germinal existences of those elements. The effect of parsing the lower pitches into imagined component pitches is the destabilization of a steady fundamental. The implied fundamentals instead fade in and out of perceivable space, creating a sonic environment of quasi-periodic harmonicity. The section begins by changing the Eb1 to a virtual Bb0 fundamental through a series of common overtones. The sustained Bb0 overtones are rhythmicized, becoming melodic fragments of varying lengths. After the surface texture of the Bb0 climaxes, the orchestration is reduced three times to solos and duets, revealing the melodies that exist in each registral area (high, middle, low). A brief transitional section of aggregate sonorities in a rhythm similar to the transitional area in section one, the implied fundamental becomes a D-1. The melodic fragments are extended through sparer orchestration, with soloists and small chamber combinations developing the ideas. The section ends with an implied C1 fundamental. The final section is the destabilization of the quasi-periodic harmonicity of the second section. The section begins in the highest register on string harmonics that do not imply any particular fundamental. The overtones are textured, and interjections of shepherd tones and noise elements add to an active surface with an unmoored harmonic space. When the surface reaches a maximally undefined pitch space, the gesture of the completed added sonority from the first section returns, implying fundamentals of five different sonorities, moving progressively away from harmonicity. A superimposition of the solo and chamber melodies against segments of previous aggregate transitions leads the harmonic space to a C2 fundamental, played in the gesture of the completed added sonority from the first section. By holding shared common tones, the harmonic space changes to an E1 fundamental, and pitches get higher and quieter until the piece ends.

Este trabalho trata da análise de problemas planos de chapa compostos por materiais anisotrópicos, definidas em uma região ou no domínio por completo, utilizando-se o método dos elementos de contorno. As soluções fundamentais para problemas anisotrópicos, embora existentes, mostram-se difíceis de serem utilizadas devido à complexidade de sua formulação matemática ou da necessidade de se encontrar partes da solução numericamente. Nesse sentido, a formulação alternativa mostrada nesse trabalho permite o estudo de meios anisotrópicos utilizando-se as soluções fundamentais para meios isotrópicos nas representações integrais de problemas planos com campo de tensões iniciais. A região do domínio com propriedades anisotrópicas ou diferentes das propriedades elásticas de um meio isotrópico usado como referência é discretizada em células triangulares, enquanto que o contorno do problema é discretizado em elementos lineares. As componentes do tensor de tensões iniciais da região anisotrópica são definidas como uma correção das tensões elásticas do material isotrópico de referência através de uma matriz de penalização. Essa matriz, por sua vez, é obtida através de relações envolvendo as constantes elásticas de rigidez do meio desejado e os coeficientes elásticos de flexibilidade do meio isotrópico de referência. Essa técnica é particularmente adequada para a análise de inclusões anisotrópicas onde há a necessidade de discretizar apenas uma parte pequena do domínio, aumentando, portanto, pouco o número de graus de liberdade do sistema. Os resultados obtidos com a formulação proposta são comparados com os resultados numéricos existentes na literatura.
This work deals with elastic 2D problems characterized by the presence of zones with different materials and anisotropic inclusions using the boundary element method. The anisotropy can be assumed either over the whole domain or defined only over some particular inclusions, which is the most usual case. Fundamental solutions for anisotropic domains, although well-known, lead to more complex formulations and may introduce difficulties when the analysis requires more complex material models as for instance plastic behavior, finite deformations, etc. The alternative formulation proposed in this work can be applied to anisotropic bodies using the classical fundamental solutions for 2D elastic isotropic domains plus correction given by an initial stress field. The domain region with anisotropic properties or only with different isotropic elastic parameters has to be discretized into cells to allow the required corrections, while the complementary part of the body requires only boundary discretization. The initial stress tensor to be applied to the anisiotropic region is defined as the isotropic material elastic stress tensor correction by introducing a local penalty matrix. This matrix is obtained by the difference between the elastic parameters between the reference values and the anisotropic material. This technique is particularly appropriate for anisotropic inclusion analysis, in which the domain discretization is required only over a small region, therefore increasing very little the number of degrees of freedom of the final algebraic system. The numerical results obtained by using the proposed formulation have demonstrated to be very accurate in comparison with either analytical solutions or the other numerical values.

In this diploma thesis were investigated in terms of microviscosity liquid and condensed systems composed of hyaluronan (Hya) and cationic surfactant cetyltrimethylammonium bromide (CTAB). The excitation and emission spectra, lifetime, steady-state fluorescence anisotropy and time-resolved fluorescence anisotropy of the samples were measured. First, was studied the formation of hydrophobic domains in the system Hya-CTAB at concentration of CTAB lower than its critical micelle concentration in an aqueous solution and 0.15M NaCl. It was found that in an aqueous solution small hydrophobic domains linked to chains Hya are formed. Then an increasing concentration of CTAB leads to phase separation and formation of gel. Due to the addition of NaCl then leads to the reorganization of this system and probably the formation of free micelles in the solution. Were also studied condensed phase of system Hya-CTAB-NaCl at high concentrations of surfactant during fourteen days of ageing. It was found that the microviscosity of hydrophobic domains is constant, but the microviscosity of hydrophilic parts gradually decreases.

