No description available.

No description available.

La magnétohydrodynamique (MHD) est la science et le formalisme qui décrivent les mouvements d'un fluide conducteur d'électricité. Il est possible que de tels mouvements donnent lieu à l'effet dynamo qui consiste en la génération d'un champ magnétique stable et de grande échelle. Ce phénomène est vraisemblablement à l'origine des champs magnétiques des planètes, des étoiles et des galaxies. Il est surprenant qu'alors que les mouvements fluides à l'intérieur de ces objets célestes sont turbulents, les champs magnétiques généré soient de grande échelle spatiale et stables sur de longues périodes de temps. De plus, ils peuvent présenter une dynamique temporelle régulière comme c'est le cas pour le champ magnétique solaire dont la polarité s'inverse tous les onze ans. Décrire et prédire les mouvements d'un fluide turbulent reste l'un des problèmes les plus difficiles de la mécanique classique. %La description aussi bien analytique que numérique d'un fluide hautement turbulent est d'une effroyable complexité, si pas tout simplement impraticable. Dans cette situation, Il est donc utile de construire des modèles aussi proches que possible du système de départ mais de moindre complexité de sorte que des études théoriques et numériques deviennent envisageables. Deux approches ont été considérées ici. D'une part, nous avons développé des modèles présentant un très petit nombre de degrés de liberté (de l'ordre de la dizaine). Une étude analytique est alors possible. Ces modèles ont une dépendance en les paramètres physiques - nombres de Reynolds cinétique et magnétique et injection d'hélicité - qualitativement similaire aux dynamos célestes et expérimentales. D'autre part, les modèles en couches permettent de caractériser les transferts d'énergie entre les structures de différentes tailles présentes au sein du champ de vitesse. Nous avons développé un nouveau formalisme qui permet d'étudier aussi les échanges avec le champ magnétique. De plus, nous proposons une étude de la MHD dans le cadre de la décomposition hélicoïdale des champs solénoïdaux - une idée similaire à la décomposition de la lumière en composantes polarisées et que nous sommes les premiers à appliquer à la MHD. Nous avons montré comment exploiter cette approche pour déduire systématiquement des modèles simplifiés de la MHD. En particulier, nos méthodes multiplient le nombre de situations descriptibles par les modèles en couche comme par exemple le problème anisotrope de la turbulence en rotation. Elles permettent aussi de construire des modèles à basse dimension en calquant les résultats de simulations numériques directes. Ces modèles peuvent alors être étudiés à moindre coûts. _______________ Magnetohydrodynamics (MHD) is both the science and the formalism that describe the motion of an electro-conducting fluid. Such motion may yield the dynamo effect consisting in the spontaneous generation of a large scale stationary magnetic field. This phenomenon is most likely the reason behind the existence of planetary, stellar and galactic magnetic fields. It is quite surprising that also the fluid motion within these objects is turbulent, the generated magnetic fields present large spatial structures evolving over long time scales. Moreover these fields can present a very regular non trivial dynamics like in the case of the Sun, the magnetic field of which switches polarity every eleven years. To describe and predict the motion of a turbulent flow remains one of the most challenging problem of classical mechanics. It is therefore useful to build models as close to the initial system as possible but of a lesser complexity so that their theoretical and numerical analysis become tractable. Two approaches have been considered here. Low dimensional models have been developed that present about ten degrees of freedom. An analytical study of the resulting dynamical system is then possible. Interestingly, the dependance of these models on the physical parameters - kinetic and magnetic Reynolds number as well as injection of kinetic helicity - qualitatively matches that of the cosmic and experimental dynamos. On the other hand, shell models allow to characterise the energy transfers between structures of different sizes within the velocity field. A new formalism is presented which makes possible to also study the exchanges with the magnetic field. Furthermore, a description of MHD in the helical decomposition is proposed. I show how to use this decomposition to build new shell and low dimensional models. The methods developed here allow to broaden the scope of possible applications of the models. In particular, shell models are generalised in such a way that they can now describe anisotropic situations like that of rotating turbulence.

