A teoria quântica de campos pode ser vista como um conjunto de métodos e idéias que além de sua importância no estudo das partículas elementares, tem sido amplamente usada em outras áreas. Em especial, ela constitui uma ferramenta indispensável no estudo moderno de transições de fases e fenômenos críticos. A origem dessa constante relação entre a teoria de campos e a matéria condensada deve-se ao fato que, apesar de suas diferenças superficiais, ambas tratam de problemas envolvendo um grande número de graus de liberdade. Assim, não é surpreendente que as mesmas técnicas possam ser úteis nos dois campos. Este trabalho trata de problemas nessas duas áreas e está essencialmente divido em duas partes. A primeira parte é dedicada ao estudo de teorias de campos com uma anisotropia entre o espaço e o tempo, o que implica uma quebra da simetria de Lorentz. Uma das motivações para considerar esse tipo de teoria vem justamente do estudo de transições de fase em sistemas da matéria condensada. Análises do grupo de renormalização com ênfase na possibilidade de restauração da simetria de Lorentz e também uma discussão sobre identidades de Ward são realizadas. Na segunda parte, a atenção é voltada para a mecânica estatística mas com uma abordagem típica da teoria de campos, em especial, voltada para o estudo de transições de fase clássicas e quânticas a partir da versão quantizada do modelo esférico e de sua extensão supersimétrica. / Quantum field theory can be seen as a set of methods and ideas that, besides its importance in the study of the elementary particles, has been widely used in other areas. In particular, it constitutes an indispensable framework in the modern approach to phase transitions and critical phenomena. The origin of this constant relationship between field theory and condensed matter is due to the fact that despite their superficial differences, both deal with problems involving a large number of degrees of freedom. Thus, it is not surprising that the same techniques may be useful in both fields. This work addresses problems in these two areas and it is essentially divided in two parts. The first part is devoted to the study of field theories with an anisotropy between space and time, which implies a breaking of the Lorentz symmetry. One of the moti- vations for considering this kind of theory is precisely the study of phase transitions in condensed matter systems. Renormalization group analysis with emphasis on the possi- bility of restoration of the Lorentz symmetry and also a discussion about Ward identities are performed. In the second part, the attention is centered on statistical mechanics but with an approach typical of field theory, in particular, focused to the study of classical and quantum phase transitions from the quantized version of the spherical model and its supersymmetric extension.

Dada uma ação isométrica livre do grupo binário tetraedral G sobre esferas de dimensão ímpar, obtemos uma decomposição celular finita explícita para as formas espaciais esféricas tetraedrais, fazendo uso do conceito de região (ou domínio) fundamental. A estrutura celular deixa explícita uma descrição do complexo de cadeias sobre o grupo G. Como aplicações, utilizamos o complexo de cadeias e a interpretação geométrica do produto cup para calcular o anel de cohomologia da forma espacial esférica tetraedral em dimensão três, e também calculamos a torção de Reidemeister destes espaços para uma determinada representação de G / Given a free isometric action of a binary tetrahedral group G on odd dimensional spheres, we obtain an explicit finite cellular decomposition of the tetrahedral spherical space forms, using the concept of fundamental domain. The cellular structure gives an explicit description of the associated cellular chain complex over the group G. As applications we use the chain complex and the geometric interpretation of the cup product to calculate the cohomology ring of the tetrahedral spherical space form in three dimension, and also compute the Reidemeister torsion of these spaces for a determined representation of G

Diffusion of water molecules in biological tissues depends on several microstructural properties. Therefore, diffusion Magnetic Resonance Imaging (dMRI) is a useful tool to infer and study microstructural brain changes in the context of human development, ageing and neuropathology. In this thesis, the state-of-the-art of advanced dMRI techniques is explored and strategies to overcome or reduce its pitfalls are developed and validated. Firstly, it is shown that PCA denoising and Gibbs artefact suppression algorithms provide an optimal compromise between increased precision of diffusion measures and the loss of tissue's diffusion non-Gaussian information. Secondly, the spatial information provided by the diffusion kurtosis imaging (DKI) technique is explored and used to resolve crossing fibres and generalize diffusion measures to cases not limited to well-aligned white matter fibres. Thirdly, as an alternative to diffusion microstructural modelling techniques such as the neurite orientation dispersion and density imaging (NODDI), it is shown that spherical deconvolution techniques can be used to characterize fibre crossing and dispersion simultaneously. Fourthly, free water volume fraction estimates provided by the free water diffusion tensor imaging (fwDTI) are shown to be useful to detect and remove voxels corrupted by cerebrospinal fluid (CSF) partial volume effects. Finally, dMRI techniques are applied to the diffusion data from the large collaborative Cambridge Centre for Ageing and Neuroscience (CamCAN) study. From these data, the inference provided by diffusion anisotropy measures on maturation and degeneration processes is shown to be biased by age-related changes of fibre organization. Inconsistencies of previous NODDI ageing studies are also revealed to be associated with the different age ranges covered. The CamCAN data is also processed using a novel non-Gaussian diffusion characterization technique which is invariant to different fibre configurations. Results show that this technique can provide indices specific to axonal water fraction which can be linked to age-related fibre density changes.