Tectonic and geological processes on Earth often result in structural anisotropy of the subsurface, which can be imaged by various geophysical methods. In order to achieve appropriate and realistic Earth models for interpretation, inversion algorithms have to allow for an anisotropic subsurface. Within the framework of this thesis, I analyzed a magnetotelluric (MT) data set taken from the Cape Fold Belt in South Africa. This data set exhibited strong indications for crustal anisotropy, e.g. MT phases out of the expected quadrant, which are beyond of fitting and interpreting with standard isotropic inversion algorithms. To overcome this obstacle, I have developed a two-dimensional inversion method for reconstructing anisotropic electrical conductivity distributions. The MT inverse problem represents in general a non-linear and ill-posed minimization problem with many degrees of freedom: In isotropic case, we have to assign an electrical conductivity value to each cell of a large grid to assimilate the Earth's subsurface, e.g. a grid with 100 x 50 cells results in 5000 unknown model parameters in an isotropic case; in contrast, we have the sixfold in an anisotropic scenario where the single value of electrical conductivity becomes a symmetric, real-valued tensor while the number of the data remains unchanged. In order to successfully invert for anisotropic conductivities and to overcome the non-uniqueness of the solution of the inverse problem it is necessary to use appropriate constraints on the class of allowed models. This becomes even more important as MT data is not equally sensitive to all anisotropic parameters. In this thesis, I have developed an algorithm through which the solution of the anisotropic inversion problem is calculated by minimization of a global penalty functional consisting of three entries: the data misfit, the model roughness constraint and the anisotropy constraint. For comparison, in an isotropic approach only the first two entries are minimized. The newly defined anisotropy term is measured by the sum of the square difference of the principal conductivity values of the model. The basic idea of this constraint is straightforward. If an isotropic model is already adequate to explain the data, there is no need to introduce electrical anisotropy at all. In order to ensure successful inversion, appropriate trade-off parameters, also known as regularization parameters, have to be chosen for the different model constraints. Synthetic tests show that using fixed trade-off parameters usually causes the inversion to end up by either a smooth model with large RMS error or a rough model with small RMS error. Using of a relaxation approach on the regularization parameters after each successful inversion iteration will result in smoother inversion model and a better convergence. This approach seems to be a sophisticated way for the selection of trade-off parameters. In general, the proposed inversion method is adequate for resolving the principal conductivities defined in horizontal plane. Once none of the principal directions of the anisotropic structure is coincided with the predefined strike direction, only the corresponding effective conductivities, which is the projection of the principal conductivities onto the model coordinate axes direction, can be resolved and the information about the rotation angles is lost. In the end the MT data from the Cape Fold Belt in South Africa has been analyzed. The MT data exhibits an area (> 10 km) where MT phases over 90 degrees occur. This part of data cannot be modeled by standard isotropic modeling procedures and hence can not be properly interpreted. The proposed inversion method, however, could not reproduce the anomalous large phases as desired because of losing the information about rotation angles. MT phases outside the first quadrant are usually obtained by different anisotropic anomalies with oblique anisotropy strike. In order to achieve this challenge, the algorithm needs further developments. However, forward modeling studies with the MT data have shown that surface highly conductive heterogeneity in combination with a mid-crustal electrically anisotropic zone are required to fit the data. According to known geological and tectonic information the mid-crustal zone is interpreted as a deep aquifer related to the fractured Table Mountain Group rocks in the Cape Fold Belt.
Tektonische und geologische Prozesse verursachen häufig eine strukturelle Anisotropie des Untergrundes, welche von verschiedenen geophysikalischen Methoden beobachtet werden kann. Zur Erstellung und Interpretation geeigneter, realistischer Modelle der Erde sind Inversionsalgorithmen notwendig, die einen anisotropen Untergrund einbeziehen können. Für die vorliegende Arbeit habe ich einen magnetotellurischen (MT) Datensatz vom Cape Fold Gürtel in Südafrika untersucht. Diese Daten weisen auf eine ausgeprägte Anisotropie der Kruste hin, da z.B. die MT Phasen außerhalb des erwarteten Quadranten liegen und nicht durch standardisierte isotrope Inversionsalgorithmen angepasst und ausgewertet werden können. Um dieses Problem zu beheben, habe ich eine zweidimensionale Inversionsmethode entwickelt, welche eine anisotrope elektrische Leitfähigkeitsverteilungen in den Modellen zulässt. Die MT Inversion ist im allgemeinen ein nichtlineares, schlecht gestelltes Minimierungsproblem mit einer hohen Anzahl an Freiheitsgraden. Im isotropen Fall wird jeder Gitterzelle eines Modells ein elektrischer Leitfähigkeitswert zugewiesen um den Erduntergrund nachzubilden. Ein Modell mit beispielsweise 100 x 50 Zellen besitzt 5000 unbekannte Modellparameter. Im Gegensatz dazu haben wir im anisotropen Fall die sechsfache Anzahl, da hier aus dem einfachen Zahlenwert der elektrischen Leitfähigkeit ein symmetrischer, reellwertiger Tensor wird, wobei die Anzahl der Daten gleich bleibt. Für die erfolgreiche Inversion von anisotropen Leitfähigkeiten und um die Nicht-Eindeutigkeit der Lösung des inversen Problems zu überwinden, ist eine geeignete Einschränkung der möglichen Modelle absolut notwendig. Dies wird umso wichtiger, da die Sensitivität von MT Daten nicht für alle Anisotropieparameter gleich ist. In der vorliegenden Arbeit habe ich einen Algorithmus entwickelt, welcher die Lösung des anisotropen Inversionsproblems unter Minimierung einer globalen Straffunktion berechnet. Diese besteht aus drei Teilen: der Datenanpassung, den Zusatzbedingungen an die Glätte des Modells und die Anisotropie. Im Gegensatz dazu werden beim isotropen Fall nur die ersten zwei Parameter minimiert. Der neu definierte Anisotropieterm wird mit Hilfe der Summe der quadratischen Abweichung der Hauptleitfähigkeitswerte des Modells gemessen. Die grundlegende Idee dieser Zusatzbedingung ist einfach. Falls ein isotropes Modell die Daten ausreichend gut anpassen kann, wird keine elektrische Anisotropie zusätzlich in das Modell eingefügt. Um eine erfolgreiche Inversion zu garantieren müssen geeignete Regularisierungsparameter für die verschiedenen Nebenbedingungen an das Modell gewählt werden. Tests mit synthetischen Modellen zeigen, dass bei festgesetzten Regularisierungsparametern die Inversion meistens entweder in einem glatten Modell mit hohem RMS Fehler oder einem groben Modell mit kleinem RMS Fehler endet. Die Anwendung einer Relaxationsbedingung auf die Regularisierung nach jedem Iterationsschritt resultiert in glatteren Inversionsmodellen und einer höheren Konvergenz und scheint ein ausgereifter Weg zur Wahl der Parameter zu sein. Die vorgestellte Inversionsmethode ist im allgemeinen in der Lage die Hauptleitfähigkeiten in der horizontalen Ebene zu finden. Wenn keine der Hauptrichtungen der Anisotropiestruktur mit der vorgegebenen Streichrichtung übereinstimmt, können nur die dazugehörigen effektiven Leitfähigkeiten, welche die Projektion der Hauptleitfähigkeiten auf die Koordinatenachsen des Modells darstellen, aufgelöst werden. Allerdings gehen die Informationen über die Rotationswinkel verloren. Am Ende meiner Arbeit werden die MT Daten des Cape Fold Gürtels in Südafrika analysiert. Die MT Daten zeigen in einem Abschnitt des Messprofils (> 10 km) Phasen über 90 Grad. Dieser Teil der Daten kann nicht mit herkömmlichen isotropen Modellierungsverfahren angepasst und daher mit diesen auch nicht vollständig ausgewertet werden. Die vorgestellte Inversionsmethode konnte die außergewöhnlich hohen Phasenwerte nicht wie gewünscht im Inversionsergebnis erreichen, was mit dem erwähnten Informationsverlust der Rotationswinkel begründet werden kann. MT Phasen außerhalb des ersten Quadranten können für gewöhnlich bei Anomalien mit geneigter Streichrichtung der Anisotropie gemessen werden. Um diese auch in den Inversionsergebnissen zu erreichen ist eine Weiterentwicklung des Algorithmus notwendig. Vorwärtsmodellierungen des MT Datensatzes haben allerdings gezeigt, dass eine hohe Leitfähigkeitsheterogenität an der Oberfläche in Kombination mit einer Zone elektrischer Anisotropie in der mittleren Kruste notwendig sind um die Daten anzupassen. Aufgrund geologischer und tektonischer Informationen kann diese Zone in der mittleren Kruste als tiefer Aquifer interpretiert werden, der im Zusammenhang mit den zerrütteten Gesteinen der Table Mountain Group des Cape Fold Gürtels steht.

We investigate elliptic pseudodifferential operators which degenerate in an anisotropic way on a submanifold of arbitrary codimension. To find Fredholm problems for such operators we adjoint to them boundary and coboundary conditions on the submanifold.The algebra obtained this way is a far reaching generalisation of Boutet de Monvel's algebra of boundary value problems with transmission property. We construct left and right regularisers and prove theorems on hypoellipticity and local solvability.

We have qualitatively explained the experiments of McCloud and Maher (McCloud and Maher (95)) for the viscous fingering problem in which an anisotropy in the surface tension parameter was imposed by engraving a grid in one of the plates of the Hele-Shaw cell. We saw the need to approach the problem in an analytical form. Therefore we decided to extend solvability theory to incorporate the effect of anisotropy. We have introduced the anisotropy through a moving boundary condition by considering an effective anisotropic surface tension with an anisotropy entering as the simplest cosine term having the right symmetry for a square lattice. We carried out the singular perturbation appropriate for the surface tension parameter assuming the length scale introduced by the anisotropy is small in comparison with the length scale introduced by the surface tension. In this sense, the perturbation can be said to be microscopic. For the case in which the surface tension has a maximum at the finger tip, our theory provides two possible solutions: one corresponding to the solution of the isotropic case and a new solution which, below a threshold of the surface tension parameter, predicts a wider finger than the isotropic solution. Intuitively, we expect the "old" solution, namely the one that does not differ from the isotropic case, to be the selected solution for large values of the surface tension parameter and we expect the new solution to be selected for small values of the surface tension parameter. This was confirmed by dynamical simulations of the interface done by David Jasnow. His simulation predicts that for the case in which the surface tension has a maximum at the finger tip, anisotropy is irrelevant for large values of the surface tension parameter. Furthermore below a threshold in this surface tension parameter, the selected finger width is systematically wider than the corresponding isotropic case. We conclude that our solvability theory together with the dynamic

