The phase equilibria relationships in the Na₃AlF₆-AlF₃-LiF ternary system have been investigated using a combination of quenching, optical microscopy, DTA, and x-ray powder diffraction techniques. The compatibility relations at 500°C, the binary system Na₃AlF₆-Li₃AlF₆, and the ternary liquidus surface were determined. The liquidus surface was found to contain the following five important invariant points: 1) eutectic - 81% LiF, 9.5% Na₃AlF₆, 9.5% AlF₃ and 685°C 2) eutectic - 56% LiF, 6% Na₃AlF₆, 38% AlF₃ and 585°C 3) eutectic - 37% LiF, 17% Na₃AlF₆, 46% AlF₃ and 620°C 4) peritectic - 30% LiF, 37% Na₃AlF₆, 33% AlF₃ and 660°C 5) reaction point - 65% LiF, 9% Na₃AlF₆, 26% AlF₃ and 675°C The 500°C isothermal section contains 7 three-phase regions and 2 large two-phase regions. The binary system Na₃AlF₆-Li₃AlF₆ contained 2 incongruently melting compounds, many polymorphic transformations, and a eutectic at 690°C and 67 mole % Li₃AlF₆. / Master of Science

The phase equilibria relationships in the Li₃A1F₆-A1₂0₃ binary system, the Li₃A1F₆-Na₃AlF₆-A1₂0₃ ternary system and the LiF-A1F₃-Na₃A1F₆-Al₂0₃ quaternary system have been investigated using a combination of X-ray powder diffraction, DTA, quenching and optical microscopy techniques. The compatibility relations at 500°C for the ternary and quaternary systems, the Li₃A1F₆-A1₂0₃ binary system and the ternary liquidus surface were determined. The binary system was found to have a eutectic at 754°C and 1 mole % Al₂0₃. The liquidus surface was found to contain the following three invariant points: 1. eutectic - 66 mole % Li₃A1F₆, 29% Na₃A1F₆, 5% A1₂0₃ and 670°C 2. peritectic - 51 mole % Li₃A1F₆, 42.5% Na₃A1F₆, 65% A1₂0₃ and 683°C 3. reaction point - 65 mole % Li₃A1F₆, 33% Na₃A1F₆, 2% A1₂0₃ and 693°C. The 500°C isothermal section contains three 3-phase regions and one 2-phase region. The quaternary system contains 7 compatibility tetrahedra at 500°C. / Master of Science

Master of Science

Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation. / Doctor of Philosophy / Quantum computers (QCs) have the potential to perform certain tasks much more efficiently than today0 s supercomputers. One primary challenge in realizing a practical QC is maintaining the stored information, the loss of which is known as decoherence. This work attributes decoherence to dissipation (a classical analogue being heat generated due to friction) occurring while an algorithm is run on the QC. Standard quantum modeling approaches assume that for any dissipation to occur, the QC must interact with its environment. However, in this work, steepest-entropy-ascent quantum thermodynamics (SEAQT) is used to model the evolution of the QC as it runs an algorithm. SEAQT, developed by Hatsopolous, Gyftopolous, Beretta, and others over the past 40 years, supplements the laws of quantum mechanics with those of thermodynamics and in contrast to the standard quantum approaches does not require the presence of an environment to account for the dissipation which occurs. This work first applies the SEAQT framework to modeling single qubits (quantum bits) to characterize the effect of dissipation on the information stored on the qubit. This is later extended to a nuclear-magnetic-resonance (NMR) QC of 7 qubits. Additionally, SEAQT is used to predict experimentally observed dissipation in a two-qubit NMR QC. Afterwards, several methods for constrained perturbations of a QC0 s state are presented. These methods are then used with SEAQT to analyze the effect of dissipation on the entanglement of two qubits. Finally, a model is derived within the SEAQT framework accounting for a qubit interacting with its environment, which is at a constant temperature. This model is then used to develop a method for limiting the decoherence and shown to significantly lowering the resulting error due to decoherence.

It became the purpose of this study to design, build and test an electronic oscillator capable of exciting an electrodeless discharge in hydrogen in which the Doppler shifts would be exhibited in a regular manner. / M.S.

