In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear. Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects. Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom. For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results. Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.

This study explores the utilisation of spatial technologies as a tool to analyse and combat crime. The study deals specifically with remote sensing and its potential for being integrated with geographical information systems (GIS). The integrated spatial approach resulted in the understanding of land use class behaviour over time and its relationship to specific crime incidents per police precinct area. The incorporation of spatial technologies to test criminological theories in practice, such as the ecological theories of criminology, provides the science with strategic value. It proves the value of combining multi-disciplinary scientific fields to create a more advanced platform to understand land use behaviour and its relationship to crime. Crime in South Africa is a serious concern and it impacts negatively on so many lives. The fear of crime, the loss of life, the socio-economic impact of crime, etc. create the impression that the battle against crime has been lost. The limited knowledge base within the law enforcement agencies, limited logistical resources and low retention rate of critical staff all contribute to making the reduction of crime more difficult to achieve. A practical procedure of using remote sensing technology integrated with geographical information systems (GIS), overlaid with geo-coded crime data to provide a spatial technological basis to analyse and combat crime, is illustrated by a practical study of the Tshwane municipality area. The methodology applied in this study required multi-skilled resources incorporating GIS and the understanding of crime to integrate the diverse scientific fields into a consolidated process that can contribute to the combating of crime in general. The existence of informal settlement areas in South Africa stresses the socio-economic problems that need to be addressed as there is a clear correlation of land use data with serious crime incidents in these areas. The fact that no formal cadastre exists for these areas, combined with a great diversity in densification and growth of the periphery, makes analysis very difficult without remote sensing imagery. Revisits over time to assess changes in these areas in order to adapt policing strategies will create an improved information layer for responding to crime. Final computerised maps generated from remote sensing and GIS layers are not the only information that can be used to prevent and combat crime. An important recipe for ultimately successfully managing and controlling crime in South Africa is to strategically combine training of the law enforcement agencies in the use of spatial information with police science. The researcher concludes with the hope that this study will contribute to the improved utilisation of spatial technology to analyse and combat crime in South Africa. The ultimate vision is the expansion of the science of criminology by adding an advanced spatial technology module to its curriculum. / Criminology / D.Litt. et Phil. (Criminology)

This study explores the utilisation of spatial technologies as a tool to analyse and combat crime. The study deals specifically with remote sensing and its potential for being integrated with geographical information systems (GIS). The integrated spatial approach resulted in the understanding of land use class behaviour over time and its relationship to specific crime incidents per police precinct area. The incorporation of spatial technologies to test criminological theories in practice, such as the ecological theories of criminology, provides the science with strategic value. It proves the value of combining multi-disciplinary scientific fields to create a more advanced platform to understand land use behaviour and its relationship to crime. Crime in South Africa is a serious concern and it impacts negatively on so many lives. The fear of crime, the loss of life, the socio-economic impact of crime, etc. create the impression that the battle against crime has been lost. The limited knowledge base within the law enforcement agencies, limited logistical resources and low retention rate of critical staff all contribute to making the reduction of crime more difficult to achieve. A practical procedure of using remote sensing technology integrated with geographical information systems (GIS), overlaid with geo-coded crime data to provide a spatial technological basis to analyse and combat crime, is illustrated by a practical study of the Tshwane municipality area. The methodology applied in this study required multi-skilled resources incorporating GIS and the understanding of crime to integrate the diverse scientific fields into a consolidated process that can contribute to the combating of crime in general. The existence of informal settlement areas in South Africa stresses the socio-economic problems that need to be addressed as there is a clear correlation of land use data with serious crime incidents in these areas. The fact that no formal cadastre exists for these areas, combined with a great diversity in densification and growth of the periphery, makes analysis very difficult without remote sensing imagery. Revisits over time to assess changes in these areas in order to adapt policing strategies will create an improved information layer for responding to crime. Final computerised maps generated from remote sensing and GIS layers are not the only information that can be used to prevent and combat crime. An important recipe for ultimately successfully managing and controlling crime in South Africa is to strategically combine training of the law enforcement agencies in the use of spatial information with police science. The researcher concludes with the hope that this study will contribute to the improved utilisation of spatial technology to analyse and combat crime in South Africa. The ultimate vision is the expansion of the science of criminology by adding an advanced spatial technology module to its curriculum. / Criminology and Security Science / D.Litt. et Phil. (Criminology)