Optical components made of anisotropic materials, such as crystal polarizers and crystal waveplates, are widely used in many complex optical system, such as display systems, microlithography, biomedical imaging and many other optical systems, and induce more complex aberrations than optical components made of isotropic materials. The goal of this dissertation is to accurately simulate the performance of optical systems with anisotropic materials using polarization ray trace. This work extends the polarization ray tracing calculus to incorporate ray tracing through anisotropic materials, including uniaxial, biaxial and optically active materials. The 3D polarization ray tracing calculus is an invaluable tool for analyzing polarization properties of an optical system. The 3×3 polarization ray tracing P matrix developed for anisotropic ray trace assists tracking the 3D polarization transformations along a ray path with series of surfaces in an optical system. To better represent the anisotropic light-matter interactions, the definition of the P matrix is generalized to incorporate not only the polarization change at a refraction/reflection interface, but also the induced optical phase accumulation as light propagates through the anisotropic medium. This enables realistic modeling of crystalline polarization elements, such as crystal waveplates and crystal polarizers. The wavefront and polarization aberrations of these anisotropic components are more complex than those of isotropic optical components and can be evaluated from the resultant P matrix for each eigen-wavefront as well as for the overall image. One incident ray refracting or reflecting into an anisotropic medium produces two eigenpolarizations or eigenmodes propagating in different directions. The associated ray parameters of these modes necessary for the anisotropic ray trace are described in Chapter 2. The algorithms to calculate the P matrix from these ray parameters are described in Chapter 3 for anisotropic ray tracing. This P matrix has the following characteristics: (1) Multiple P matrices are calculated to describe the polarization of the multiple eigenmodes at an anisotropic intercept. (2) Each P matrix maps the orthogonal incident basis vectors (Ê_m, Ê_n, Ŝ) before the optical interface into three orthogonal exiting vectors (a_m Ê'_m, a_n Ê'_n, Ŝ') after the interface, where a_m and a_n are the complex amplitude coefficients induced at the intercept. The ray tracing algorithms described in this dissertation handle three types of uncoated anisotropic interfaces isotropic/anisotropic, anisotropic/isotropic and anisotropic/anisotropic interfaces. (3) The cumulative P matrix associated with multiple surface interactions is calculated by multiplying individual P matrices in the order along the ray path. Many optical components utilize anisotropic materials to induce desired retardance. This important mechanism is modeled as the optical phase associated with propagation. (4) The optical path length OPL of an eigenpolarization along an anisotropic ray path is incorporated into the calculation of each P matrix. Chapter 4 presents the data reduction of the P matrix of a crystal waveplate. The diattenuation is embedded in the singular values of P. The retardance is divided into two parts: (A) The physical retardance induced by OPLs and surface interactions, and (B) the geometrical transformation induced by geometry of a ray path, which is calculated by the geometrical transform Q matrix. The Q matrix of an anisotropic intercept is derived from the generalization of s- and p-bases at the anisotropic intercept; the p basis is not confined to the plane of incidence due to the anisotropic refraction or reflection. Chapter 5 shows how the multiple P matrices associated with the eigenmodes resulting from propagation through multiple anisotropic surfaces can be combined into one P matrix when the multiple modes interfere in their overlapping regions. The resultant P matrix contains diattenuation induced at each surface interaction as well as the retardance due to ray propagation and total internal reflections. The polarization aberrations of crystal waveplates and crystal polarizers are studied in Chapter 6 and Chapter 7. A wavefront simulated by a grid of rays is traced through the anisotropic system and the resultant grid of rays is analyzed. The analysis is complicated by the ray doubling effects and the partially overlapping eigen-wavefronts propagating in various directions. The wavefront and polarization aberrations of each eigenmode can be evaluated from the electric field distributions. The overall polarization at the plane of interest or the image quality at the image plane are affected by each of these eigen-wavefronts. Isotropic materials become anisotropic due to stress, strain, or applied electric or magnetic fields. In Chapter 8, the P matrix for anisotropic materials is extended to ray tracing in stress birefringent materials which are treated as spatially varying anisotropic materials. Such simulations can predict the spatial retardance variation throughout the stressed optical component and its effects on the point spread function and modulation transfer function for different incident polarizations. The anisotropic extension of the P matrix also applies to other anisotropic optical components, such as anisotropic diffractive optical elements and anisotropic thin films. It systematically keeps track of polarization transformation in 3D global Cartesian coordinates of a ray propagating through series of anisotropic and isotropic optical components with arbitrary orientations. The polarization ray tracing calculus with this generalized P matrix provides a powerful tool for optical ray trace and allows comprehensive analysis of complex optical system.

Standard models of cosmology use inflation as a mechanism to resolve the isotropy and homogeneity problem of the universe as well as the flatness problem. However, due to various well known problems with the inflationary paradigm, there has been an ongoing search for alternatives. Perhaps the most famous among these are the cyclic universe scenarios which incorporate bounces. As these scenarios have a contracting phase in the evolution of the universe, anisotropies and inhomogeneities would be expected to blow up on approach to the bounce. Thus, it is reasonable to ask whether the problems of homogeneity and isotropy can still be resolved in these scenarios. In this thesis, I will focus on the problem of the resolution of the isotropy problem. I begin with a brief review of anisotropic, spatially homogeneous geometries of cosmological interest. Next, I review the existing literature on bouncing cosmologies, and discuss the mechanism of bounce studied in previously proposed models, as well as their theoretical and observational advantages and disadvantages. I then discuss the process of isotropisation in the contracting phase of each bounce. In this phase of the evolution, the mechanism of ekpyrosis is used in most cosmological scenarios which incorporate a contracting phase to mitigate the problem of anisotropies blowing up on approaching the bounce. I start by studying anisotropic universes and I then examine the effect of the addition of ultra-stiff anisotropic pressures on the ekpyrotic phase. I then consider evolving such anisotropic universes through several cycles with increasing expansion maxima at each successive bounce. This eventually leads to flatness in the isotropic case. My aim is to see if the resolution of the flatness problem also leads to a simultaneous resolution of the isotropy problem. In the next chapter, I consider the effect of non comoving velocities on the shape of this anisotropic bouncing universe. In the final section of my thesis, I consider anisotropic cosmological models within the context of canonical quantum cosmology and investigate the quantum behaviour of anisotropies.

The present-day challenges in the transport industry, steered by the increasing environmental awareness, necessitate manufacturers to take measures to reduce emissions related to the movements of goods and humans. In particular, the measures aiming at a reduced mass or higher load capacity to increase fuel efficiency,  generally deteriorate the noise and vibration insulation properties of their products. In order to comply with the regulations and customer demands, modern vehicles increasingly move towards a multifunctional integrated design approach, if possible for all subcomponents involved. Such a multifunctional design approach is an iterative process, evaluating the proposed solutions in every stage, and is therefore best performed in a virtual testing environment. \\Poroelastic materials are interesting to include in a multifunctional design, offering reasonably good vibro-acoustic insulation properties at a low weight penalty. These materials can also be combined in multilayer arrangements to further enhance the overall performance. \\In order to achieve an accurate modelling of the vibro-acoustic behaviour of poroelastic materials, the input data describing the material properties should be of a high quality. Two characteristics inherent to these materials encumber a precise characterisation with traditional techniques. Poro-elastic aggregates are anelastic due to the constituent material used, and anisotropic as a consequence of the production process. Characterisation techniques allowing for an accurate determination of the material properties need to take these intrinsic characteristics into account.\\The objective in this thesis is to enable the characterisation of a constitutive material model for poroelastic materials which is as general as possible, and includes the inherent material anelasticity and anisotropy. For this purpose, a set of advanced characterisation techniques has been developed to characterise the anisotropic flow resistivity tensor and the anisotropic dynamic Hooke's tensor. \\These advanced characterisation techniques are based on an inverse estimation procedure, used consistently throughout the work, and includes both experiments and numerical predictions. The property to characterise is isolated in a specially designed set-up such that it can be modelled by physics solely involving this property. The obtained experimental and numerical data then serve as the input to an optimisation, which returns the material properties for which the difference between both is as small as possible. These methods have been successfully applied to melamine foam, which is found to be both anisotropic and anelastic, confirming the need for such advanced characterisation techniques.

QC 20131219

The subject of this thesis includes the design of new partitioning methods for the approximation of a function f on a domain C Rd, d 2, by piecewise linear functions, and the derivation of errors estimations in Lp-norm and W1 p - seminorm. In the two-dimensional setting, we develop a construction of a sequence of anisotropic triangulations, where the approximation provided by the piecewise linear interpolant for a given f C2() with a positive definite Hessian, is asymptotically optimal in Lp-norm and in the same time optimal in W1 p - seminorm with respect to the number of degrees of freedom. As a preparation for this result, we review various local error bounds for the interpolation by linear polynomials on a triangle, and derive a number of new estimates of this type. In addition, for functions of d 2 variables, we propose a new approximation method, where several overlaying partitions of are designed such that the sum of piecewise constant or piecewise linear polynomials over these partitions provides a better approximation order than the one obtainable by using a single partition.