Neste trabalho estudamos diferentes noções de diferenciabilidade para funções definidas na esfera unitária S^n-1 de R^n, n>=2. Em relação à derivada usual, encontramos condições necessárias e/ou suficientes para que uma função seja diferenciável até uma ordem fixada. Para as outras duas, a derivada forte de Laplace-Beltrami e a derivada fraca, apresentamos algumas propriedades básicas e procuramos condições que garantam a equivalência destas com a diferenciabilidade usual. / In this work we study different notions of differentiability for functions defined on the unit sphere S^n-1 of R^n, n>=2. With respect to the usual derivative, we find necessary and/or sufficient conditions in order that a function be differentiable up to a fixed order. As for the other two, the strong Laplace-Beltrami derivative and the weak derivative, we present some basic properties about them and search for conditions that guarantee the equivalence of them with the previous one.

Un nouveau capteur acoustique sphérique autonome est proposé. Il est destiné à être immergé dans un milieu liquide ou pâteux pour mesurer certaines propriétés physiques du milieu et récupérer l'énergie vibratoire ambiante pour assurer son autonomie. Le capteur est composé de deux coquilles hémisphériques en plexiglas et d'une bague piézoélectrique en PZ26 fixée entre les deux coquilles. Cette structure peut être utilisée aussi bien en excitateur que capteur. Un modèle de simulation de la récupération d'énergie vibratoire a été développé en considérant seulement deux modes de vibration: mode épaisseur et mode radial. Pour chaque mode, le comportement de l’anneau est décrit par un circuit électromécanique équivalent reliant les ports mécaniques (forces et vitesses) au port électrique (tension et courant). Ce choix est guidé par la possibilité de combiner la partie électromécanique avec l'électronique qui traite l'énergie directement dans un simulateur basé sur Spice. Pour valider cette approche, une simulation par éléments finis a été réalisée et comparée aux résultats produits par le circuit électromécanique. Les fréquences de résonance ont également été vérifiées expérimentalement avec un analyseur d'impédance. Toutes ces vérifications donnent des résultats en très bon accord avec le modèle électromécanique proposé en termes de fréquences de résonance, de tension et de puissance collectées. Enfin, plusieurs validations expérimentales sont présentées avec un prototype de capteur sphérique. Ces validations montrent l’adéquation des prédictions avec les résultats expérimentaux. Finalement, un test du circuit de récupération est effectué en situation réelle. / A new spherical autonomous acoustic sensor is proposed. It is intended to be immersed in a liquid or pasty medium to measure some physical properties of the medium and should harvest ambient energy to ensure its autonomy. The sensor is composed of two Plexiglas half-spherical shells and a PZ26 piezoelectric ring clamped between the two shells. This structure can be used as well as in exciter or sensor. A simulation model of vibrational energy harvesting has been developed considering only two modes of vibration: thickness and radial modes. For each mode, the ring behavior is described by an equivalent electromechanical circuit connecting the mechanical ports (forces and velocities) to the electrical port (voltage and current). This choice is guided by the possibility to combine the electromechanical part with the electronics that process the energy directly in a Spice based simulator. To validate this approach, a finite elements simulation was realized and compared to the electromechanical circuit results. Resonance frequencies were also verified experimentally with an impedance analyzer. All these verifications give results in very good agreement with the proposed electromechanical model, as well as in terms of resonant frequencies, harvested voltage and power. Finally several experimental investigations are presented with a prototype of spherical sensor. These validations show the adequacy of the predictions with the experimental results. Finally, a test of the harvesting circuit is done in real situation.

