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Graduate

Free energy techniques provide the basis for an analysis of aspects of the liquid-vapour interface undertaken in this study. The main focus of this work is an extensive theoretical investigation into properties of the surface tension, including curvature dependance and supersaturation effects, using Monte Carlo computer simulation techniques. / Thesis (PhD)--University of South Australia, 2002.

Thesis (PhD)--University of South Australia, 1999

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.

Includes 4 reprints by the author / [159] leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Radial distribution functions gab(r) for a dense hydrogenous plasma in equilibrium near the ionization temperature are obtained by two methods / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics, 1968

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2007.