First published in the Notices of the American Mathematical Society in Vol.35, 1988, published by the American Mathematical Society

No description available.

No description available.

Dans cette thèse nous étudions des représentations du groupe de Lorentz dans les sections du fibré cotangent sur le cône isotrope. Grâce aux transformations de Fourier et de Poisson nous construisons explicitement tous les opérateurs de brisure de symétrie qui apparaissent dans les lois de branchement des produits tensoriels de telles représentations. / In this thesis we study representations of the Lorentz group acting on sectionsof the cotangent bundle over the isotropic cone. Using Fourier and Poisson transforms we construct explicitly all the symmetry breaking operators that appear in branching laws of tensor products of such representations.

No description available.

No description available.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. March 2016. / We investigate the two-dimensional turbulent wake and derive the governing equations for the mean velocity components using both the eddy viscosity and the Prandtl mixing length closure models to complete the system of equations. Prandtl’s mixing length model is a special case of the eddy viscosity closure model. We consider an eddy viscosity as a function of the distance along the wake, the perpendicular distance from the axis of the wake and the mean velocity gradient perpendicular to the axis of thewake. We calculate the conservation laws for the system of equations using both closure models. Three main types of wakes arise from this study: the classical wake, the wake of a self-propelled body and a new wake is discovered which we call the combination wake. For the classical wake, we first consider the case where the eddy viscosity depends solely on the distance along the wake. We then relax this condition to include the dependence of the eddy viscosity on the perpendicular distance from the axis of the wake. The Lie point symmetry associated with the elementary conserved vector is used to generate the invariant solution. The profiles of the mean velocity show that the role of the eddy viscosity is to increase the effective width of the wake and decrease the magnitude of the maximum mean velocity deficit. An infinite wake boundary is predicted fromthis model. We then consider the application of Prandtl’s mixing length closure model to the classical wake. Previous applications of Prandtl’s mixing length model to turbulent wake flows, which neglected the kinematic viscosity of the fluid, have underestimated the width of the boundary layer. In this model, a finite wake boundary is predicted. We propose a revised Prandtl mixing length model by including the kinematic viscosity of the fluid. We show that this model predicts a boundary that lies outside the one predicted by Prandtl. We also prove that the results for the two models converge for very large Reynolds number wake flows. We also investigate the turbulentwake of a self-propelled body. The eddy viscosity closure model is used to complete the system of equations. The Lie point symmetry associated with the conserved vector is derived in order to generate the invariant solution. We consider the cases where the eddy viscosity depends only on the distance along the wake in the formof a power law and when a modified version of Prandtl’s hypothesis is satisfied. We examine the effect of neglecting the kinematic viscosity. We then discuss the issues that arisewhenwe consider the eddy viscosity to also depend on the perpendicular distance from the axis of the wake. Mean velocity profiles reveal that the eddy viscosity increases the boundary layer thickness of the wake and decreases the magnitude of the maximum mean velocity. An infinite wake boundary is predicted for this model. Lastly, we revisit the discovery of the combination wake. We show that for an eddy viscosity depending on only the distance along the axis of the wake, a mathematical relationship exists between the classical wake, the wake of a self-propelled body and the combination wake. We explain how the solutions for the combination wake and the wake of a self-propelled body can be generated directly from the solution to the classical wake. / GR 2016

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / Includes bibliographical references. / Ph.D.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography : leaves 176-178. / Ph.D.

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy