Thesis--Catholic University of America. / Includes bibliographical references.

Dans cette thèse, nous étudions les équations d’Einstein dans le vide avec un champ de Killing de translation. En présence de cette symétrie, les équations d’Einstein dans le vide en dimension 3+1 peuvent s’écrire, dans le cas polarisé, comme un système d’équations d’Einstein couplées à un champ scalaire en dimension 2+1. Dans la première partie de cette thèse, nous étudions les équations de contraintes dans le cas asymptotiquement plat. Les équations de contraintes sont des équations de compatibilité qui doivent être satisfaites par les données initiales. Nous montrons l’existence de solutions pour des données assez petites, et introduisons un développement asymptotique faisant intervenir des quantités correspondant aux charges globales. Dans une deuxième partie nous montrons la stabilité de l’espace-temps de Minkowski avec un champ de Killing de translation, en temps exponentiellement grand par rapport à la petitesse de la donnée initiale. Nous travaillons dans les coordonnées d’onde généralisées. Nous introduisons une famille de métriques Ricci plates, et imposons le comportement asymptotique de nos solutions à l’extérieur du cône de lumière en choisissant un élément de cette famille de manière adéquate. Ce choix permet la convergence de nos solutions à l’intérieur du cône de lumière vers la solution de Minkowski. Dans la dernière partie de cette thèse nous étudions les équations de contraintes dans le cas compact hyperbolique. Nous montrons l’existence d’une équation limite associée aux équations de contraintes. / This thesis aim sat studying vacuum Einstein equations with a space-like Killing vector field. With this symmetry, 3+1 vacuum Einstein equations reduce, in the polarized case, to Einstein equations coupled to a scalar field in 2+ 1 dimensions. In the first part of this thesis, we study the constraint equations in the asymptotically flat case. The constraint equations correspond to computability conditions that the initial data must satisfy. We show the existence of solutions for small data, and we introduce an asymptotic expansion involving quantities which are the 2 dimensional equivalents for the global charges. In the second part, we show the stability of Minkowski space-time with a translation space-like Killing vector field in exponential time with respect to the smallness of initial data. We introduce a family of Ricci flat metrics, and we impose the asymptotic behaviour of our solutions in the exterior of the light cone by picking the right element in the family. This choice allows for the convergence to Minkowski solution in the interior of the light cone. In the last part of this thesis, we study the constraint equations in the compact hyperbolic case. We show the existence of a limit equation associated to the constraint equations.

A method of writing the solution of a second order differential equation through a Volterra Integral Equation is developed. The method is applied to initial value problems, to special functions, and to bounded Quantum Mechanical problems. Some of the results obtained are original, and other results agree essentially with the work done previously by others. / Science, Faculty of / Mathematics, Department of / Graduate

The Lielmezs-Merriman equation of state has been modified in such a way that it can be applied over the entire PVT surface except along the critical isotherm. The dimensionless T* coordinate has been defined according to the two regions on the PVT surface as: [Formula Omitted] The two substance-dependent constants p and q are generated from the vapor pressure data. The applicability of the proposed modification has been tested by comparing its predictions of various pure compound physical and thermodynamic properties with known experimental data and with predictions from the Soave-Redlich-Kwong and Peng-Robinson equations of state. The proposed equation is the most accurate equation of state for calculating vapor pressure, and saturated vapor and liquid volumes. The Peng-Robinson equation is the best for enthalpy and entropy of vaporization estimations. The Soave-Redlich-Kwong equation is the least accurate equation for pressure and volume predictions in the single phase regions. For temperature prediction, all three equations of state give similar results in the subcritical and supercritical regions. None of the three equations is capable of representing all departure functions accurately. The Peng-Robinson equation and the proposed equation are very similar in accuracy except in the region where the temperature is near the critical. That is, between 0.95 ≤ Tr ≤ 1.05, the proposed equation gives rather poor results. For isobaric heat capacity calculation, both Soave-Redlich-Kwong and Peng-Robinson equations are adequate. The Soave-Redlich-Kwong equation gives the lowest overall average RMS % error for Joule-Thomson coefficient estimation. The Soave-Redlich-Kwong equation also provides the most reliable prediction for the Joule-Thomson inversion curve right up to the maximum inversion pressure. None of the cubic equations of state studied in this work is recommended for second virial coefficient calculation below Tr = 0.8. An α-function specifically designed for the calculation of second virial coefficient has been included in this work. The estimation from the proposed function gives equal, if not better, accuracy than the Tsonopoulos correlation. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

No description available.

In the first part of this work, two nonlinear partial differential equations, namely, a modified Camassa-Holm-Degasperis-Procesi equation and the generalized Kortewegde Vries equation with two power law nonlinearities are studied. The Lie symmetry method along with the simplest equation method is used to construct exact Solutions for these two equations. The second part looks at two systems of partial differential equations, namely, the generalized Boussinesq-Burgers equations and the (2+1)-dimensional Davey-Stewartson equations. The Lie symmetry method and the travelling wave hypothesis approach are utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the (2+ 1 )-dimensional Davey-Stewartson equations. / Thesis (Msc. in Applied Mathematics) North-West University, Mafikeng Campus, 2012

A Research Report submitted to the Department of Physics, Faculty of Science, University of the Witwatersrand, Johannesburg, in partial ful lment of the requirements for the degree of Master of Science. Signed on the 24th March 2016 in Johannesburg. / This research report uses cosmological N-body simulations to examine the the large scale mass distribution of the Universe, known as the cosmic web. The cosmic web can be classi ed into nodes, laments, sheets and voids - each with its own characteristic density and velocity elds. In this work, the author proposes a new Lagrangian cosmic web classi- cation algorithm, based on smoothed particle hydrodynamics. This scheme o ers adaptive resolution, resolves smaller substructure and obeys similar statistical properties with existing Eulerian methods. Using the new classi cation scheme, halo clustering dependence on cosmic web type is examined. The author nds halo clustering is signi cantly correlated with web type. Consequently, the mass dependence of halo clustering may be explained by the fractions of web types found for a particular halo mass. Finally, an analysis of dark matter halo spin, shape and fractional anisotropy is presented per web type to suggest avenues for future work.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulflment of the requirements for the degree of Master of Science. / The Method of Equivalent Lagrangians is used to find the solutions of a given differential equation by exploiting the possible existence of an isomorphic Lie point symmetry algebra and, more particularly, an isomorphic Noether point symmetry algebra. Applications include ordinary differential equations such as the Kummer Equation and the Combined Gravity-Inertial-Rossby Wave Equation and certain classes of partial differential equations related to the (1 + 1) linear wave equation. We also make generalisations to the (2 + 1) and (3 + 1) linear wave equations.

Thesis (Ph. D.)--Oregon State University, 1964. / Typescript. Includes bibliographical references (leaves 67-68). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Chicago, 1915. / Vita. "A Private Edition Distributed by the University of Chicago Libraries." "Extracted from the Proceedings of the London mathematical society, series 2, vol. 15, part 4." Includes bibliographical references. Also available on the Internet.