A complex arrangement of electronic states within materials can manifest exotic quantum-mechanical effects. These systems are often referred to as quantum materials. Increased understanding of quantum materials has historically lead to the development of new technologies. It is therefore extremely important to develop and test precise methods for calculating the behaviour of electronic states within a material. For decades, the workhorse of electronic structure calculations has been density functional theory (DFT). DFT is often referred to as a first-principles method because it allows for the calculation of the distribution of electrons throughout a material with only specification of the lattice geometry and atomic components. From the results of a DFT calculation, it is possible to study the orbital character of electronic wavefunctions, topology of electronic band structure, and some aspects of superconductivity. This provides insight into many quantum properties of a system which may otherwise be difficult or impossible to ascertain from experiments. DFT is, however, sometimes limited by the approximations necessary for practical implementation. Further methods have been developed to systematically correct the limitations of DFT. In particular, the combination of DFT with dynamical mean-field theory (DFT+DMFT) is among the most widely accepted methods for correcting the inadequacy of DFT in handling strong electron-electron correlations. In this thesis, I use methods from DFT and DFT+DMFT to study the quantum properties of materials. / Thesis / Master of Science (MSc)

Three- different groups of materials were chosen to investigate the uniaxial compaction of particulate solids. Dentritic and cubic sodium chloride were chosen as plastically deforming, dicalcium phosphcte and sugar as fragmentary and styrocell, homopolymer and copolyrinier as non-compactable materials. The uniaxial compaction of the materials was continuously followed by measurement. of 1-.h e applied force, the force transmitted radially to the die wall and the upper punch displacement. The data obtained was presented in the form of Mohr circles, stress pathways (shear-mean compaction stress planes) and a three dimensional representation in mean compaction stress, shear stress and volume change. The yield loci evaluated from Mohr circles and shear-mean compaction stress relationships of compactable and non-compactable materials were found to be similar in shape. The unloading stress profiles were however more informative. All unloading shear-mean compaction stres's curves of the compactable materials cross the mean compaction stress axis to give negative values of shear stress and reach a minimum value of T min' which was material and compaction p.,- essure dependent. The unloading curves of non-compactable materials gaye approximately zero shear. The parameters evaluated from the characteristic stress profiles were correlated to the tensile strength and hardness of compacts. Mathematical expressions have been proposed for the shear-mean compaction stress relationships of the materials investigated. TI he materials were characterised before and after compaction in terms of specific surface aroa, porosity and mechanical strength of compacts with ccrnpaction pressure. / Sudan Government and the Institution of Chemical Engineers.

A globular cluster is a collection of stars that orbits the center of its galaxy as a single satellite. Understanding what influences the formations of these clusters provides understanding of galaxy structure and insight into their early development. We continue the work of Harris et al. (2013), who identified a set of predictors that accurately determined the number of clusters Ngc, through analysis of an incomplete dataset. We aimed to improve upon these results through imputation of the missing data. A small amount of precision was gained for the slope of Ngc~ R_e*sigma_ e, while the intercept suffered a small loss of precision. Estimates of intrinsic variance also increased with the addition of imputed data. We also found galaxy morphological type to be a significant predictor of Ngc in a model with R_e*sigma_ e. Although it increased precision of the slope and reduced the residual variance, its overall contribution was negligible. / Thesis / Master of Science (MSc)

The origin of cosmic magnetic fields is a important area of astrophysics. The process by which they are created falls under the heading of dynamo theory, and is the topic of this thesis. Our focus for the location of where these magnetic fields operate is one the most ubiquitous objects in the universe, the accretion disk. By studying the accretion disk and the dynamo process that occurs there we wish to better understand both the accretion process and the dynamo process in stars and galaxies as well. We analyse the output from a stratified zero net flux shearing box simulation performed using the ATHENA MHD code in collaboration with Shane Davis. The simulation has turbulence which is naturally forced by the presence of a linear instability called the magnetorotational instability (MRI). We utilise Fourier filtering and the tools of mean field dynamo theory to establish a connection between the calculated EMF and the model predictions of the dynamically quenched alpha model. We find a positive correlation for both components parallel to the large scale magnetic field and the azimuthal components. We have explored many aspects of the theory including additional contributions from magnetic buoyancy and an effect arising from the large scale shear and the current density. We also directly measure the turbulent correlation time for the velocity and magnetic fields both large scale and small. We can also observe the effects of the dynamo cycle, with the azimuthal component of the large scale magnetic field flipping sign in this analysis. We find a positive correlation between the divergence of the eddy scale magnetic helicity flux and the component of the electromotive force parallel to the large scale magnetic field. This correlation directly links the transfer of magnetic helicity to the dynamo process in a system with naturally driven turbulence. This highlights the importance of magnetic helicity and its conservation even in a system with triply periodic boundary conditions. / Thesis / Doctor of Philosophy (PhD)

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