>Magister Scientiae - MSc / The study of ²²Na beta decay offers an opportunity to test the Standard Model of Particle Physics via measurements of the β−γ angular correlation. A previous measurement of this correlation yielded a non-zero value, indicating the need for a higher-order matrix element to the decay, beyond the allowed V − A approximation. On assuming the Conserved Vector Current (CVC) hypothesis for weak interactions and using the magnetic dipole M1 width of the analog 2+ state in ²²Na, one obtains an unexpectedly large 'second-class' form factor for 22Na β decay that is in disagreement with the Standard Model prediction. This thesis describes an analysis of data obtained from a previous ²¹Ne(p, γ) experiment to obtain the M1 width of the 2+ state of interest in ²²Na. This work aims to use the M1 width and the independently measured of the β − γ angular correlation to obtain a higher-order Standard-Model-allowed weak magnetism form factor for the decay, in an attempt to explain the observed anomaly mentioned above. / National Research Foundation (NRF)

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Este trabalho apresenta uma formulação tensorial genérica para parametrização das rotações do tipo vetorial destinada ao estudo de grandes rotações no espaço tridimensional. Esta formulação é compatível com as parametrizações de Euler e de Rodrigues. É dada ênfase aos que aqui se denominou parâmetros generalizados de Rodrigues, que fornecem expressões simples, computacionalmente mais eficientes que a parametrização clássica de Euler. A formulação apresentada é adequada para uso em métodos numéricos baseados nas projeções de Galerkin, como o método dos elementos finitos, podendo ser implementada com facilidade em programas já existentes de elementos finitos. Apresentam-se aqui expressões para o tensor das rotações e suas derivadas, bem como os tensores necessários à análise incremental. As formas fracas são construídas tanto com projeção ortogonal como não-ortogonal, correspondentes à aplicação do Teorema dos Trabalhos Virtuais e Teorema das Potências Virtuais, respectivamente. Os modelos propostos foram aplicados em um programa de elementos finitos utilizando formulações cinemáticas Lagrangiana total e Lagrangiana atualizada e foram resolvidos vários exemplos, dentre eles alguns clássicos da literatura, de forma a avaliar sua validade e aplicação. / This work presents a generic formulation of vector-type for the parameterization of large rotations in three-dimensional space. This formulation adapts to the Euler and the Rodrigues parameterization. Special distinction is made to the here named generalized Rodrigues parameters which result in very simple and computationally efficient expressions. The attained formulation is convenient for numerical procedures employing Galerkin projection like the finite element method and can be readily implemented in a FE code. The expressions of rotation tensor and its derivatives, which lead to a consistent linearization, are herein derived. The necessary tensor quantities employed in the derivation of the tangent bilinear weak form of incremental analysis are obtained too. The weak forms are constructed here with both orthogonal and non-orthogonal projections, corresponding to the application of the virtual work theorem or virtual power theorem respectively. The formulation is implemented within a finite element code in total Lagrangian and updated Lagrangian framework and assessment of the scheme is made by means of several numerical simulations.

No description available.

Este trabalho apresenta uma formulação tensorial genérica para parametrização das rotações do tipo vetorial destinada ao estudo de grandes rotações no espaço tridimensional. Esta formulação é compatível com as parametrizações de Euler e de Rodrigues. É dada ênfase aos que aqui se denominou parâmetros generalizados de Rodrigues, que fornecem expressões simples, computacionalmente mais eficientes que a parametrização clássica de Euler. A formulação apresentada é adequada para uso em métodos numéricos baseados nas projeções de Galerkin, como o método dos elementos finitos, podendo ser implementada com facilidade em programas já existentes de elementos finitos. Apresentam-se aqui expressões para o tensor das rotações e suas derivadas, bem como os tensores necessários à análise incremental. As formas fracas são construídas tanto com projeção ortogonal como não-ortogonal, correspondentes à aplicação do Teorema dos Trabalhos Virtuais e Teorema das Potências Virtuais, respectivamente. Os modelos propostos foram aplicados em um programa de elementos finitos utilizando formulações cinemáticas Lagrangiana total e Lagrangiana atualizada e foram resolvidos vários exemplos, dentre eles alguns clássicos da literatura, de forma a avaliar sua validade e aplicação. / This work presents a generic formulation of vector-type for the parameterization of large rotations in three-dimensional space. This formulation adapts to the Euler and the Rodrigues parameterization. Special distinction is made to the here named generalized Rodrigues parameters which result in very simple and computationally efficient expressions. The attained formulation is convenient for numerical procedures employing Galerkin projection like the finite element method and can be readily implemented in a FE code. The expressions of rotation tensor and its derivatives, which lead to a consistent linearization, are herein derived. The necessary tensor quantities employed in the derivation of the tangent bilinear weak form of incremental analysis are obtained too. The weak forms are constructed here with both orthogonal and non-orthogonal projections, corresponding to the application of the virtual work theorem or virtual power theorem respectively. The formulation is implemented within a finite element code in total Lagrangian and updated Lagrangian framework and assessment of the scheme is made by means of several numerical simulations.

No description available.

No description available.