L'objectif de ces travaux de thèse a été de démontrer la possibilité, en se basant sur une approche prédictive, de contrôler avec précision la fonctionnalisation d'un matériau composite, d'isotrope à anisotrope, sous l'application d'un champ électrique. Ces derniers matériaux présentent en effet un fort potentiel pour des applications futures telles que des condensateurs intégrés ou bien encore des composites conducteurs thermiques. Une première approche théorique des différentes forces et mécanismes entrant en jeux lors de l'élaboration de composites anisotropes par chaînage a permis d'identifier les paramètres impactant le procédé d'élaboration. A la suite de cette étude théorique, un modèle de formation de chaînes de particules sous champ électrique a été développé afin de prédire la dynamique de chaînage. Le modèle choisi (méthode moment dipolaire effectif) a permis la simulation de plus de 4500 particules. Les paramètres ayant au préalable été identifiés ont ensuite été mesurés. Pour la permittivité des particules, une méthode de mesure diélectrophorétique a été développée, ce qui est une première dans le cas de particules céramiques. L'élaboration des composites anisotropes a été couplé avec un suivi novateur, en temps réel, d'un marqueur (permittivité) de la formation de chaînes, permettant d'obtenir la dynamique de structuration des particules. Afin de valider l'aspect prédictif du modèle numérique, une comparaison a été effectuée entre la dynamique mesurée et simulée. Les résultats obtenus ont démontré une très bonne fiabilité des prédictions du modèle, même si des progrès sont encore réalisables aux faibles taux de chargement. Dans un dernier temps, une preuve de concept a été démontrée, de la réalisation de composites anisotropes dont les particules sont alignées perpendiculairement au champ électrique
This study was aimed to demonstrate the possibility, based on a predictive approach, to tailor the structure of a composite from isotropic to anisotropic when applying an electric field. This composites have great potential for future applications such as embed capacitors or thermally conductive composites. A theoretical approach of the forces and mechanisms acting in the elaboration of anisotropic composites by chaining allowed identifying the key parameters. Based on this approach a model of particle chaining under electric field was established to predict the structuration dynamics. This model (effective dipole moment) allowed simulating more than 4500 particles. The parameters previously identified were then measured, and for the particle permittivity, a dielectrophoretic measurement method was developed, which was a first for ceramic particles. The elaboration of anisotropic composites was coupled to a novel on-line monitoring of a chaining marker (permittivity), allowing to obtain the structuration dynamics. To validate the predictive aspect of the model, experimental and numerical dynamics were compared showing the robustness and accuracy of the model, even if improvement is still possible at low filler content. In the last part, a proof of concept was demonstrated of the elaboration of anisotropic composites with fillers oriented normally to the direction of the electric field

This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.

Mit dem Einzug numerischer Verfahren zur Dimensionierung von Verkehrskonstruktionen, im Speziellen für Asphaltbefestigung, werden charakteristische Materialkenngrößen benötigt. Des Weiteren wird mit der fortschreitenden Entwicklung von FEM-Programmen, die in Zusammenhang mit Strukturanalysen und Simulationsrechnungen ihren Einsatz finden, die Kenntnis detaillierter Materialkennwerte essentiell. Dass Asphalte mit ihrem charakteristischen Materialverhalten eine Temperatur- und Frequenzabhängigkeit aufweisen, ist anerkannter Stand von Wissenschaft und Technik. In Bezug auf weitere Einflussgrößen existieren nur sehr begrenzte Erkenntnisse. Im Besonderen gilt dies für Abhängigkeiten der Materialkenngrößen von aus der äußeren Beanspruchung resultierenden Spannungszuständen in der Asphaltbefestigung. Ein wesentliches Ziel der Arbeit war die Untersuchung von möglichen Spannungsabhängigkeiten der charakteristischen Materialkenngrößen von Asphalt. In diesem Zusammenhang wurden auch Fragestellungen zu anisotropen Effekten im Materialverhalten aufgegriffen. Die Untersuchungen erfolgten an zwei ausgewählten Asphaltdeckschichtmaterialien, die sich in ihrer Zusammensetzung und granularen Struktur grundlegend voneinander unterscheiden. Zum einen wurden ein Splittmastixasphalt (SMA11S mit PmB 25/55-55A) und zum anderen ein offenporiger Asphalt (PA8 mit PmB 40/100-65A) in das Versuchsprogramm aufgenommen. Die Ansprache des Materialverhaltens erfolgte versuchstechnisch mittels uniaxialer und triaxialer Versuche. Im Ergebnis der Untersuchungen zur Anisotropie von Asphaltmaterialien konnte festgestellt werden, dass die in der Regel gerichtete Verdichtung von Asphalt anisotrope Materialeigenschaften nach sich zieht, unabhängig von der Kornform der verwendeten Gesteinskörnungen und der Ausprägung der Mörtelphase. Des Weiteren war ein wesentliches Ergebnis, dass Asphaltmaterialien in weiten Bereichen der Gebrauchstemperatur ein ausgeprägtes spannungsabhängiges Materialverhalten aufweisen. Erst bei sehr tiefen Temperaturen nähert sich das Materialverhalten von Asphalt einem linear elastischen Festkörperverhalten an. Die granulare Struktur des Asphaltmaterials sowie die Ausprägung der Mörtelphase und der damit verbundenen Bindemittelfilmdicken haben maßgebenden Einfluss auf die Art und Größe der charakteristischen Materialeigenschaften sowie auf die Auswirkungen der jeweiligen Spannungsabhängigkeiten. Als Schlussfolgerung bzw. Ausblick der im Rahmen dieser Arbeit durchgeführten Untersuchungen bleibt festzuhalten, dass für die Erweiterung der Kenntnisse des grundlegenden Materialverhaltens von Asphalt weiterführende Untersuchungen speziell in Bezug auf die Eigenschaften der Einzelbestandteile sowie deren Wechselwirkungen innerhalb der Asphaltstruktur essentiell sind
Characteristic material parameters especially for asphalt pavements are required due to the introduction of numerical pavement design methods. Furthermore, the continuous development of FEM programs, which are used for structural analysis and simulation calculations, also requires the knowledge of detailed material properties. It is state of the art that asphalt shows a significant temperature and frequency dependent behavior. The knowledge regarding additional impact parameters is very limited. This is especially valid for the stress dependency of the material parameters resulting from the stress state within the asphalt pavement based on the external loads. The main aim of this work was the investigation of the possible stress dependencies of the characteristic material parameters of asphalt. In this context, questions related to the anisotropic effects of the material behavior have also been taken up. Two asphalt surface layer materials, which have significant differences in the material composition and the granular structure were investigated in this context. On the one hand a stone mastic asphalt (SMA11S with PmB 25/55-55A) and on the other hand a porous asphalt (PA8 with PmB 40/100-65A) were included in the testing scheme. Uniaxial and triaxial tests were selected to determine the material behavior at the laboratory. Within the determination of the anisotropic material behavior of asphalt, it could be proven that the usually vertical compaction direction during the compaction process effects anisotropic material properties. This behavior can be determined independent from the particle shape, the used aggregate material and the specification of the asphalt mastic. Another essential result is, that asphalt materials show a significant stress dependent material behavior in a wide range of the performance temperature. Only on very low temperatures the material behavior of asphalt can be assumed to be linear elastic. The granular structure of asphalt material as well as the specification of the asphalt mastic and the thickness of the binder between the particles have a significant influence on the type and size of the characteristic material properties and the effect of stress dependency. Finally, it can be concluded, that it is essential to investigate the material behavior of each ingredient and their interaction within the asphalt structure to expand the knowledge regarding the fundamental material behavior of asphalt

