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Research on interfacial phenomena has a long history, which has attracted tremendous interest in recent years. One of the most successful tools is the phase-field approach. As phase-field models usually involve very complex dynamics and it is nontrivial to obtain analytical solutions, numerical methods have played an important role in various simulations. This thesis is mainly devoted to developing accurate, efficient and robust numerical methods and the related numerical analysis for three representative phase-field models, namely the Allen-Cahn equation, the Cahn-Hilliard equation and the thin film models. The first part of this thesis is mainly concentrated on the stability analysis for these three models, with particular attention to the Allen-Chan equation. We have established three stability criterion, i.e., nonlinear energy stability, L∞-stability and L2-stability. As shared by most phase-field models, one of the intrinsic properties of the Allen- Cahn and the Cahn-Hilliard equations is that they satisfy a nonlinear stability re- lationship, usually expressed as a time-decreasing free energy functional. We have studied several stabilized temporal discretization for both the Allen-Cahn and the Cahn-Hilliard equations so that the relevant nonlinear energy stability can be pre- served. The corresponding temporal discretization schemes are linear and are of second-order accuracy. We also apply multi-step implicit-explicit methods to ap- proximate the Allen-Cahn equation. We demonstrate that by suitably choosing the parameters in multi-step implicit-explicit methods the nonlinear energy stability can be preserved. Apart from studying the energy stability for the Allen-Cahn equation, we also establish the numerical maximum principle for some fully discretized schemes. We further extend our analysis technique to the fractional-in-space Allen-Cahn equation. A more general Allen-Cahn-type equation with a nonlinear degenerate mobility and a logarithmic free energy is also considered. The third stability under investigation is the L2-stability. We prove that the con- tinuum Allen-Cahn equation satisfies a uniform Lp-stability. Furthermore, we show that both semi-discretized Fourier Galerkin and Fourier collocation methods can in- herit this stability for p = 2, i.e., L2-stability. Based on the established L2-stability, we accomplish the spectral convergence estimate for the Fourier Galerkin methods. We adopt the second-order Strang splitting schemes in the temporal direction with Fourier collocation methods to demonstrate the uniform L2-stability in the fully dis- cretized scheme. Another contribution of this thesis is to propose a p-adaptive spectral deferred correction methods for the long time simulations for all three models. We develop a high-order accurate and energy stable scheme to simulate the phase-field models by combining the semi-implicit spectral deferred correction method and first-order stabilized semi-implicit schemes. It is found that the accuracy improvement may affect the overall energy stability. To compromise the accuracy and stability, a local p- adaptive strategy is proposed to enhance the accuracy by sacrificing some local energy stability in an acceptable level. Numerical results demonstrate the high effectiveness of our proposed numerical strategy. Keywords: Phase-field models, Allen-Cahn equations, Cahn-Hilliard equations, thin film models, nonlinear energy stability, maximum principle, L2-stability, adaptive simulations, stabilized semi-implicit schemes, finite difference, Fourier spectral meth- ods, spectral deferred correction methods, convex splitting

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Magnetic nanoparticles (NPs) with sizes ranging from 2 to 20 nm in diameter represent an important class of artificial nanostructured materials, since the NP size is comparable to the size of a magnetic domain. They have potential applications in data storage, catalysis, permanent magnetic nanocomposites, and biomedicine. To begin with, a brief overview on the background of Fe-based bimetallic NPs and their applications for data-storage and catalysis was presented in Chapter 1. In Chapter 2, L10-ordered FePt NPs with high coercivity were directly prepared from a novel bimetallic acetylenic alternating copolymer P3 by a one-step pyrolysis method without post-thermal annealing. The chemical ordering, morphology and magnetic properties were studied. Magnetic measurements showed that a record coercivity of 3.6 T (1 T = 10 kOe) was obtained in FePt NPs. By comparison of the resultant FePt NPs synthesized under Ar and Ar/H2, the