published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Mathematics. / Microfiche copy available in Archives and Science. / Bibliography: leaves 53-54. / M.S.

Chiu Ho Man Edward. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 36-39). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Some Preliminary Analysis --- p.11 / Chapter 3 --- An Auxiliary Linear problem --- p.16 / Chapter 4 --- Construction of natural constraint --- p.22 / Chapter 5 --- Energy computation for reduced energy functional --- p.26 / Chapter 6 --- Proof of Theorem 1.1 --- p.29 / Bibliography --- p.36

No description available.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 71-74).

Thesis (Ph. D.)--University of Hong Kong, 1982.

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

A nonlinear wave equation invariant with respect to unitary representations of the Lorentz group is considered in an attempt to describe extended particles with spin and positive definite energy by means of a self-confined classical field. The wave function has an infinite number of components and, in the specific representations used, the corresponding internal degree of freedom is identified with the spin. A fractional power of the scalar bilinear invariant appears as an appropriate choice for the nonlinearity in order that all the stationary states be localized. Two approximation methods are proposed and both lead to results that bear a resemblance to the results of the MIT bag model.

Most real world phenomena is modeled by ordinary and/or partial differential equations. Most of these equations are highly nonlinear and exact solutions are not always possible. Exact solutions always give a good account of the physical nature of the phenomena modeled. However, existing analytical methods can only handle a limited range of these equations. Semi-numerical and numerical methods give approximate solutions where exact solutions are impossible to find. However, some common numerical methods give low accuracy and may lack stability. In general, the character and qualitative behaviour of the solutions may not always be fully revealed by numerical approximations, hence the need for improved semi-numerical methods that are accurate, computational efficient and robust. In this study we introduce innovative techniques for finding solutions of highly nonlinear coupled boundary value problems. These techniques aim to combine the strengths of both analytical and numerical methods to produce efficient hybrid algorithms. In this work, the homotopy analysis method is blended with spectral methods to improve its accuracy. Spectral methods are well known for their high levels of accuracy. The new spectral homotopy analysis method is further improved by using a more accurate initial approximation to accelerate convergence. Furthermore, a quasi-linearisation technique is introduced in which spectral methods are used to solve the linearised equations. The new techniques were used to solve mathematical models in fluid dynamics. The thesis comprises of an introductory Chapter that gives an overview of common numerical methods currently in use. In Chapter 2 we give an overview of the methods used in this work. The methods are used in Chapter 3 to solve the nonlinear equation governing two-dimensional squeezing flow of a viscous fluid between two approaching parallel plates and the steady laminar flow of a third grade fluid with heat transfer through a flat channel. In Chapter 4 the methods were used to find solutions of the laminar heat transfer problem in a rotating disk, the steady flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation and the classical von Kάrmάn equations for boundary layer flow induced by a rotating disk. In Chapter 5 solutions of steady two-dimensional flow of a viscous incompressible fluid in a rectangular domain bounded by two permeable surfaces and the MHD viscous flow problem due to a shrinking sheet with a chemical reaction, were solved using the new methods. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.