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.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 85-91). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of California, San Diego, 1997. / Vita. Includes bibliographical references (leaves 102-106).

Part of Thesis--Catholic University of America. / Bibliography: p. 43-47.

University Of The Witwatersrand Department Of Computational And Applied Mathematics Masters’ Dissertation 2015 / The ideal hitting location on a cricket bat, the ‘sweet-spot’, is taken to be defined in two parts: 1) the Location of Impact on a cricket bat that transfers the maximum amount of energy into the batted ball and 2) the Location of Impact that transfers the least amount of energy to the batsman’s hands post-impact with the ball; minimizing the unpleasant stinging sensation felt by the batsman in his hands. An analysis of di↵erent hitting locations on a cricket bat is presented with the cricket bat modelled as a one dimensional beam which is approximated by the Euler-Lagrange Beam Equation. The beam is assumed to have uniform density and constant flexural rigidity. These assumptions allow for the Euler-Lagrange Beam Equation to be simplified considerably and hence solved numerically. The solution is presented via both a Central Time, Central Space finite di↵erence scheme and a Crank-Nicolson scheme. Further, the simplified Euler-Lagrange Beam Equation is solved analytically using a Separation of Variables approach. Boundary conditions, initial conditions and the framework of various collision scenarios between the bat and ball are structured in such a way that the model approximates a batsman playing a defensive cricket shot in the first two collision scenarios and an aggressive shot in the third collision scenario. The first collision scenario models a point-like, impulsive, perpendicular collision between the bat and ball. A circular Hertzian pressure distribution is used to model an elastic, perpendicular collision between the bat and ball in the second collision scenario, and an elliptical Hertzian pressure distribution does similarly for an elastic, oblique collision in the third collision scenario. The pressure distributions are converted into initial velocity distributions through the use of the Lagrange Field Equation. The numerical solution via the Crank-Nicolson scheme and the analytical solution via the Separation of Variables approach are analysed. For di↵erent Locations of Impact along the length on a cricket bat, a post-impact analysis of the displacement of points along the bat and the strain energy in the bat is conducted. Further, through the use of a Fourier Transform, a post-impact frequency analysis of the signals travelling in the cricket bat is performed. Combining the results of these analyses and the two-part definition of a ‘sweet-spot’ allows for the conclusion to be drawn that a Location of Impact as close as possible to the fixed-end of the cricket bat (a point just below the handle of the bat) results in minimum amount of energy transferred to the hands of the batsman. This minimizes the ‘stinging’ sensation felt by the batsman in his hands and satisfies the second part of the definition of a sweet-spot. Due to the heavy emphasis of the frequency analysis in this study, the conclusion is drawn that bat manufacturers should consider the vibrational properties of bats more thoroughly in bat manufacturing. Further, it is concluded that the solutions from the numerical Crank-Nicolson scheme and the analytical Separation of Variables approach are in close agreement.

Thesis (Ph. D.)--Oregon State University, 1980. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thèse de doctorat : Mathèmatique : Metz : 2006. / Thèse soutenue sur ensemble de travaux. Bibliogr. f. 83-87.

Thesis (Ph. D.)--Oregon State University, 1992. / Typescript (photocopy). Includes bibliographical references (leaves 68-70). Also available on the World Wide Web.

Thesis (Ph. D.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains x, 166 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 154-161).