A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Doctor of Philosophy. Johannesburg 2016 / Quantifying risk in the absence of hard data presents a significant challenge. Onshore mining of the diamondiferous linear beach deposit along the south western coast of Namibia has been ongoing for more than 80 years. A historical delineated campaign from the 1930s to 1960s used coast perpendicular trenches spaced 500 m apart, comprising a total of 26 000 individual samples, to identify 6 onshore raised beaches. These linear beaches extend offshore and are successfully mined in water depths deeper than 30 m. There is, however, a roughly 4 km wide submerged coast parallel strip adjacent to the mostly mined out onshore beaches for which no real hard data is available at present. The submerged beaches within the 4 km coast parallel strip hold great potential for being highly diamondiferous. To date hard data is not yet available to quantify or validate this potential. The question is how to obtain sufficient hard data within the techno economic constraints to enable a resource with an acceptable level of confidence to be developed. The work presented in this thesis illustrates how virtual orebodies (VOBs) are created based on geological proxies in order to have a basis to assess and rank different sampling and drilling strategies. Overview of 4 papers Paper I demonstrates the challenge of obtaining a realistic variogram that can be used in variogram-based geostatistical simulations. Simulated annealing is used to unfold the coastline and improve the detectable variography for a number of the beaches. Paper II shows how expert opinion interpretation is used to supplement sparse data that is utilised to create an indicator simulation to study the presence and absence of diamondiferous gravel. When only the sparse data is used the resultant simulation is unsuitable as a VOB upon which drilling strategies can be assessed. Paper III outlines how expert opinion hand sketches are used to create a VOB. The composite probability map based on geological proxies is adjusted using a grade profile based on adjacent onshore data before it is seeded with stones and used as a VOB for strategy testing. Paper IV illustrates how the Nachman model based on a Negative Binomial Distribution (NBD) is used to predict a minimum background grade by considering only the zero proportions (Zp) of the grade data. v Conclusions and future work In the realm of creating spatial simulations that can serve as VOBs it is very difficult to attempt to quantify uncertainty when no hard data is available. In the absence of hard data, geological proxies and expert opinion are the only inputs that can be used to create VOBs. Subsequently these VOBs are used as a base to be analysed in order to evaluate and rank different sampling and drilling strategies based on techno economic constraints. VOBs must be updated and reviewed as hard data becomes available after which sampling strategies should be reassessed. During early stage exploration projects the Zp of sample results can be used to predict a minimum background grade and rank different targets for further sampling and valuation. The research highlights the possibility that multi point statistics (MPS) can be used. Higher order MPS should be further investigated as an additional method for creating VOBs upon which sampling strategies can be assessed. / MT2017

The performances of two D-Wave 2 machines (476 and 496 qubits) and of a 1097-qubit D-Wave 2X were investigated. Each chip has a Chimera interaction graph G. Problem input consists of values for the fields hj and for the two-qubit interactions Ji,j of an Ising spin-glass problem formulated on G. Output is returned in terms of a spin configuration {sj}, with sj = +1 or -1. We generated random spanning trees (RSTs) uniformly distributed over all spanning trees of G. On the 476-qubit D-Wave 2, RSTs were generated on the full chip with Ji,j = -1 and hj = 0 and solved one thousand times. The distribution of solution energies and the average magnetization of each qubit were determined. On both the 476- and 1097-qubit machines, four identical spanning trees were generated on each quadrant of the chip. The statistical independence of the these regions was investigated.

The present study focuses on the evolving microstructure of Mg alloy AZ31. The material is subjected to channel die compression at room temperature to simulate a reduction stage in the rolling process. Samples are annealed to provoke recovery, static recrystallization, and grain growth. Annealing is carried out at three temperatures for times ranging from 10s to 10,000s. The material’s response is exhibited through the use of data collection methods such as microhardness, optical microscopy, and electron backscatter diffraction (EBSD). Methodology behind experimentation and data collection techniques are documented in detail. Conclusions are made about the effects of the compression and annealing processes on the material’s microstructure. The Johnson-Mehl-Avrami-Kolmogorov (JMAK) model is introduced, and a simple recrystallization kinetics plot is attempted.

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Met-enkephalin, one of the smallest opiate peptides and an important neurotransmitter, is a widely used benchmarking problem in the field of molecular simulation. Through its range of possible low-temperature conformations separated by free-energy barriers it was previously found to be hard to thermalize using straight canonical molecular dynamics simulations. Here, we demonstrate how one can use the recently proposed population annealing molecular dynamics scheme to overcome these difficulties. We show how the use of multihistogram reweighting allows one to accurately estimate the density of states of the system and hence derive estimates such as the potential energy as quasi continuous functions of temperature. We further investigate the free-energy surface as a function of end-to-end distance and radius of-gyration and observe two distinct basins of attraction.

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The canonical technique for Monte Carlo simulations in statistical physics is importance sampling via a suitably constructed Markov chain. While such approaches are quite successful, they are not particularly well suited for parallelization as the chain dynamics is sequential, and if replicated chains are used to increase statistics each of them relaxes into equilibrium with an intrinsic time constant that cannot be reduced by parallel work. Population annealing is a sequential Monte Carlo method that simulates an ensemble of system replica under a cooling protocol. The population element makes it naturally well suited for massively parallel simulations, and bias can be systematically reduced by increasing the population size. We present an implementation of population annealing on graphics processing units and discuss its behavior for different systems undergoing continuous and first-order phase transitions.