O objetivo desta dissertação é a busca de anisotropias em grandes escalas angulares no fluxo de raios cósmicos acima de 4 × 10^{18} eV e o confronto dos resultados obtidos com as previsões dos principais modelos astrofísicos na região de ultra altas energias. Com esse propósito foram analisados os dados de chuveiros atmosféricos extensos registrados pelo Observatório Pierre Auger no período de 01 de janeiro de 2004 até 31 de agosto de 2016, compreendendo um total de 108 480 eventos detetados com ângulos zenitais entre 0 e 80 graus acima de 4 × 10^{18} eV. Efeitos sistemáticos locais como a influência da variação das condições atmosféricas e a influência do campo geomagnético nos estimadores de energia das cascatas atmosféricas foram corrigidos cuidadosamente para evitar a introdução de sinais espúrios de anisotropias na análise. Especial ênfase foi dedicada à construção de um mapa bidimensional na esfera celeste com os valores da exposição para cada direção no céu, calculado com uma precisão de 1% a partir da informação da área de coleção efetiva no Observatório Pierre Auger a cada minuto. Da mesma forma, a distribuição das direções de chegada dos eventos foi registrada em mapas bidimensionais na esfera celeste que, após corrigidos pela exposição, são transformados nos mapas de fluxo usados na análise quantitativa para a busca de anisotropias. Neste trabalho procurou-se padrões dipolares de anisotropias, os quais foram quantificados usando o método de expansão multipolar em harmônicos esféricos. Diferentemente do método bidimensional de Rayleigh usado na maioria dos estudos deste tipo, o método aqui utilizado fornece de maneira direta as três componentes cartesianas do dipolo, por meio das quais a reconstrução da amplitude e orientação espacial do dipolo é feita de maneira mais natural. A busca de anisotropias foi realizada em dois intervalos de energia independentes, assim foram analisados por separado os eventos com energias entre 4 × 10^{18} e 8 × 10^{18} eV e de energias maiores que 8 × 10^{18} eV. No primeiro intervalo não foi encontrado nenhum sinal de anisotropia estatisticamente significativo. No segundo intervalo foi encontrada uma anisotropia dipolar de amplitude d = (7.9 ± 1.1)% com coordenadas equatoriais (_d , _d ) = (103 ± 10 , 38 ± 7 ) graus e uma probabilidade de ocorrência ao acaso de 6.90 × 10^{8} , correspondendo a uma significância estatística acima do limiar de descoberta de 5 . Tal amplitude e direção são melhor explicadas assumindo-se uma origem extragaláctica para os raios cósmicos com energias acima de 8 × 10^{18} eV.
The aim of this dissertation is the search for large scale anisotropies in the cosmic ray flux above 4 × 10^{18} eV and the comparison of the results with the predictions of the main astrophysical models in the ultra high energy region. With this purpose we analyzed the data of extensive air showers detected by the Pierre Auger Observatory in the period of 1st January 2004 to 31st August 2016 comprising a total of 108 480 events with zenith angles between 0 and 80 degrees above the threshold of 4 × 10^{18} eV. Local systematic effects such as the influence of the variation of the atmospheric conditions and the effect of the geomagnetic field in the energy estimators were properly corrected to avoid the introduction of spurious anisotropy signals in the analysis. Special emphasis was placed on the construction of a two-dimensional map on the celestial sphere with the exposure values for each direction on the sky, calculated with an accuracy of 1% from the information of the effective collection area of the observatory at every minute. Likewise, the arrival directions distribution of the events was recorded in two-dimensional maps on the celestial sphere that after correcting by the exposure were transformed into the flux maps to be used in the quantitative analysis for the anisotropies search. In this work we search for dipolar-like anisotropy patterns, which were quantified by performing a spherical harmonics decomposition of the cosmic ray flux map. Unlike the traditional two-dimensional Rayleigh method used in the majority of the studies of this kind, the method used here directly provides the three cartesian components of the dipole, allowing the reconstruction of its amplitude and orientation in a more natural way. The anisotropy search was made in two independent energy bins, so the distributions of the events with energies between 4 × 10^{18} and 8 × 10^{18} eV and those with energies greater than 8 × 10^{18} eV were analyzed separately. In the first energy bin no statistically significant departure from isotropy was found. In the second energy bin a dipole anisotropy of amplitude d = (7.9 ± 1.1)% with equatorial coordinates (_d , _d ) = (103 ± 10 , 38 ± 7 ) degrees and a chance probability of 6.90 × 10^{8} was found, corresponding to a statistical significance above the discovery threshold of 5 . Such amplitude and direction for the reconstructed dipole is better explained if an extragalactic origin is assumed for the bulk of cosmic rays above 8 × 10^{18} eV.

The present work describes investigations on the anisotropic strength behavior of rocks in the splitting tensile test (Brazilian test). Three transversely isotropic rocks (gneiss, slate and sandstone) were studied in the Lab. A total of more than 550 indirect tensile strength tests were conducted, with emphasis was placed on the investigation of the influence of the spatial position of anisotropic weakness plane to the direction of the load on the fracture strength and fracture or fracture mode. In parallel, analytical solutions were evaluated for stress distribution and developed 3D numerical models to study the stress distribution and the fracture mode at the transversely isotropic disc. There were new findings on the fracture mode of crack propagation, the influence of the disc thickness, the influence of the applying loading angle and angle of the loading-foliation for transversely isotropic material
Inhalt der Arbeit sind Untersuchungen zum anisotropen Festigkeitsverhalten von Gesteinen beim Spaltzugversuch (Brazilian Test). Laborativ wurden drei transversalisotrope Gesteine (Granit, Schiefer und Sandstein) untersucht. Insgesamt wurden mehr als 550 Spaltzugversuche durchgeführt, wobei der Schwerpunkt auf die Untersuchung des Einflusses der räumlichen Lage der Anisotropieebene zur Richtung des Lasteintrages auf die Bruchfestigkeit und das Bruchbild bzw. den Bruchmodus gelegt wurde. Parallel dazu wurden analytische Lösungen zur Spannungsverteilung ausgewertet sowie numerische 3D-Modelle entwickelt, um die Spannungsverteilung sowie den Bruchmodus bei einer transversalisotropen Scheibe zu untersuchen. Es wurden neue Erkenntnisse zum Bruchmodus, der Rissausbreitung, des Einflusses der Scheibendicke, dem Einfluss des Lasteinleitungswinkel sowie des Winkels Lasteintrag - Anisotropieebene für transversalisotropes Material gewonnen

We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions.

Cell-substrate interactions are of interest in modern biology. The system of surface bound hydrogels is commonly used as a cell culture surface in the field of cell biomechanics. However, the effect gel geometry (thickness, width and length) has on both the mechanics of the gel and the cells behaviour has usually been ignored. It was discovered that a cell differentially spreads and preferentially accumulates at a certain position with respect to the local variation in thickness along a wedge gel (thickness varied from ~50 to 400 µm). This happened although this range of thickness is supposed to be sufficient to prevent the cells from sensing the underlying rigidity of the supporting glass. The mechanical anisotropy of the gel due to its being bound to the substrate was hypothesised to be the cause of the cell behaviour observed. It was later proven that lateral swelling varies exponentially with thickness. The consequences are the decrease in lateral compression and the lateral dilution of gel network density with increasing gel thickness. Both could cause variations of substrate mechanics. The amount of crosslinker, the geometry of the bound area and type of bathing medium all changed the degree of lateral swelling, and thus are contributing factors influencing the lateral mechanics of the swollen gel. Surface bound square gels (50-2000 μm thick) were found to be stiffer with increasing thickness as measured with an atomic force microscope (AFM). This could be due to a change in osmotic pressure. These indentation based measurements of vertical mechanics might be of little relevance with respect to the cellular response though. This was supported with another set of cell experiments on such samples, where the cell did not respond in accordance with the stiffness as measured by AFM. It was therefore implied that the difference in cell behaviour observed on the substrates of different height might be a result of an interplay between the lateral mechanics and the rate of liquid flow though the gel. The x-, y-aspect ratio was also found to influence cell alignment. Cells tended to align randomly on square (aspect ratio: 1:1), and perpendicular to the direction of the long axis of the gels in high aspect ratio (1:4 – 1:11) gels. This preference could be impaired by inhibition of the interaction between actin and myosin II using blebbistatin treatment. This suggests that actomyosin activity is necessary for such the behaviour. The set of studies stressed the importance of x-, y- and z- macrogeometries of surface bound gels as these factors influence mechanical surface anisotropy. These results could have an implication not only in pure cell biology and cell biomechanics but also in regenerative medicine, physiology, wound healing, embryo development, and oncogenesis, wherever cells are in contact with soft biomaterials or orient themselves with respect to mechanical or other features

Research was directed towards further understanding the process of templating, whereby the crystallisation of the bulk material (branched polyethylene) Is altered from unoriented to oriented after melt shear by mapping it on to a pre-existing minority structure (linear polyethylene). Due to the rotational component in shear flow It Is considered a weaker flow, as compared to elongatlonal flow, for providing chain extension. Removal of the rotational component might lead to higher levels of anisotropy being detected in the melt, thus aiding in the understanding of templating. This was achieved by utilising a custom-built channel die to impart plane-strain compression in the melt.