characterization proved that the incorporation of H2 would affect the nucleation and promote the growth of FePt NPs. The L10 FePt NPs were also successfully patterned on Si substrate by nanoimprinting lihthography (NIL). The highly ordered ferromagnetic arrays on a desired substrate for bit-patterned media (BPM) were studied and promised bright prospects for the progress of data-storage. Furthermore, we also reported a new FePt-containing metallopolymer P4 as the single-source precursor for metal alloy NPs synthesis, where the metal fractions were on the side chain and the ratio could be easily controlled. This polymer was synthesized from random copolymer poly(styrene-4-ethynylstyrene) PES-PS and bimetallic precursor TPy-FePt ([Pt(4’-ferrocenyl-(N^N^N))Cl]Cl) by Sonogashira coupling reaction. After pyrolysis of P4, the stoichiometry of Fe and Pt atoms in the synthesized NPs (NPs) is nearly close to 1:1, which is more precise than using TPy-FePt as precursor. Polymer P4 was also more favorable for patterning by high throughout NIL as compared to TPy-FePt. Ferromagnetic nanolines, potentially as bit-patterned magnetic recording media, were successfully fabricated from P4 and fully characterized. In Chapter 3, a novel organometallic compound TPy-FePd-1 [4’-ferrocenyl-(N^N^N)PdOCOCH3] was synthesized and structurally characterized, whose crystal structure showed a coplanar Pd center and Pd-Pd distance (3.17 Å). Two metals Fe and Pd were evenly embedded in the molecular dimension and remained tightly coupled between each other benefiting to the metalmetal (Pd-Pd) and ligand ππ stacking interactions, all of which made it facilitate the nucleation without sintering during preparing the FePd NPs. Ferromagnetic FePd NPs of ca. 16.2 nm in diameter were synthesized by one-pot pyrolysis of the single-source precursor TPy-FePd-1 under getter gas with metal-ion reduction and minimal nanoparticle coalescence, which have a nearly equal atomic ratio (Fe/Pd = 49/51) and exhibited coercivity of 4.9 kOe at 300 K. By imprinting the mixed chloroform solution of TPy-FePd-1 and polystyrene (PS) on Si, reproducible patterning of nanochains was formed due to the excellent self-assembly properties and the incompatibility between TPy-FePd-1 and PS under the slow evaporation of the solvents. The FePd nanochains with average length of ca. 260 nm were evenly dispersed around the PS nanosphere by self-assembly of TPy-FePd-1. In addition, the orientation of the FePd nanochains could also be controlled by tuning the morphology of PS, and the length was shorter in confined space of PS. Orgnic skeleton in TPy-FePd-1 and PS were carbonized and removed by pyrolysis under Ar/H2 (5 wt%) and only magnetic FePd alloy nanochains with domain structure were left. Besides, a bimetallic complex TPy-FePd-2 was prepared and used as a single-source precursor to synthesize ferromagnetic FePd NPs by one-pot pyrolysis. The resultant FePd NPs have a mean size of 19.8 nm and show the coercivity of 1.02 kOe. In addition, the functional group (-NCMe) in TPy-FePd-2 was easily substituted by a pyridyl group. A random copolymer PS-P4VP was used to coordinate with TPy-FePd-2, and the as-synthesized polymer made the metal fraction disperse evenly along the flexible chain. Fabrication of FePd NPs from the polymers was also investigated, and the size could be easily controlled by tuning the metal fraction in polymer. FePd NPs with the mean size of 10.9, 14.2 and 17.9 nm were prepared from the metallopolymer with 5 wt%, 10 wt% and 20wt% of metal fractions, respectively. In Chapter 4, molybdenum disulfide (MoS2) monolayers decorated with ferromagnetic FeCo NPs on the edges were synthesized through a one-step pyrolysis of precursor molecules in an argon atmosphere. The FeCo precursor was spin coated on the MoS2 monolayer grown on Si/SiO2 substrate. Highly-ordered body-centered cubic (bcc) FeCo NPs were revealed under optimized pyrolysis conditions, possessing coercivity up to 1000 Oe at room temperature. The FeCo NPs were well-positioned along the edge sites of MoS2 monolayers. The vibration modes of Mo and S atoms were confined after FeCo NPs decoration, as characterized by Raman shift spectroscopy. These MoS2 monolayers decorated with ferromagnetic FeCo NPs can be used for novel catalytic materials with magnetic recycling capabilities. The sizes of NPs grown on MoS2 monolayers are more uniform than from other preparation routines. Finally, the optimized pyrolysis temperature and conditions provide receipts for decorating related noble catalytic materials. Finally, Chapters 5 and 6 present the concluding remarks and the experimental details of the work described in Chapters 2-4.