Coatings are frequently applied on gas turbine components inorder to restrict surface degradation such as corrosion andoxidation of the structural material or to thermally insulatethe structural material against the hot environment, therebyincreasing the efficiency of the turbine. However, in order toobtain accurate lifetime expectancies and performance of thecoatings system it is necessary to have a reliableunderstanding of the mechanical properties and failuremechanisms of the coatings. In this thesis, mechanical and fracture behaviour have beenstudied for a NiAl coating applied by a pack cementationprocess, an air-plasma sprayed NiCoCrAlY bondcoat, a vacuumplasma-sprayed NiCrAlY bondcoat and an air plasma-sprayed ZrO2+ 6-8 % Y2O3topcoat. The mechanical tests were carried out ata temperature interval between room temperature and 860oC.Small punch tests and spherical indentation were the testmethods applied for this purpose, in which existing bending andindentation theory were adopted for interpretation of the testresults. Efforts were made to validate the test methods toensure their relevance for coating property measurements. Itwas found that the combination of these two methods givescapability to predict the temperature dependence of severalrelevant mechanical properties of gas turbine coatings, forexample the hardness, elastic modulus, yield strength, fracturestrength, flow stress-strain behaviour and ductility.Furthermore, the plasma-sprayed coatings were tested in bothas-coated and heat-treated condition, which revealedsignificant difference in properties. Microstructuralexamination of the bondcoats showed that oxidation with loss ofaluminium plays an important role in the coating degradationand for the property changes in the coatings. Keywords:small punch test, miniaturised disc bendingtests, spherical indentation, coatings, NiAl, APS-NiCoCrAlY,VPS-NiCrAlY, mechanical properties

Over the past decade, fusion research has showed the potential of being a main candidate for energy production for future generations. Further advances in improved fusion performance are therefore vital. This thesis focuses on advanced fusion plasma scenarios and their diagnostic requirements. In particular the design of a motional Stark effect (MSE) diagnostic at the MAST spherical tokamak and the analysis of magneto-hydrodynamic mode feedback control and pulsed poloidal current drive (PPCD) at the reversed field pinch (RFP) experiment EXTRAP T2R are discussed. The MSE diagnostic is important for the determination of the plasma current profile, information that is necessary for studies in advanced confinement scenarios like reversed shear profiles or current holes. The MAST MSE system has two channels and selects the spectral components using 1Å FWHM interference filters. The diagnostic has been commissioned during the fall of 2006 and the results show the feasibility of the technique with rms-noise ~0.5° using a time resolution of 1 ms. Investigations of mirror labyrinths for the future ITER MSE diagnostic highlight the need for careful calibration considerations. Feedback control and PPCD are techniques for improved confinement. Feedback control dramatically decreases impurity influx at the end of discharges while transport in the bulk plasma is largely unaffected. During PPCD the transport is seen to decrease and it is demonstrated that PPCD and feedback control can be employed simultaneously. New and innovative techniques for fusion spectroscopy are furthermore described. This includes the use of correlations in line integrated signals to determine ion emission profiles in poloidally symmetric environments. Good agreement with other diagnostic methods is obtained. The assessment of electron temperature profiles using measured differences between Thomson scattering and vacuum ultra-violet spectroscopy is also shown. / QC 20100907