PROGRAMA NACIONAL DE COOPERAÇÃO ACADÊMICA
Esta tese apresenta uma análise de uma estrutura de corneta cônica corrugada com dielétrico anisotrópico, com eixo óptico na direção axial da corneta. Esta configuração de corneta pode ser conseguida utilizando-se a estrutura de uma corneta corrugada com a adição de um cone dielétrico anisotrópico uniaxial. A anisotropia pode ser conseguida artificialmente dopando-se o material dielétrico isotrópico ou utilizando-se uma técnica de perfuração na direção axial do cone. Esta técnica de perfuração é sugerida e apresentada nesta Tese. Partindo-se da geometria definida, foram desenvolvidas as expressões dos campos transversais e o equacionamento para a obtenção das curvas características da estrutura. É apresentado ainda um estudo comparativo dos campos transversais com os casos degenerados já conhecidos de guias cilíndricos, entre eles, guia cilíndrico corrugado oco, guia cilíndrico metálico com bastão dielétrico, guia cilíndrico corrugado com bastão dielétrico isotrópico. As expressões para o cálculo dos campos radiados distantes foram obtidas para o guia cilíndrico corrugado com dielétrico anisotrópico. Em adição, expressões para o cálculo dos campos radiados distantes para a corneta cilíndrica corrugada com dielétrico anisotrópico com pequenos ângulos de abertura (flare angle) utilizando-se a aproximação por capa esférica foram obtidas e apresentadas. Estas expressões foram baseadas na terceira definição de Ludwig. Foram realizadas análises para estruturas já conhecidas geradas a partir da degeneração do caso mais geral apresentado nesta tese com o objetivo de validar a teoria desenvolvida e os resultados provaram a validade do material teórico desenvolvido. Finalmente, foi desenvolvida uma análise paramétrica da estrutura apresentada com o intuito de verificar o comportamento dos campos radiados e da polarização cruzada máxima em função da anisotropia e da frequência de operação. Verificou-se que a largura de feixe de meia potência foi pouco influenciada pela anisotropia do dielétrico e apresentou comportamento esperado em função da frequencia. A variação da máxima polarização cruzada em função da frequência foi estudada. Em determinados valores de permissividade e anisotropia, para a configuração considerada, foi alcançada a condição híbrida balanceada. Nesta condição a estrutura apresentou baixos níveis de máxima polarização cruzada em uma faixa larga de frequência. Comportamento este muito superior ao da corneta corrugada, corneta metálica com dielétrico e corneta corrugada com dielétrico isotrópico.
This thesis presents an analysis of a corrugated conic horn structure with anisotropic dielectric. This dielectric cone is positioned inside the horn and has an optical axis in its longitudinal direction. This horn configuration can be obtained using the structure of corrugated horn and adding an anisotropic dielectric cone. The anisotropy can artificially be obtained by doping the isotropic dielectric or using a perforation technique. This perforation technique is suggested and presented in this Thesis. Expressions for the transverse fields and the propagation constant curves were developed considering this new geometry. It is also presented a comparative study of the degenerated transversal fields with well-known structures. These structures are: hollow cylindrical guide, corrugated cylindrical guide, cylindrical metallic guide with dielectric and corrugated cylindrical guide with dielectric. The expressions to calculate the radiated far fields were obtained for the corrugated cylindrical guide with anisotropic dielectric. In addition, expressions to calculate the radiated far fields for the corrugated cylindrical horn with anisotropic dielectric were developed and presented. These expressions considered horns with small flare angle and used the spherical cap approximation theory. All expressions considered the 3th Ludwig definition for the radiated far field. Far field analyses were conducted for well-known structures. These structures were obtained by degenerating the new configuration presented in this thesis and aimed to validate the theoretical developed theory. The results proved its validity. Finally, a parametric analysis was performed. This analysis considered, for a given structure configuration, the behavior of the radiated far fields and its maximum cross polar levels as a function of the anisotropy and frequency. It was verified that the dielectric anisotropy had very little effect on the half power beam width characteristic. The maximum cross polar level as a function of the frequency was analyzed. For some specific values of permittivity and anisotropy, for the considered configuration, the balanced hybrid condition was reached. In this condition the structure presented very low cross polar values in a large frequency band. This behavior is much more superior to the corrugated horn, dielectric horn and the isotropic dielectric corrugated horn.

Silicon micromachining is the collective name for several processes by which three dimensional structures may be constructed from or on silicon wafers. One of these processes is anisotropic etching, which utilizes etchants such as KOH and ethylene diamine pyrocatechol (EDP) to fabricate structures from the wafer bulk. This project is a study of the use of KOH to anisotropically etch (lOO)-oriented silicon wafers. The thesis provides a thorough review of the theory and principles of anisotropic etching as applied to (100) wafers, followed by a few examples which serve to illustrate the theory. Next, the thesis describes the development and experimental verification of a standardized procedure by which anisotropic etching may be reliably performed in a typical research laboratory environment. After the development of this procedure, several more etching experiments were performed to compare the effects of various modifications of the etching process. Multi-step etching processes were demonstrated, as well as simultaneous doublesided etching using two different masks. The advantages and limitations of both methods are addressed in this thesis. A comparison of experiments performed at different etchant temperatures indicates that high temperatures (800 C) produces reasonably good results at a very high etch rate, while lower temperatures (500 C) are more suited to high-precision structures since they produce smoother, higher-quality surfaces.
Master of Science

The generalized radiation conditions at infinity of Sommerfeld-Kupradze type are established in the theory of thermoelasticity of anisotropic bodies. Applying the potential method and the theory of pseudodifferential equations on manifolds the uniqueness and existence theorems of solutions to the basic three-dimensional exterior boundary value problems are proved and representation formulas of solutions by potential type integrals are obtained.

Le rayonnement d'une source ultrasonore située sur l'une des interfaces d'une plaque anisotrope est étudié. Le calcul du tenseur de Green est effectué dans le cas général d'un problème 3D. Une décomposition en multiples réflexions /réfractions, constituant une série de rayons au sein de la plaque, est utilisée pour une comparaison théorie-expérience dans le cas d'un mono cristal de Cuivre. La vitesse de phase et la vitesse d'énergie sont mesurées en fonction de la fréquence ou de la direction d'observation, pour une plaque de carbone-époxy unidirectionnels, et comparées avec la théorie
The ultrasonic radiation from a source located on one of the interfaces of an anisotropic plateis studied. The calculation of the Green tensor is performed in the general case of a 3Dproblem. Decomposition into multiple reflections /refractions, as a series of rays in the plate,is used for comparison between theory and experiment in the case of a single crystal of copper. The phase velocity and energy velocity are measured in terms of frequency ordirection of observation, for a plate of unidirectional carbon-epoxy, and compared withtheory