This study explored energy solutions for Ghana by analysing alternative pathways from 2010 to 2040. The Long-range Energy Alternating Pathways (LEAP) tool was used the scenarios analysis. Four scenarios were developed based on key influencing factors identified in the literature. These are Base case, Coal, Modest Renewable Energy Technology (RET), and High RET scenarios. The Base case scenario was based on government-planned expansion and assumed no shift in policy. The Coal scenario assumed the same expansion trend as Base case with introduction of coal plants replacing a percentage of natural gas generation. Modest and High RET scenarios examined the development of the system with increased renewable energy integration. The results revealed that overall benefits are achieved with higher integration of renewable energy technologies. Economic benefits of 0.5 –13.23% is achieved in the RET scenarios depending on the cost development over the 30 year study period. The high RET offers the highest economic and environmental benefits. Subsequently, the optimal development of the system was examined using the LEAP/OSeMOSYS (Open Source Energy Modelling System) optimisation methodology. The least cost system developed by LEAP (Optimum scenario), was used as a reference to examine future possible energy policy direction in Ghana. The policy constraints analysed included emission targets, carbon taxes and transmission, distribution losses improvements and demand side efficiency. The results show that: suitable policies for clean power generation have an important role in CO2 mitigation in Ghana. The introduction of carbon minimisation policies will also promote diversification of the generation mix with higher penetration of renewable energy technologies. The study proposes promoting energy efficiency and improvement in transmission and distribution losses and utilisation of renewable energy as the best energy strategy for Ghana. Ghana needs ambitious targets, policies and implementation strategies to enhance energy efficiency, and decrease demand in the long term. Stable funding and promotion of transparent policies are required to promote high development of renewable energy technologies.

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The use of neutron and charged particle induced reactions is briefly discussed and the experimental facilities employed in this work are described. The qualitative elemental composition of human lung tissues, taken from individuals deceased from non-lung-related causes, was determined by prompt gamma-ray neutron activation analysis (PGNAA), cyclic neutron activation analysis (CNAA), conventional neutron activation and proton induced X-ray emission analyses. In addition elemental concentrations were determined by CNAA and conventional activation. Concentration values for elements previously not extensively reported in the literature, Ce, Cl, F, Hf and Sc were obtained as well as values for 18 other elements. Fingernail samples were investigated in order to study the uptake of Se and Zn supplementation. The effect of the rate of excretion through fingernails of Se and Zn on the level of Na is described. The variations in the elemental concentrations from finger to finger are shown for Se, Cl, Na and K and the variations from hand to hand, of a control, are shown for Br, Cl, K, Mg, Na, Rb, S, Se and Zn. Concentration values for Br, Ce, S, and Se, for which values available in the literature are very few , are presented. Bone biopsy samples were collected from the iliac crest of subjects, divided into four groups depending on the length of dialysis treatment, aluminium levels in blood and bone pathology in terms of osteoporosis. Fluorine concentration in the samples were determined by CNAA and proton Induced gamma-ray emission (PIGE) in conjunction with Rutherford backscattering (RBS). The relation between the A1 levels in the system and the F concentrations in the bone samples was investigated and the existence of a positive correlation between A1 and F was found. The effect of mass fractionation was tested for small and large sample fractions of Bowen's kale and the detection sensitivities were determined in counts/mg of sample. The concept of the sampling factor in CNAA was established for the comparative determination of elemental concentrations and the representative mass of Bowen's kale required for the determination of Br, Ca, Cl, K, Mg, Na, Rb, S, Se, Sm and V were found. Following the Chernobyl reactor accident, measurements of University of Surrey students returning from Kiev and Minsk were conducted for the neck region and the chest region. The activity of iodine (I-131) in the thyroid and the effective dose equivalent were calculated. The activities in the chest region for Cs-137, Zr-95 and the annihilation radiation were determined using a chest water-phantom. Measurement of radioactive particulates in air filters, collected from air ventilation units in the London area, a month after the radioactive cloud from Chernobyl had passed over the U.K., was carried out and the concentrations of 17 fission products in the atmosphere were calculated.