Despite the immense advances of science and medicine in recent years, several aspects regarding the physiology and the anatomy of the human brain are yet to be discovered and understood. A particularly challenging area in the study of human brain anatomy is that of brain connectivity, which describes the intricate means by which different regions of the brain interact with each other. The study of brain connectivity is deeply dependent on understanding the organization of white matter. The latter is predominantly comprised of bundles of myelinated axons, which serve as connecting pathways between approximately 10¹¹ neurons in the brain. Consequently, the delineation of fine anatomical details of white matter represents a highly challenging objective, and it is still an active area of research in the fields of neuroimaging and neuroscience, in general. Recent advances in medical imaging have resulted in a quantum leap in our understanding of brain anatomy and functionality. In particular, the advent of diffusion magnetic resonance imaging (dMRI) has provided researchers with a non-invasive means to infer information about the connectivity of the human brain. In a nutshell, dMRI is a set of imaging tools which aim at quantifying the process of water diffusion within the human brain to delineate the complex structural configurations of the white matter. Among the existing tools of dMRI high angular resolution diffusion imaging (HARDI) offers a desirable trade-off between its reconstruction accuracy and practical feasibility. In particular, HARDI excels in its ability to delineate complex directional patterns of the neural pathways throughout the brain, while remaining feasible for many clinical applications. Unfortunately, HARDI presents a fundamental trade-off between its ability to discriminate crossings of neural fiber tracts (i.e., its angular resolution) and the signal-to-noise ratio (SNR) of its associated images. Consequently, given that the angular resolution is of fundamental importance in the context of dMRI reconstruction, there is a need for effective algorithms for de-noising HARDI data. In this regard, the most effective de-noising approaches have been observed to be those which exploit both the angular and the spatial-domain regularity of HARDI signals. Accordingly, in this thesis, we propose a formulation of the problem of reconstruction of HARDI signals which incorporates regularization assumptions on both their angular and their spatial domains, while leading to a particularly simple numerical implementation. Experimental evidence suggests that the resulting cross-domain regularization procedure outperforms many other state of the art HARDI de-noising methods. Moreover, the proposed implementation of the algorithm supersedes the original reconstruction problem by a sequence of efficient filters which can be executed in parallel, suggesting its computational advantages over alternative implementations.

En este trabajo se describe un simulador visual de óptica adaptativa (SVOA) empleado con dos objetivos: primero, el testeo y diseño de perfiles de fase progresivos para extender la profundidad de foco y segundo el estudio del efecto de la aberración cromática longitudinal y su acoplamiento con la aberración esférica en el ojo humano.Diversos perfiles de fase progresivos fueron analizados en el SVOA, resultando un excelente acuerdo con las simulaciones teóricas. Algunos de estos perfiles fueron implementados físicamente en lentes de contacto y evaluados visualmente. La buena concordancia que se encontró entre esta evaluación y la obtenida simulando el perfil con el SVOA validan todo el procedimiento y el sistema.También se llevaron a cabo medidas de la capacidad visual combinando la corrección de las aberraciones cromática y esférica. Los resultados indican que la mejor calidad de visión se produce al eliminar al mismo tiempo ambas aberraciones. / An adaptive optics visual simulator (AOVS) is described in this work. It was used to test and design progressive phase profiles to extend depth of focus, and to study the combined effect of both, the longitudinal chromatic aberration and the spherical aberration in the human eye.A set of progressive phase profiles were tested using the AOVS, obtaining an excellent agreement with the theoretical simulations. Some of these phase profiles were implemented on contact lenses and visually tested. Again the results agreed with the evaluation carried out through the AOVS, validating the instrument.Visual performance was also tested correcting either chromatic aberration or spherical aberration or both, resulting the best performance when both aberrations are simultaneously corrected.

In this thesis, we propose and evaluate two novel scale-based decomposable representations of shape for the segmentation and morphometric analysis of anatomical structures in medical imaging. We propose two representations that are adapted to a particular class of anatomical structures and allow for a richer shape description and a more fine-grained control over the deformation of models based on these representations, when compared to previous techniques. In the first part of this thesis, we introduce the concept of a scale-space shape filter for implicit shape representations that measures the deviation from a tubular shape in a local neighborhood of points, given a particular scale of analysis. We use these filters for the segmentation of blood vessels, and introduce the notion of segmentation with a soft shape prior, where the segmented model is not globally constrained to a predefined shape space, but is penalized locally if it deviates strongly from a tubular structure. Using this filter, we derive a region-based active contour segmentation algorithm for tubular structures that penalizes leakages. We present results on synthetic and real 2D and 3D datasets. In the second part of this thesis, we present a novel multi-scale parametric shape representation using spherical wavelets. Our proposed shape representation encodes shape variations in a population at various scales to be used as prior in a probabilistic segmentation framework. We derive a probabilistic active surface segmentation algorithm using the multi-scale prior coefficients as parameters for our optimization procedure. One nice benefit of this algorithm is that the optimization method can be applied in a coarse-to-fine manner. We present results on 3D sub-cortical brain structures. We also present a novel method of statistical surface-based morphometry based on the use of non-parametric permutation tests and the spherical wavelet shape representation. As an application, we analyze two sub-cortical brain structures, the caudate nucleus and hippocampus.