published_or_final_version / abstract / toc / Orthopaedics and Traumatology / Master / Master of Philosophy

Interaction potentials for the double-perovskite cryolite, Na3AlF6, have been developed for use in classical Molecular Dynamics (MD) simulations using a method whereby ionic configurations are generated with empirical pair potentials, the multipoles and forces on the ions and the stress tensor of the cell are extracted from ab initio single-point DFT calculations, and then the multipoles, forces and stresses from the MD simulations are ‘fit’ to the ab initio quantities in a series of steps in which the potential parameters are optimized, for models of varying complexity. Previously, interaction potentials have been developed empirically by tuning the parameters to reproduce experimentally-derived properties such as structure factors and densities, and so the testing and development of the newer method is necessary in order to standardize a way of obtaining potentials from first principle considerations. A fitted potential was then used to characterize the ion dynamics in crystalline cryolite: a monoclinic to orthorhombic phase transition and the low-temperature-phase tilt-domain structure of the AlF3− 6 , the dominant structural features, are reproduced. The motional processes, which have been studied indirectly in NMR, conductivity and diffraction experiments, include oscillation of the AlF3− 6 and sodium ion diffusion - it has been suggested that these occur at a remarkably fast rate. The nature of the AlF3− 6 oscillatory motion is studied in more depth than accessible to experiment, and its connection with diffusion is investigated. Given the intrinsically defective nature of cryolite and the absence of diffusion in the initial simulations, defects are introduced to observe their effect on the dynamics: they are shown to be necessary for diffusion. This work has been written up in an article accepted for publication in the Journal of Physical Chemistry. The ab initio potentials developed as above involve representing a system with formally charged monatomic ions. We extended the scope of the method significantly with technical developments to allow for the inclusion of molecular ions, such as the hydroxide ion, the sulphate ion or the uranyl ion, where the intraionic bonding has significant covalent character. The appropriate modifications of the MD code were made and a modified force-fitting procedure was developed. The new method was applied to Mg(OH)2 which is an important mineral (brucite) and to the melts of uranyl chloride which are of interest in nuclear waste reprocessing. Although we found good potentials were harder to obtain for these compounds, we found this arose from their layered structure rather than the molecular nature of the ions, and that our method could achieve a level of success approaching that used in the cryolite work on further iterations of the fitting process.

Molecular dynamics simulation performed on modern computer workstations provides a powerful tool for the investigation of the static and dynamic characteristics of liquid crystal phases. In this thesis molecular dynamics computer simulations have been performed for two model systems. Simulations of 4,4'-di-n-pentyl-bibicyclo[2.2.2]octane demonstrate the growth of a structurally ordered phase directly from an isotropic fluid. This is the first time that this has been achieved for an atomistic model. The results demonstrate a strong coupling between orientational ordering and molecular shape, but indicate that the coupling between molecular conformational changes and molecular reorientation is relatively weak. Simulations have also been performed for a hybrid Gay-Berne/Lennard-Jones model resulting in thermodynamically stable nematic and smectic phases. Frank elastic constants have been calculated for the nematic phase formed by the hybrid model through analysis of the fluctuations of the nematic director, giving results comparable with those found experimentally. Work presented in this thesis also describes the parameterisation of the torsional potential of a fragment of a dimethyl siloxane polymer chain, disiloxane diol (HOMe(_2)Si)(_2)O, using ab initio quantum mechanical calculations.

