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This project will investigate mixing in microchannels. Specifically, the advection and diffusion of a passive scalar, using a split step Monte Carlo method. Numerically the implementation of this method is well understood. The current experimental geometry is a rectangular pipe with grooves on one wall. Mixing results with straight walls agree closely with experiment. The velocity field over grooves is also studied.

There are many problems in mathematical finance which require the evaluation of a multivariate integral. Since these problems typically involve the discretisation of a continuous random variable, the dimension of the integrand can be in the thousands, tens of thousands or even more. For such problems the Monte Carlo method has been a powerful and popular technique. This is largely related to the fact that the performance of the method is independent of the number of dimensions. Traditional quasi-Monte Carlo techniques are typically not independent of the dimension and as such have not been suitable for high-dimensional problems. However, recent work has developed new types of quasi-Monte Carlo point sets which can be used in practically limitless dimension. Among these types of point sets are Sobol' sequences, Faure sequences, Niederreiter-Xing sequences, digital nets and lattice rules. In this thesis, we will concentrate on results concerning lattice rules. The typical setting for analysis of these new quasi-Monte Carlo point sets is the worst-case error in a weighted function space. There has been much work on constructing point sets with small worst-case errors in the weighted Korobov and Sobolev spaces. However, many of the integrands which arise in the area of mathematical finance do not lie in either of these spaces. One common problem is that the integrands are unbounded on the boundaries of the unit cube. In this thesis we construct function spaces which admit such integrands and present algorithms to construct lattice rules where the worst-case error in this new function space is small. Lattice rules differ from other quasi-Monte Carlo techniques in that the points can not be used sequentially. That is, the entire lattice is needed to keep the worst-case error small. It has been shown that there exist generating vectors for lattice rules which are good for many different numbers of points. This is a desirable property for a practitioner, as it allows them to keep increasing the number of points until some error criterion is met. In this thesis, we will develop fast algorithms to construct such generating vectors. Finally, we apply a similar technique to show how a particular type of generating vector known as the Korobov form can be made extensible in dimension.

Graduation date: 1998

This thesis deals with Symbol Error Rate (SER)-simulation of wireless communications and its application into throughput analysis of UltraWideband (UWB) systems. The SERs will be simulated in C++ using the Monte Carlo method and when some are calculated, the rest will be estimated using a novel extrapolation method. These SER values will be very accurate and in this thesis go as low as 1.0e-14. Reaching that low values would otherwise be impossible using the traditional Monte Carlo method, because of very large computation time. However, the novel extrapolation method, can simulate a SER-curve in less than 30 seconds. It is assumed that the noise belongs to the Generalized Gaussian distribution family and among them noise from the Normal distribution (Gaussian noise) gives the best result. It is to be noted that Gaussian noise is the most commonly used in digital communication simulations. Although the program is used for throughput analysis of UWB, the program could easily be adapted to various signals. In this thesis, throughput analysis means a plot with symbol rate vs distance. From any given symbols, the user can, with a desired minimum SER, generate an extrapolated SER-curve and see what symbol rate can be achieved by the system, while obeying power constraints of signals imposed by international laws. The developed program is, by comparing with published theoretical results, tested for QAM and PSK cases, but can easily be extended to UWB systems.

Turbo Molecular pumps, abbreviated as TMP, can create a high vacuum environment for some special industries, especially the semiconductor and IC industries. The turbo blade design is one of the main technologies that affect the performance of a TMP. The object of this study is to investigate what kind of blade design parameters, e.g. blade angle, blade spacing, blade chord, blade velocity, etc., will affect the performance of TMP. It is hope that an analysis methodology of these parameters can be setup in the viewpoint of pumping rate curve. The results of this study will be useful for the design of TMP.

Thesis (M. Phil.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 52-54). Also available online.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves [87]-89).

Thesis (M. Sc.(Mathematics and Applied Mathematics))--University of Pretoria, 2009. / Summary in English. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Department of Statistics, June 2001. / Includes bibliographical references. Also available on the Internet.