Apresentaremos uma série de estudos realizados sobre o tema anisotropias magnéticas induzidas (Kind) em 1igas amorfas. Foram usados vários tipos de tratamentos térmico, com o objetivo de obtermos uma visão amp1a do assunto. A análise teórica dos dados de Kind e de \"after-effect\" magnético (MAE) foi feita com um modelo baseado em sistemas de dois níveis (TLS). A partir da análise dos dados experimentais obtém-se um largo espectro de energias de ativação. Estas energias estão relacionadas aos tempos de re1axação, através da equação de Arrhenius: = 0 exp (E/kT), onde o pré-fator 0 é da ordem do inverso da frequência de Debye. Construiu-se um forno para tratamentos térmicos em ligas amorfas, que opera em um eletroimã de 6 kOe e desenvolveu-se os programas para análise de dados experimentais. Essas facilidades, associadas ao traçador de curvas de histerese, permitiram os seguintes estudos de anisotropias induzidas em ligas amorfas ferromagnéticas: 1. Estudo da cinética de indução de anisotropia por tratamentos térmicos na faixa de temperatura de 190 a 250 °C, para fitas amorfas \"as cast\" de composição C070.4Fe4.6 Si15B10. Com o modelo TLS pode-se obter o espectro de energias de ativação, que se apresentou na faixa de energia de 1.50 a 1.85eV, com 0 = 1.6 x 10-13s. 2. Realizou-se também o estudo da indução de anisotropia na presença de um campo magnético de 5 kOe, para amostras pré-tratadas a 400 °C por 10 minutos. Estas são de composição Co77-X Mnx Si14 B9, com X = 2 e 6 e foram submetidas a tratamentos isotérmicos a temperaturas entre 240 e 325 °C. Neste caso pode-se verificar que para as duas composiQ6es 0 pré-fator é maior ( 10-8S). Quanto ao espectro de energias de ativação, em ambos os casos, apresenta-se na faixa de energias de 1.10 a 1.55 eV. 3.Outro experimento, neste caso com amostras de composição Co67Fe4Mo1Si12B16 consistiu na aplicação, à temperatura ambiente, de tensão mecânica ( 800 MPa) na fita, enquanto se monitorava a energia de anisotropia magnética. Pudemos então observar uma variação continua dessa propriedade e posteriormente uma recuperação completa da condição inicial, com a remoção da tensão aplicada, mostrando um processo de caráter anelástico. Procuramos estudar os efeitos de tensões mecânicas sobre as propriedades magnéticas de amostras com composição Co67Fe4Mo1Si12B16. Duas linhas de trabalho foram adotadas: 4) Numa olhou-se para a isotropia induzida em amostras pré-tratadas, quando submetidas a tratamentos térmicos na faixa de temperatura de 200 a 400 °C, sob tensão mecânica de 500 MPa e posteriormente na ausência de tensão. A partir desses ensaios foi possível se separar uma componente plástica e outra anelástica na anisotropia induzida. 5) Noutra, obteve-se o comportamento do MAE, para amostras com e sem tensão mecânica aplicada, no intervalo de 300 a 500 K. Os resultados obtidos demonstram a não existência de efeitos plásticos ou anelásticos nas energias de ativação dos processos envolvidos no \"after-effect\". Por outro lado verificamos uma grande alteração na intensidade do MAE, devido à tensão.
In this thesis we will present a series of studies related to induced magnetic anisotropies (Kind) in amorphous alloys. In order to get a more general view of this theme, we used several different kinds of annealings. The theoretical analysis of the data of Kind and magnetic after-effect (MAE) was performed using a model based on two-level systems (TLS). From the analysis of the experimental data we get a large actiyation energy spectrum. These energies are related to the relaxation times, through the Arrheniu \'s expression: = 0 exp(E/kT), where the pre-factor 0 is of the order of the inverse of the Debye frequency . We constructed a furnace for thermal annealing of the amorphous alloys, which operates within an electromagnet producing 6 kOe. We also wrote, the computer programs for the analysis of the experimental data. These facilities, together with the hysteresis loop tracer permitted the followings studies of the induced anisotropies in amorphous alloys: 1) A study of the kinetics of the induced anisotropy by annealing in the temperature range from 190 to 250 °C, in as cast amorphous ribbons of composition Co70.4Fe4.6Si15B10. Using the TLS model we obtained the activation energy spectrum. It presents two peaks in the energy range from 1.50 to 1.85eV and a pre-factor 0= 1.6x10-13 s. 2) Using a 5 KOe magnetic field we studied the effects of a Field annealing treatment in samples pre-annealed at 400 °C for 10 minutes. The isothermal annealings were made in Co70-XMnXSi14B9 with x = 2 and 6, in the temperature range from 240 to 325 °C. In this case we observed for these two compositions a larger pre-factor ( 10-8s) than before. The activation-energy spectra, for the both composition, are found in the energy range from 1.10 to 1.55eV. 3) Another experiment was done using samples of Co67Fe4Mo1Si12B16. We applied a tensile stress (800MPa) to the ribbon and measured the magnetic anisotropy energy. We observed a continuous variation of this energy and, after removal of the stress, the sample recuperated its initial condition, showing a process characteristically anelastic. We studied the effects of mechanic stress on the magnetic properties of samples of composition Co67Fe4Mo1Si12B16. We worked in two directions: 4) We studied the induced anisotropy in pre-annealed samples, submitted to annealing in the range from 200 to 400 °C, under a tensile stress of 500MPa and without applied stress. From these resul ts we can separate a plastic and an anelastic component in the induced anisotropy. 5) In other, we studied the behavior of the MAE, for samples with and with and without applied tensile stress, in the range from 300 to 500 K. The results obtained show neither plastic nor anelastic effects on the activation energies of the processes involved in the MAE. On the other h~nd we can see a strong alteration in the intensity of the MAE, due the stress.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Anisotropic magnetoresistance (AMR) corresponds to the change of R in an ferromagnetic material with the angle between electric current and magnetization. Sensors using this effect are suited to detect both angular and linear displacements. In this work, structural, magnetic and electric characterization were performed in order to study the exchange interaction between antiferromagnetic IrMn and ferromagnetic NiFe, in a bilayer and a multilayer. Simulations of the AMR measurements were performed and showed good agreement with the experimental data. Different anisotropy field values were observed. The difference between the anisotropy field and the exchange field values is responsible for the different AMR data sets extracted from each sample. The model takes into account the, anisotropy (uniaxial), Zeeman, and exchange-bias (unidirectional) energies was used to explain the observed behavior.
Magnetorresistência anisotrópica (AMR) consiste na variação da resistência de um material ferromagnético em função do ângulo entre a corrente elétrica e a magnetização do material, o que faz com que sensores que utilizam este efeito sejam promissores para medidas de posição tanto angulares quanto lineares. Neste trabalho, caracterização estrutural, magnética e elétrica foram realizadas para estudar a interação de troca entre camadas antiferromagnética de IrMn e ferromagnética de NiFe em uma bicamada e uma multicamada. Simulações das medidas de AMR foram realizadas e boa concordância entre os dados experimentais e os simulados foi obtida. Diferentes valores de campos de anisotropias foram observados. A diferença entre o campo de anisotropia unidirecional e o campo de exchange é responsável pela diferença entre as medidas de AMR obtidas. Um modelo que considera as energias de anisotropia (uniaxial), Zeeman e de exchangebias (unidirecional) foi usado para explicar o comportamento observado.

Les ferrofluides sont des suspensions colloïdales de nanoparticules magnétiques dispersées dans un liquide porteur. La possibilité de moduler les propriétés des ferrofluides in situ en appliquant un champ magnétique externe leur procure un fort potentiel d’étude, à la fois d’un point de vue fondamental ou pour des applications industrielles variées. En particulier, les nanospinels de ferrite ferrimagnétiques MFe2O4 (M = Fe2+, Co2+, Mn2+…) sont largement étudiés pour leurs propriétés électriques et magnétiques. Plus spécifiquement, une forte énergie d’anisotropie de ces matériaux à l’échelle nanométrique est requise pour des applications dans le stockage de l’information ou l’hyperthermie pour lesquels ils sont considérés. Une connaissance fine des mécanismes régissant ces propriétés d’anisotropies magnétiques est ainsi primordiale pour la création de nouveaux objets aux propriétés magnétiques contrôlées à l’échelle nanométrique. L’originalité de notre approche consiste à utiliser une technique fine du magnétisme, le dichroïsme magnétique circulaire des rayons X (XMCD) à l’étude des anisotropies et couplages magnétiques des nanospinels composants les ferrofluides. Au cours de cette thèse, nous nous sommes intéressés à différentes stratégies possibles pour induire une forte énergie d’anisotropie aux nanospinels de ferrite par l’utilisation de cobalt. Des nanoparticules de tailles et compositions variées ont été obtenues par différentes voies de synthèse, et nous démontrons que l’anisotropie magnétique de ces systèmes est fortement gouvernée par la symétrie de site du Co2+ en structure spinel qui peut être directement corrélé au processus de synthèse utilisé. Nous nous sommes aussi intéressés à l’ordre et au couplage magnétique de ferrite spinels structurés en coeur-coquille, dont le cœur et la coquille sont réalisés à partir de matériaux aux propriétés magnétiques intrinsèques différentes. Nous montrons ainsi que pour des nanospinels MnFe2O4@CoFe2O4, la très fine coquille formée de CoFe2O4 impose une forte anisotropie magnétique au cœur doux de MnFe2O4. Enfin, nous nous sommes intéressés à une troisième classe de ferrofluide à base de nanospinels, les ferrofluides binaires, constitué d’un mélange physique de ferrofluides aux propriétés magnétiques intrinsèques différentes. Pour de tels systèmes, il est essentiel de préserver le liquide porteur du ferrofluide pour ne pas dénaturer les interactions entre particules existantes. L’un des objectifs de cette thèse fut donc d’étendre la technique du XMCD à l’étude d’échantillons de ferrofluides in situ, dans leur phase liquide ou gelée. Nous avons débuté la conception d’une cellule liquide compatible avec les rayons X mous et un environnement ultra-vide sur la ligne de lumière DEIMOS (SOLEIL) qui est toujours en développement
Ferrofluids are colloidal suspensions of magnetic nanoparticles dispersed in a carrier liquid. The intimate interaction between the magnetic nanoparticles and the liquid provides a unique system, from both fundamental and industrial application point of views, whose flow and properties can be precisely controlled using an external magnetic field. Magnetic nanoparticles of spinel ferrites MFe2O4 (M = Fe2+, Co2+, Mn2+…) are of particular scientific interest and have been extensively studied for their electrical and magnetic properties. Spinel ferrites find potential applications, notably in storage devices, for computers, or hyperthermia, for cancer treatment, where high magnetic anisotropy energies are required at the nanoscale. However, deeper knowledges of the fine mechanisms playing a significant role on the magnetic anisotropies existing in the nanospinels are necessary to help the creation of rationalized materials with controlled magnetic anisotropies for the requirement of the system. In this thesis, we have used X-ray Magnetic Circular Dichroism (XMCD) as an original approach for probing the magnetic anisotropies and magnetic couplings of nanospinels obtained in ferrofluids. The nanoparticles are iron bearing spinels for which cobalt ions have been introduced in the spinel structure of the nanoparticles as a true makers of magnetic anisotropy. First, magnetic nanospinels have been synthesized by tuning their size and composition and using different synthesis processes. XMCD investigations revealed that the coercive field of the nanospinels is governed by the concentration of Co2+ ions sitting in octahedral sites of the spinel structure, and this can be directly linked to some synthesis parameters. Then, we have investigated core@shell nanoparticles, which can be synthesized with an appropriate choice of magnetic anisotropies for the core and the shell in order to tailor optimal magnetic properties. In the case of MnFe2O4@CoFe2O4, our findings reveal that the very thin CoFe2O4 shell imposes a strong magnetic anisotropy to the otherwise very soft MnFe2O4 core. The other class of ferrofluids that has been investigated during this thesis are binary ferrofluids that are constituted of two different types of magnetic nanoparticles. For such systems, the carrier liquid must be preserved to understand the magnetic interactions in the ferrofluid as they are. Another motivation of this thesis was thus to extend XMCD to the in situ investigation of the nanospinels dispersed in ferrofluids. We have been started a liquid cell development in the DEIMOS beamline at SOLEIL. The setup is still in progress and is aimed at being compatible with soft X-Rays short penetration depth and ultra-high vacuum environment. Hard X-ray photon-in/photon-out spectroscopy coupled to XMCD (1s2p RIXS-MCD) can be a very valuable alternative to soft X-ray XMCD at K-edge of 3d elements when liquid cell sample environment is required. The instrumental development of a liquid cell used with 1s2p RIXS-MCD spectroscopy allowed us to investigate the nanoparticles directly in the ferrofluids revealing interparticles magnetic couplings in binary ferrofluids