Introduction Capillarity describes the effects caused by the surface tension on liquids. When considering small amounts ofliquid,thesurfacetension becomes the dominating parameter. In this situation the arising mathematical task is to determine the occurring capillary surface. At the beginning of the research on this topic, problems such as the ascent of fluids in a circular tube, on a vertical wall or on a wedge were some of the first problems scientists were concerned with. At the beginning of the 19th century, scientists like Young1, Laplace2, Taylor 3 and Gauß 4 established the mathematical foundations of this field. For the capillary tube5 they found, by applying variational methods, the so called mean curvature equation or capillary equation with the associated boundary condition. As Finn in [Fin86, Chapter 1] describes, this leads to the following boundary value problem: divTu = u + in , · Tu = cos on @ where Tu = ∇u p 1 + |∇u|2 . is called the Lagrange6 multiplier and is the contact angle, established between the capillary surface and the container wall. In the past, one tried to solve the problem by linearisation – with more or less satisfying results. In the last decades, expedited by the developing of micromechanics and the arising space-technology, capillary effects became more and more significant. Thereby the observed results differed from the predicted. The reason is the strong non-linearity of the problem. Interior molecular forces are responsible for the establishing of equilibrium surfaces. The force, operating between two materials, is called adhesion and cohesion is the molecular force within a medium. Under some specifications there arises a non-negligible force, called disjoining pressure. This pressure causes an additional term in the capillary equation, which 1Thomas Young (*13 June 1773, Milverton; †10 May 1829, London); Englisch polymath; made notable contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony and Egyptology, found the Young–Laplace equation 2Pierre-Simon (Marquis de) Laplace (28 March 1749, Beaumont-en-Auge; †5 March 1827, Paris); French mathematician and astronomer; found the Young–Laplace equation 3Brook Taylor (*18 August 1685, Edmonton; †29 December 1731, Somerset House/London); English mathematician; experiments in capillary attraction 4Johann Carl Friedlich Gauß (*30 April 1777, Braunschweig; †23 February 1855, G¨ottingen); German mathematician and scientist; contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics 5A capillary tube is a container with cross-section and perpendicular container walls, which contains an amount of liquid. 6Joseph-Louis de Lagrange (*25 January 1736, Turin; †10 April 1813, Paris); Italian mathematician and astronomer. 7 is called the disjoining pressure potential, denoted by P(x, u(x)). That is, we are led to the following modified capillary equation, see [MMS08]: divTu = u + P + in , with a similar boundary condition (see Section 1.3 for more details). The main task of this paper is to examine the behaviour of the capillary problem, considering the disturbance P. A generic example for such configurations is vapour nitrogen//liquid nitrogen//quartz, see also [Isr92, Chapter 11] or [MMS08]. The present work with regard to contents is divided in three parts. In the first part, inspired by the work of Concus and Finn [CF74], [FH89], we prove a Comparison Principle. As in the classical context, this principle is a powerful tool to find solutions of the boundary problem. Thus we can see that the disjoining pressure potential is the key for the asymptotic of the solutions. The second part is concerned with the asymptotic behaviour of the solutions for some classical cases. In particular for the capillary tube with circular cross-section (see [Mie93b], [Mie94], [Mie96] for the classical setting) the ascent on a horizontal wall and between two parallel horizontal plates, results are presented. There we are able to specify the asymptotic behaviour up to a constant term. In the last part we observe the solution of the problem on a corner. There it is more difficult to obtain a result. But in return, we gain a better result near the cusp of the edge. In the articles of Miersemann [Mie88], [Mie89], [Mie90] or Scholz [Sch04] some results for the classical setting are given. The formal arrangement is divided into three main chapters. The first of them is a summary of some notations which will be needed in the following chapters and also the physical background is illuminated. The main part, where asymptotic results are presented, is contained in Chapter 2. To afford a better reading, most of the proofs are given in Chapter 3.8

Copies of author's previously published articles inserted. / Bibliography: leaves I-LXIV. / xxxviii, 239 [77], Lxiv leaves : ill. (chiefly col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Assesses the diagnostic and prognostic value of early electroencephalography (EEG) and somatosensory evoked potential studies in cortical and non-cortical ischaemic stroke. Both conventional and topographic/quantitative studies were performed. A parallel study was carried out on healthy volunteers to provide an effective control. Equipment and quantitative EEG (qEEG) variability was also assessed. / Thesis (Ph.D.)--University of Adelaide, Dept. of Medicine, 1998?

Thesis (Ph. D.)--University of Adelaide, Dept. of Medicine, 1998? / Copies of author's previously published articles inserted. Includes bibliographical references (leaves I-LXIV).

Thesis (Ph. D.)--University of Sydney, 2001. / Includes published articles. Title from title screen (viewed Apr. 24, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Physics, Faculty of Science. Includes bibliography. Also available in print form.

Thesis (M.S. in neuroscience)--Washington State University, August 2008. / Includes bibliographical references (p. 22-29).

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [95]-106).

Thesis (Ph. D.)--UCLA, 2009. / Vita. Description based on print version record. Includes bibliographical references (leaves 69-79).