Capillary Electrophoresis (CE) is a high resolution analytical technique that may be employed in the separation and quantification of a wide range of analytes. The enormous efficiency obtained in CE are well suited for complex mixtures in which resolution of a large number of peaks in a short time is desirable. Therefore, CE has a promising future in pharmaC-eutical analysis. The separation mechanism of CE is based on the differential electrophoretic mobility of the solutes inside a buffer filled capillary upon the application of a voltage. Capillary electrophoresis is especially suitable for ionic species. The full potential of this technique can only be realised through the manipulation of numerous experimental parameters. In the present study, a CE method has been developed for the analysis of the macrolide antibiotics: erythromycin, oleandomycin, troleandomycin and josamycin. The selection of initial analysis conditions and optimisation of selectivity are reviewed. A systematic approach to method development was used to maximise analyte differential electrophoretic mobilities, by adjusting the pH. Thereafter, the influences of electrolyte molarity and electrolyte additives were investigated. In addition, some instrumental parameters, such as capillary length emf diameter, applied voltage and injection conditions were varied. The effect of the sample solvent and oncapillary concentration techniques such as FASI, were investigated. Also, the influence of injecting a water plug on the quantity of sample injected was demonstrated. Full resolution was achieved with the addition of methanol to the electrolyte. The applicability of CE for the assay of erythromycin and its related substances was investigated. Two methods were developed and successfully validated using CE: one for the quantitative determination of erythromycin alone and another for erythromycin related substances in the presence of large quantities of erythromycin A. Several related substances and impurities that result from the fermentation process used to produce erythromycin as well as degradation products are known to be present in commercial sa~ples. These impurities include erythromycin B, C, D, E, F, erythromycin enol ether, anhydroerythromycin and N-demethylerythromycin. Currently both the USP and BP official assays for the analysis of erythromycin involve the use of microbiological assays. These methods are limited as they are unable to differentiate between erythromycin and its related substances and degradation products. Furthermore, the microbiological assays are time-consuming and tedious to perform. 11 The CE methods developed for the analysis of erythromycin and for its related substances were fully validated in terms of precision, linearity, accuracy, sensitivity and stability. In addition, erythromycin was subjected to six stress modes and the stressed samples were analysed. An intemal standard was employed to provide acceptable precision for the migration time « 1.80 % RSD) and peak area « 4.44 % RSD). Optimum sensitivity was obtained using low UV wavelengths, with LOO values of less than 10 % for the related substances. The developed method was accurate for erythromycin C, anhydroerythromycin and N-demethylerythromycin, even in the presence of large concentrations of the parent. The method for~ erythromycin related substances was applied to the determination of impurities in three commercial erythromycin bases. The CE methods developed were rapid, precise, specific and stability-indicating and may be used to provide additional information to augment that attained by HPLC for purity assessment and in stability studies of erythromycin. Capillary electrophoresis is a simple, cost-effective technique that is capable of generating high quality data. This technique will become firmly established within pharmaceutical analysis for main peak and related impurity determination assays as familiarity becomes more widespread across the pharmaceutical industry and improvements in instrumentation are performed.