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Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
Many astronomical observations in the last few years are strongly suggesting that the current Universe is spatially flat and dominated by an exotic form of energy. This unknown energy density accelerates the universe expansion and corresponds to around 70% of its total density being usually called Dark Energy or Quintessence. One of the candidates to dark energy is the so-called cosmological constant (Λ) which is usually interpreted as the vacuum energy density. However, in order to remove the discrepancy between the expected and observed values for the vacuum energy density some current models assume that the vacuum energy is continuously decaying due to its possible coupling with the others matter fields existing in the Cosmos. In this dissertation, starting from concepts and basis of General Relativity Theory, we study the Cosmic Microwave Background Radiation with emphasis on the anisotropies or temperature fluctuations which are one of the oldest relic of the observed Universe. The anisotropies are deduced by integrating the Boltzmann equation in order to explain qualitatively the generation and c1assification of the fluctuations. In the following we construct explicitly the angular power spectrum of anisotropies for cosmologies with cosmological constant (ΛCDM) and a decaying vacuum energy density (Λ(t)CDM). Finally, with basis on the quadrupole moment measured by the WMAP experiment, we estimate the decaying rates of the vacuum energy density in matter and in radiation for a smoothly and non-smoothly decaying vacuum
Muitas observa??es astron?micas feitas nos ?ltimos anos sugerem fortemente que o universo ? espacialmente plano e dominado por uma forma de energia ex?tica. Esta densidade de energia desconhecida acelera a expans?o do universo e corresponde a cerca de 70% da densidade total de energia sendo chamada de Energia Escura ou Quintess?ncia. Um dos candidatos a energia escura, ? a chamada constante cosmol?gica (Λ) que ? usualmente interpretada como a densidade de energia do v?cuo. Contudo, para remover a discrep?ncia entre os valores esperado e observado para a densidade de energia do v?cuo, alguns modelos atuais assumem que a energia do v?cuo decai continuamente devido a seu poss?vel acoplamento com os outros campos materiais do cosmos. Nesta disserta??o, partindo dos conceitos e fundamentos da teoria da relatividade geral, estudamos a radia??o c?smica de fundo com ?nfase nas anisotropias ou flutua??es em sua temperatura que servem de base observacional para o modelo do Big Bang e ? uma das rel?quias mais antigas do universo. As anisotropias s?o deduzidas a partir da integra??o da equa??o de Boltzrnann, que fazemos em primeira ordem para explicar qualitativamente a gera??o e c1assifica??o destas flutua??es. Em seguida construimos o espectro angular de pot?ncia das anisotropias e deduzimos sua forma expl?cita em grandes escalas para o modelo com constante cosmol?gica (ACDM) e para um modelo com decaimento do v?cuo (Λ(t)CDM). Com base no momento de quadrup?lo medido pelo experimento do WMAP; estimamos as raz?es de decaimento da densidade de energia do v?cuo em mat?ria e em radia??o tanto no decaimento homog?neo como no n?o- homog?neo

When the finite element method is used to solve boundary value problems, the corresponding finite element mesh is appropriate if it is reflects the behavior of the true solution. A posteriori error estimators are suited to construct adequate meshes. They are useful to measure the quality of an approximate solution and to design adaptive solution algorithms. Singularly perturbed problems yield in general solutions with anisotropic features, e.g. strong boundary or interior layers. For such problems it is useful to use anisotropic meshes in order to reach maximal order of convergence. Moreover, the quality of the numerical solution rests on the robustness of the a posteriori error estimation with respect to both the anisotropy of the mesh and the perturbation parameters. There exist different possibilities to measure the a posteriori error in the energy norm for the singularly perturbed reaction-diffusion equation. One of them is the equilibrated residual method which is known to be robust as long as one solves auxiliary local Neumann problems exactly on each element. We provide a basis for an approximate solution of the aforementioned auxiliary problem and show that this approximation does not affect the quality of the error estimation. Another approach that we develope for the a posteriori error estimation is the hierarchical error estimator. The robustness proof for this estimator involves some stages including the strengthened Cauchy-Schwarz inequality and the error reduction property for the chosen space enrichment. In the rest of the work we deal with adaptive algorithms. We provide an overview of the existing methods for the isotropic meshes and then generalize the ideas for the anisotropic case. For the resulting algorithm the error reduction estimates are proven for the Poisson equation and for the singularly perturbed reaction-difussion equation. The convergence for the Poisson equation is also shown. Numerical experiments for the equilibrated residual method, for the hierarchical error estimator and for the adaptive algorithm confirm the theory. The adaptive algorithm shows its potential by creating the anisotropic mesh for the problem with the boundary layer starting with a very coarse isotropic mesh.

In this thesis, mechanical and elastic behaviour of anisotropic materials are inves- tigated in order to understand the optimum mechanical behaviour of them in selected directions. For an anisotropic material with known elastic constants, it is possible to choose the best set of e¤
ective elastic constants and e¤
ective eigen- values which determine the optimum mechanical and elastic properties of it and also represent the material in a speci.ed greater material symmetry. For this reason, bounds on the e¤
ective elastic constants which are the best set of elastic constants and e¤
ective eigenvalues of materials have been constructed symbollicaly for all anisotropic elastic symmetries by using Hill [4,13] approach. Anisotropic Hooke.s law and its Kelvin inspired formulation are described and generalized Hill inequalities are explained in detail. For di¤
erent types of sym- metries, materials were selected randomly and data of elastic constants for them were collected. These data have been used to calculate bounds on the e¤
ective elastic constants and e¤
ective eigenvalues. Finally, by examining numerical results of bounds given in tables, it is seen that the materials selected from the same symmetry type which have larger interval between the bounds, are more anisotropic, whereas some materials which have smaller interval between the bounds, are closer to isotropy.

Techniques from the theory of partial differential equations are often used to design filter methods that are locally adapted to the image structure. These techniques are usually used in the investigation of gray-value images. The extension to color images is non-trivial, where the choice of an appropriate color space is crucial. The RGB color space is often used although it is known that the space of human color perception is best described in terms of non-euclidean geometry, which is fundamentally different from the structure of the RGB space. Instead of the standard RGB space, we use a simple color transformation based on the theory of finite groups. It is shown that this transformation reduces the color artifacts originating from the diffusion processes on RGB images. The developed algorithm is evaluated on a set of real-world images, and it is shown that our approach exhibits fewer color artifacts compared to state-of-the-art techniques. Also, our approach preserves details in the image for a larger number of iterations.
Original Publication:Åström Freddie, Felsberg Michael and Lenz Reiner, Color Persistent Anisotropic Diffusion of Images, 2011, Image Analysis, SCIA conference, 23-27 May 2011, Ystad Sweden, 262-272.http://dx.doi.org/10.1007/978-3-642-21227-7_25Copyright: Springer