This dissertation focuses on two areas of garnet porphyroblast crystallization that have until now remained largely uninvestigated: epitaxial nucleation of garnet porphyroblasts and yttrium and rare earth (Y+REE) uptake in metamorphic garnet. The mechanism of epitaxial nucleation is explored as a step towards determining which aspects of interfaces are significant to interfacial energies and nucleation rates. Garnet from the aureole of the Vedrette di Ries tonalite, Eastern Alps, shows a clear case of epitaxial nucleation in which garnet nucleated on biotite with (110)grt || (001)bt with [100]grt || [100]bt. The occurrence is remarkable for the clear genetic relationships revealed by the microstructures and for its preservation of the mica substrate, which allows unambiguous determination of the coincident lattice planes and directions involved in the epitaxy. Not all epitaxial nucleation is conspicuous; to increase the ability to document epitaxial relationships between garnet and micas, I develop and apply a method for determining whether evidence for epitaxial nucleation of garnet is present in porphyroblasts containing an included fabric. Although the magnitude of uncertainties in orientation measurements for garnets from Passo del Sole (Switzerland), the Nevado Filabride Complex (Spain), and Harpswell Neck (USA) preclude definitive identification of epitaxial relationships, the method has potential to become a viable technique for creating an inventory of instances and orientations of epitaxial nucleation with appropriate sample selection. Using lattice-dynamics simulations, I explore the most commonly documented epitaxial relationship, (110)grt || (001)ms. The range of interfacial energies resulting from variations in the intracrystalline layer within garnet at the interface, the initial atomic arrangement at the interface, and the rotational orientation of the garnet structure relative to the muscovite structure shows that the intracrystalline layer within garnet has the greatest effect on interfacial energy. A complete understanding of the role of intergranular diffusion for yttrium and rare-earth-element uptake in porphyroblastic garnet is critical because the complexities of Y+REE zoning in garnets and the mechanisms of Y+REE uptake have implications for petrologic interpretations and garnet-based geochronology. Y+REE distributions in garnets from the Picuris Mountains (USA), Passo del Sole (USA), and the Franciscan Complex (USA) imply diverse origins linked to differing degrees of mobility of these elements through the intergranular medium during garnet growth.

Controlling molecular orientation is of great importance in organic thin films due to the fact that the fundamental properties of functional nanomaterials depend on molecular orientation at the nanoscale. However, controlling molecular orientation cannot be achieved without having an extensive understanding about the controlling factors in the organic film growth processes. Most previous studies have been devoted to monolayer structures. The structure of multilayer films has not been well investigated. This study was performed using a phenomenological approach, in which the morphology and orientation of n-alkane thin films were studied as a function of substrate identity, interface treatment, substrate temperature and deposition rate. The experimental techniques that were used include IR-spectroscopy, polarized optical microscopy, and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy and X-ray microscopy. The kinetic and thermodynamic factors that govern the orientation of organic thin films were extracted from the experimental results, and generalized to make a framework by which the morphology and orientation of organic films can be predicted. Epitaxial growth was specifically considered as a method to pattern organic thin films. In epitaxial growth, the oriented crystals of an organic film grow on a crystalline substrate such that the structure of the substrate is copied by the deposit crystals. For epitaxy it is required that the lattice planes of two crystals are parallel and similar in the lattice points spacing. A minor part of this dissertation is devoted to epitaxy in an inorganic system. One of the favorable consequences of epitaxial growth in inorganic systems is lattice strain that alters the electronic properties of semiconductor devices. A synchrotron based experimental method has been developed to quantitatively measure the degree of strain in Si1-xGex alloy films grown epitaxially on the Si(100) substrate.

Different methods were developed for the preparation of bulk ZnO substrates. Remarkable improvement on the surface, optical and crystalline quality of the bulk ZnO substrate was achieved. ZnO substrates with an atomically flat surface exhibiting terrace-like features were used as a substrate for GaN grown by MBE. High-resolution x-ray diffraction and low temperature PL results show that similar high quality GaN layers can be achieved on both annealed O-face and Zn-face ZnO substrates. The prospect of the device applications of GaN epitaxy on ZnO, including AlGaN/GaN MODFET structure on ZnO and GAN/ZnO based p-n junction were discussed.

Stable and metastable phases of Fe and Al and structural anomalies of Zn and Cd have been studied by epitaxial Bain path (EBP) and minimum path (MNP) first-principles procedures, based on finding equilibrium structures from minimizing the Gibbs free energy G with respect to structure at a given hydrostatic pressure p and temperature T . The main accomplishments are as follows. (1) This dissertation illustrates the effectiveness of the MNP procedure for finding stable and metastable phases of an element by studying four Bravais phases of Fe including body-centered tetragonal (bct), body-centered cubic (bcc), face-centered cubic (fcc) and rhombohedral (rh) phases. The determination of absolute stability using MNP is new; MNP finds all the elastic constants cjj of a given state and the eigenvalues of the elastic constants matrix, which determine the absolute stability of the state. / (2) We have extended our search for stable and metastable phases from zero temperature to finite temperature, which requires the calculations of the Debye temperature Od from cjj in the case of no symmetry. The Debye theory is modified by introducing a parameter B2 that gives the fraction of the full Debye zero-point energy possessed by the actual dispersive mode frequencies. The value of the lattice parameter of fcc Al at low temperatures,a(T) , is shown to be accurately determined by the modified Debye theory of lattice vibrations and first-principles total energy band calculations with the MNP procedure. (3) The existence of structural anomalies in hcp Zn and Cd has been shown from first-principles total-energy calculations using WIEN2k with the EBP procedure. / Evaluation of the pressure dependence of various elastic quantities which are much more sensitive to the anomaly shows that the anomalies in hcp Zn and hcp Cd exist over a considerable range of pressure; several abrupt changes in the electron distribution are thereby indicated in that pressure range. (4) Calculations on the zone-center transverse optical phonon frequencies Vto(p) of hcp Zn, which found oscillatory behavior of Vto(p) in the pressure range of the anomalies, support the conclusions made in (3) on the structural anomalies. Based on this dissertation research four papers have been published in refereed journals. / by Florin Apostol. / Thesis (Ph.D.)--Florida Atlantic University, 2008. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.

by Tang Yeung Shun. / On t.p., "2", u "3", "7-x", and O"3" are subscripts following "growth of" in the title. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 87-89). / Chapter Chapter 1 ： --- Introduction --- p.1 / Chapter Chapter 2 : --- Preparation of Thin Films --- p.10 / Chapter Chapter 3 : --- Structural Analysis / Chapter 3.1 --- Setup of XRD --- p.14 / Chapter 3.2 --- θ-2θ Scan --- p.17 / Chapter 3.3 --- Rocking Curve --- p.27 / Chapter 3.4 --- Pole Figure --- p.29 / Chapter 3.5 --- Off-axis Scan --- p.33 / Chapter 3.6 --- Grazing Incidence X-ray Diffraction --- p.53 / Chapter 3.7 --- Percentage of (110) Phase --- p.59 / Chapter 3.8 --- Lattice Parameters --- p.63 / Chapter Chapter 4 : --- Transport Properties / Chapter 4.1 --- Experimental --- p.66 / Chapter 4.2 --- Results --- p.68 / Chapter Chapter 5 : --- Surface Morphology --- p.75 / Chapter Chapter 6 : --- Discussion --- p.80 / Chapter Chapter 7 : --- Conclusions --- p.85 / References --- p.87 / Appendix A : Powder Diffraction Patterns of YBCO System

by Clive Hau Ming Shiu. / On t.p., "x" and "1-x" are subscript. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves [126]-[130]). / ACKNOWLEDGEMENT --- p.i / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iii / Chapter Chapter 1 --- INTRODUCTION --- p.1 / Chapter Chapter 2 --- THEORY --- p.3 / Chapter 2.1 --- Fundamentals of GaAs and AlGaAs --- p.3 / Chapter 2.1.1 --- Crystal structure and properties of GaAs --- p.4 / Chapter 2.1.2 --- General properties of GaAs at 300K --- p.5 / Chapter 2.1.3 --- Temperature dependence of bandgap for GaAs --- p.6 / Chapter 2.1.4 --- Dopants of GaAs --- p.7 / Chapter 2.1.5 --- Properties of AlGaAs --- p.8 / Chapter 2.2 --- Phase Equilibrium of GaAs and AlGaAs --- p.10 / Chapter 2.2.1 --- Phase diagram of Ga-As binary system --- p.11 / Chapter 2.2.2 --- Phase diagram of Al-Ga-As ternary system --- p.13 / Chapter 2.3 --- Principle of LPE growth --- p.17 / Chapter 2.3.1 --- General concept of liquid phase epitaxy --- p.17 / Chapter 2.3.2 --- Fundamental methods of LPE growth --- p.19 / Chapter 2.4 --- Dopants in GaAs and AlGaAs system --- p.21 / Chapter 2.4.1 --- Common dopants in GaAs --- p.22 / Chapter 2.4.2 --- Tellurium in GaAs --- p.23 / Chapter 2.4.3 --- Silicon in GaAs --- p.24 / Chapter 2.4.4 --- Tellurium and Tin in AlGaAs --- p.26 / Chapter Chapter 3 --- LPE SYSTEM FOR GaAs AND AlGaAs --- p.28 / Chapter 3.1 --- Basic requirements for horizontal sliding LPE system --- p.30 / Chapter 3.2 --- Cleaning process of the LPE system --- p.37 / Chapter 3.2.1 --- Cleaning procedures of the quartz parts --- p.37 / Chapter 3.2.2 --- Cleaning procedures of the stainless steel tubing --- p.38 / Chapter 3.2.3 --- Cleaning procedures of the graphite boat --- p.39 / Chapter 3.3 --- Final examination for LPE growth --- p.41 / Chapter 3.3.1 --- Examining the sealing of the system --- p.41 / Chapter 3.3.2 --- Examining the palladium hydrogen purifier --- p.41 / Chapter 3.3.2.1 --- Measuring the dew point --- p.41 / Chapter 3.3.2.2 --- Measuring the content of oxygen and nitrogen --- p.42 / Chapter 3.3.3 --- Adjusting and measuring the isothermal zone in the fumace --- p.42 / Chapter 3.3.4 --- Measuring of background impurity --- p.43 / Chapter 3.3.5 --- Inspection of the operating chamber --- p.44 / Chapter Chapter 4 --- EXPERIMENTALS --- p.45 / Chapter 4.1 --- Determination of GaAs and AlGaAs content in the source melt --- p.45 / Chapter 4.2 --- Calculation of GaAs and AlGaAs content in the source melt --- p.45 / Chapter 4.3 --- Experimental determination of source melt composition --- p.48 / Chapter 4.4 --- LPE growth method --- p.49 / Chapter 4.5 --- Thickness control of LPE epilayers --- p.49 / Chapter 4.6 --- Experimental procedures --- p.50 / Chapter Chapter 5 --- RESULTS AND DISCUSSIONS --- p.63 / Chapter 5.1 --- Growth condition studies of GaAs --- p.63 / Chapter 5.1.1 --- Experimental --- p.63 / Chapter 5.1.2 --- Phase equilibrium of GaAs in the range of 780 to 840 °C --- p.63 / Chapter 5.1.3 --- Results of undoped GaAs epilayers --- p.67 / Chapter 5.1.4 --- Results of Si doped GaAs epilayers --- p.72 / Chapter 5.2 --- Growth condition studies of AlxGa1-xAs for x=0.1 to 09 --- p.73 / Chapter 5.2.1 --- Phase equilibrium of AlxGa1-xAs for x=0.1 to 09 --- p.73 / Chapter 5.2.2 --- Relation between saturation of solution and he flatness of interface between epilayer and substrate --- p.79 / Chapter 5.2.3 --- Determination of composition x in AlxGa1-xAs --- p.82 / Chapter 5.2.4 --- Relation between epilayer thickness and x in AlxGa1-xAs --- p.84 / Chapter 5.3 --- High AlxGa1-xAs with x ´ 0.9 ° at 780 °C --- p.87 / Chapter 5.3.1 --- Deposition rate of high AlxGa1-xAs epilayer versus cooling rate --- p.87 / Chapter 5.3.2 --- Thickness profiles of epilayers versus cooling rate --- p.89 / Chapter 5.3.3 --- Spectroscopic refractive index of high AlxGa1-xAs in the visible light spectrum --- p.94 / Chapter 5.3.4 --- Rocking curves of high AlxGa1-xAs --- p.96 / Chapter 5.4 --- Tellurium doped AlxGa1-xAs with x ranging from 0.1 to 09 --- p.98 / Chapter 5.4.1 --- Carrier concentration versus composition x in AlxGa1-xAs --- p.98 / Chapter 5.4.2 --- Carrier concentration of Al0.3Ga0.7As versus Te mole fraction --- p.100 / Chapter 5.4.3 --- Donor activation energy of Te Versus x in AlxGa1-xAs --- p.102 / Chapter 5.4.4 --- Refractive index of Te doped AlxGa1-xAs at 300K --- p.105 / Chapter 5.4.5 --- Dependence of solubility upon Te doping level --- p.106 / Chapter 5.5 --- Heavily tellurium doped Al0.3Ga0.7As --- p.107 / Chapter 5.5.1 --- Diffractometry study of heavily Te doped Al0.3Ga0.7As --- p.108 / Chapter 5.5.2 --- Morphological studies and interface studies of heavily Te doped Al0.3Ga0.7As --- p.112 / Chapter Chapter 6 --- CONCLUSION --- p.119 / APPENDIX Photoluminance Analysis at room temperature / REFERENCE

by Lo Wai Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references. / Text in English; abstracts in English and Chinese. / by Lo Wai Hung. / Acknowledgements --- p.1 / Abstract / 論文摘要 --- p.ii / Table of Contents --- p.iv / List of Figures --- p.vi / List of Tables --- p.viii / Chapter Chapter 1. --- Introduction / Chapter 1.1. --- Magnetoresistance --- p.1 -1 / Chapter 1.1.1. --- Giant magnetoresistance (GMR) --- p.1 -2 / Chapter 1.1.2. --- Colossal Magnetoresistace (CMR) --- p.1 -2 / Chapter 1.2. --- Doping effects in La1-xCaxMn03 --- p.1-4 / Chapter 1.3. --- Metal-Insulator transition in CMR materials --- p.1 -8 / Chapter 1.3.1. --- The sharpness in Metal-Insulator transition --- p.1 -9 / Chapter 1.3.2. --- Possible model to explain CMR in rare-earth manganites --- p.1-12 / Chapter 1.4. --- Low field magnetoresistance --- p.1-14 / Chapter 1.4.1.1. --- Single crystal and polycrystalline perovskite manganites --- p.1-14 / Chapter 1.4.1.2. --- Manganite trilayer junctions --- p.1-15 / Chapter 1.4.2. --- Possible mechanism of low field MR --- p.1-16 / Chapter 1.5. --- Our motivation --- p.1-17 / Chapter 1.5.1. --- Brief review of several manganite superlattices systems --- p.1-18 / Chapter 1.5.2. --- Scope of this thesis work --- p.1-20 / References --- p.1-21 / Chapter Chapter 2. --- Epitaxial growth of LCMO thin films / Chapter 2.1. --- Deposition techniques --- p.2-1 / Chapter 2.1.1. --- Induction --- p.2-1 / Chapter 2.1.2. --- Facing-target sputtering (FTS) --- p.2-1 / Chapter 2.1.3. --- Vacuum system --- p.2-3 / Chapter 2.2. --- Fabrication and characterization of LCMO and PCMO targets --- p.2-4 / Chapter 2.3. --- Epitaxial growth of LCMO thin films --- p.2-9 / Chapter 2.3.1. --- Substrate materials --- p.2-9 / Chapter 2.3.2 --- Deposition --- p.2-10 / Chapter 2.3.2.1. --- Sample preparation --- p.2-10 / Chapter 2.3.2.2. --- Deposition procedure --- p.2-10 / Chapter 2.3.2.3. --- Inter-target distance --- p.2-11 / Chapter 2.3.2.4. --- Deposition Rate --- p.2-15 / Chapter 2.4. --- Substrate temperature effect --- p.2-17 / Chapter 2.4.1. --- Crystal Structure --- p.2-17 / Chapter 2.4.2. --- Transport properties --- p.2-20 / Chapter 2.4.2.1. --- Sharpness of M-I transport properties --- p.2-24 / Chapter 2.4.2.2. --- Magnetoresistance of LCMO/NGO films --- p.2-27 / Chapter 2.5. --- Thickness of LCMO thin film --- p.2-28 / Chapter 2.5.1. --- Crystal Structure --- p.2-29 / Chapter 2.5.2. --- M-I transition properties --- p.2-31 / Chapter 2.5.2.1. --- Sharpness of M-I transport properties --- p.2-35 / Chapter 2.5.2.2. --- Magnetoresistance of LCMO/NGO films --- p.2-36 / Chapter 2.5.2.3. --- Surface Morphology --- p.2-38 / Chapter 2.6. --- Epitaxial growth of PCMO thin films --- p.2-40 / Chapter 2.7. --- Conclusion --- p.2-42 / References --- p.2-43 / Chapter Chapter 3. --- LCMO/PCMO superlattices --- p.3-1 / Chapter 3.1. --- Variation of the PCMO thickness in LCMO/PCMO superlattices --- p.3-2 / Chapter 3.1.1. --- Sample Preparation --- p.3-2 / Chapter 3.1.2. --- Structure characterization by XRD --- p.3-3 / Chapter 3.1.3. --- Transport properties --- p.3-10 / Chapter 3.1.3.1. --- Sharpness of M-I transport properties --- p.3-14 / Chapter 3.1.3.2. --- Magnetoresistance of LCMO/PCMO superlattices --- p.3-16 / Chapter 3.2. --- Variation of the number of LCMO/PCMO bilayer --- p.3-19 / Chapter 3.2.1. --- Sample Preparation --- p.3-19 / Chapter 3.2.2. --- Structure characterization by XRD --- p.3-21 / Chapter 3.2.3. --- Transport properties --- p.3-23 / Chapter 3.2.3.1. --- Sharpness of M-I transport properties --- p.3-27 / Chapter 3.2.3.2. --- Magnetoresistance of LCMO/PCMO superlattices --- p.3-28 / Chapter 3.3. --- Fine adjusting the thickness of PCMO around 10Ain LCMO/PCMO superlattices / Chapter 3.3.1. --- Sample Preparation --- p.3-31 / Chapter 3.3.2. --- Characterization ofLCMO/PCMO superlattices by XRD --- p.3-32 / Chapter 3.3.3. --- Transport properties --- p.3-35 / Chapter 3.3.3.1. --- Sharpness of M-I transport properties --- p.3-39 / Chapter 3.3.3.2. --- Magnetoresistance of LCMO/PCMO superlattices --- p.3-41 / Chapter 3.4. --- Conclusion --- p.3-43 / References --- p.3-44 / Chapter Chapter 4. --- Low-field magnetoresistance (LFMR) / Chapter 4.1. --- Low-field magnetoresistance --- p.4-1 / Chapter 4.2. --- Conclusion --- p.4-5 / References --- p.4-6 / Chapter Chapter 5. --- Structure characterization of LCMO/PCMO superlatticess by crater edge profiling --- p.5-1 / Chapter 5.1. --- Sample preparation --- p.5-2 / Chapter 5.2. --- Structure Characterization --- p.5-2 / Chapter 5.2.1. --- X-ray diffraction (XRD) --- p.5-2 / Chapter 5.2.2. --- The crater edge profiling --- p.5-5 / Chapter 5.2.2.1. --- SEM --- p.5-5 / Chapter 5.2.2.2. --- AES line scan --- p.5-10 / Chapter 5.3. --- Crater edge profiling of P1OO/STO --- p.5-12 / Chapter 5.4. --- Conclusion --- p.5-15 / References --- p.5-16 / Chapter Chapter 6. --- Conclusion --- p.6-1

Iu Kwan Sai = 以光致發光譜和高解析度X射線衍射譜研究砷銻化鎵外延層和量子井 / 姚昀樨. / On t.p. "̳x" is subscript. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 93-95). / Text in English; abstracts in English and Chinese. / Iu Kwan Sai = Yi guang zhi fa guang pu he gao jie xi du X she xian yan she pu yan jiu shen ti hua jia wai yan ceng he liang zi jing / Yao Yunxi. / ACKNOWLEDGMENTS --- p.i / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.v / LIST OF TABLES --- p.vii / LIST OF FIGURES --- p.viii / Chapter 1. --- INTRODUTION --- p.1 / Chapter 1.1 --- Motivations --- p.1 / Chapter 1.2 --- Historical Works --- p.1 / Chapter 1.3 --- This Study --- p.3 / Chapter 1.4 --- Growth Conditions of GaAs1-xSbx Alloy --- p.4 / Chapter 2. --- EXPERIMENTAL PROCEDURES --- p.5 / Chapter 2.1 --- High Resolution X-Ray Diffraction (HRXRD) --- p.5 / Chapter 2.1.1 --- The Use of HRXRD --- p.5 / Chapter 2.1.2 --- Setup of the High Resolution X-Ray Diffractometer --- p.7 / Chapter 2.1.3 --- Types of Measurements --- p.8 / Chapter 2.2 --- Photoluminescence (PL) Spectrometer --- p.10 / Chapter 2.2.1 --- The Use of PL --- p.10 / Chapter 2.2.2 --- Setup of PL spectrometer --- p.10 / Chapter 2.2.3 --- types of Measurements --- p.13 / Chapter 3. --- CHARACTERIZATION --- p.14 / Chapter 3.1 --- High Resolution X-Ray Diffraction (HRXRD) --- p.14 / Chapter 3.1.1 --- Principal Scattering Geometries --- p.14 / Chapter 3.1.2 --- Strains in the Epitaxial Layer --- p.16 / Chapter 3.1.3 --- Lattice Parameter --- p.21 / Chapter 3.1.4 --- Sb Composition --- p.24 / Chapter 3.1.5 --- Determination of Thickness --- p.24 / Chapter 3.2 --- Photoluminescence (PL) --- p.25 / Chapter 3.2.1 --- Basic Theory of PL --- p.25 / Chapter 3.2.2 --- Strain and Temperature Effect --- p.26 / Chapter 3.2.3 --- Type I and Type II PL --- p.27 / Chapter 3.2.4 --- The Energy Gap of GaAs1-xSbx --- p.28 / Chapter 4. --- RESULTS AND DISCUSSION --- p.31 / Chapter 4.1 --- Direct Analysis of HRXRD Rocking Curves --- p.31 / Chapter 4.1.1 --- GaAs1-xSbx / GaAs Quantum Wells (QWs) --- p.31 / Chapter 4.1.2 --- GaAs1-xSbx /InP Epitaxial Layers --- p.42 / Chapter 4.2 --- Computer Simulation of HRXRD --- p.51 / Chapter 4.2.1 --- Simulation Theory --- p.51 / Chapter 4.2.2 --- Simulation of Rocking Curves --- p.51 / Chapter 4.3 --- Room Temperature PL of GAAs1-xSBx Quantum Wells and Epitaxial Layers --- p.66 / Chapter 4.4 --- Low Temperature (LT) PL of GAAs1-xSBx Quantum Wells and Epitaxial Layers --- p.75 / Chapter 4.5 --- Excitation Power Dependent (PD) PL of GAAs1-xSBx Quantum Wells and Epitaxial Layers --- p.78 / Chapter 4.6 --- Temperature Dependent (TD) PL of GAAs1-xSBx Quantum Wells and Epitaxial Layers --- p.85 / Chapter 5. --- CONCLUSIONS --- p.90 / REFERENCES --- p.93

Operator splitting methods have been applied to nonlinear partial differential equations that involve operators of different nature. The main idea of these methods is to decompose a complex equation into simpler sub-equations, which can be solved separately. The main advantage of the operator splitting methods is that they provide a great flexibility in choosing different numerical methods, depending on the feature of each sub-problem. In this dissertation, we have developed highly accurate and efficient numerical methods for several nonlinear partial differential equations, which involve both linear and nonlinear operators. We first propose a fast explicit operator splitting method for the modified Buckley-Leverett equations which include a third-order mixed derivatives term resulting from the dynamic effects in the pressure difference between the two phases. The method splits the original equation into two equations, one with a nonlinear convective term and the other one with high-order linear terms so that appropriate numerical methods can be applied to each of the split equations: The high-order linear equation is numerically solved using a pseudo-spectral method, while the nonlinear convective equation is integrated using the Godunov-type central-upwind scheme. The spatial order of the central-upwind scheme depends on the order of the piecewise polynomial reconstruction: We test both the second-order minmod-based reconstruction and fifth-order WENO5 one to demonstrate that using higher-order spatial reconstruction leads to more accurate approximation of solutions. We then propose fast and stable explicit operator splitting methods for two phase-field models (the molecular beam epitaxy equation with slope selection and the Cahn-Hilliard equation), numerical simulations of which require long time computations. The equations are split into nonlinear and linear parts. The nonlinear part is solved using a method of lines combined with an efficient large stability domain explicit ODE solver. The linear part is solved by a pseudo-spectral method, which is based on the exact solution and thus has no stability restriction on the time step size. We have verified the numerical accuracy of the proposed methods and demonstrated their performance on extensive one- and two-dimensional numerical examples, where different solution profiles can be clearly observed and are consistent with previous analytical studies. / Zhuolin Qu

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.