This dissertation examines equilibria in epidemics and introduces novel approaches to epidemic modeling, consisting of two separate but closely related chapters. In Chapter 2, we develop an optimizing epidemic model within a dynamic urn-SIR framework, accommodating generic offspring distributions, and derive a trajectory convergence theorem. We study the mean-field equilibrium through numerical simulations. Our findings reveal two key features often overlooked in existing literature: substantial variation in epidemic outcomes despite homogeneous individual behavior, and the potential for resurgence in the number of infections. We demonstrate that the offspring distribution of infections significantly impacts epidemic dynamics, with negative binomial distributions leading to more dispersed outcomes and higher probabilities of minor outbreaks compared to geometric distributions. These results highlight the importance of stochastic modeling in epidemic forecasting and public health policy. Chapter 3 proposes and examines static and dynamic urn-SIR models, a novel approach to epidemic modeling that addresses key limitations of traditional stochastic SIR models. We focus on the critical issue of heterogeneity in individual infectiousness, which is not adequately captured by the geometric offspring distribution inherent in the continuous-time Markov chain SIR models. Our urn-SIR models accommodates generic offspring distributions, including the empirically supported negative binomial distribution. We formally formulate the static and dynamic urn-SIR models. The static model focuses on the end of the epidemic, where primary variables are the epidemic size and the total number of contacts, while the dynamic model captures the dynamic process of the disease progression. The cornerstone of our work is a proven threshold limit theorem, characterizing the asymptotic behavior of the epidemic size as the population approaches infinity. This theorem extends beyond early-stage branching process approximations in the existing literature that considers generic offspring distribution. Moreover, we also show that in the dynamic model, the trajectories of epidemic processes converges in probability to a corresponding deterministic system, allowing comprehensive analysis of entire epidemic courses. Our work bridges crucial gaps in existing literature, providing a more realistic representation of disease spread while maintaining analytical tractability. The findings have significant implications for epidemiology, public health, and related fields, informing more effective strategies for disease control and prevention.

In a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions and subject to occupation restrictions, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. When investigating the non-equilibrium relaxation of the predator density in the vicinity of the phase transition point, we observe critical slowing-down and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population's proximity to its extinction threshold. In order to study boundary effects, we split the system into two patches: Upon setting the predation rates at two distinct values, one half of the system resides in an absorbing state where only the prey survives, while the other half attains a stable coexistence state wherein both species remain active. At the domain boundary, we observe a marked enhancement of the predator population density, the minimum value of the correlation length, and the maximum attenuation rate. Boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern, with two different reaction rates assigned to neighboring patches. We furthermore add another predator species into the system with the purpose of studying possible origins of biodiversity. Predators are characterized with individual predation efficiencies and death rates, to which "Darwinian" evolutionary adaptation is introduced. We find that direct competition between predator species and character displacement together play an important role in yielding stable communities. We develop another variant of the lattice predator-prey model to help understand the killer- prey relationship of two different types of E. coli in a biological experiment, wherein the prey colonies disperse all over the plate while the killer cell population resides at the center, and a "kill zone" of prey forms immediately surrounding the killer, beyond which the prey population gradually increases outward. / Ph. D. / We utilize Monte-Carlo simulations to study population dynamics of Lotka–Volterra model and its variants. Our research topics include the non-equilibrium phase transition from a predator-prey coexistence state to an absorbing state wherein only prey survive, boundary effects in a spatially inhomogeneous system, the stabilization of a three species system with direct competition and “Darwinian” evolutionary adaption introduced, and the formation of spatial patterns in a biological experiment of two killer and prey E. coli species.

Submitted in fulfilment of the academic requirements for the Masters Degree in Technology: Chemistry, Durban University of Technology, 2012. / In this work, the thermodynamics of ternary liquid mixtures involving carboxylic acids with sulfolane, hydrocarbons including cycloalkane, and alcohols are presented. In South Africa, Sasol is one of the leading companies that produce synthesis gas from low grade coal. Carboxylic acids together with many other oxygenate and hydrocarbons are produced by Sasol using the Fischer-Tropsch process. Carboxylic acids class is one of the important classes of compounds with great number of industrial uses and applications. The efficient separation of carboxylic acids from hydrocarbons and alcohols from hydrocarbons is of economic importance in the chemical industry, and many solvents have been tried and tested to improve such recovery. This work focussed on the use of the polar solvent sulfolane in the effective separation by solvent extraction and not by more common energy intensive method of distillation. The first part of the experimental work focussed on ternary liquid-liquid equilibria of mixtures of [sulfolane (1) + carboxylic acid (2) + heptane (3) or cyclohexane or dodecane] at T = 303.15 K, [sulfolane (1) + alcohol (2) + heptane (3)] at T = 303.15 K. Carboxylic acid refers to acetic acid, propanoic acid, butanoic acid, 2-methylpropanoic acid, pentanoic acid and 3-methylbutanoic acid. Alcohol refers to methanol, ethanol, 1- propanol, 2-propanol, 1-butanol, 2-butanol, 2-methyl-1-propanol and 2-methyl-2-propanol. Ternary liquid- liquid equilibrium data are essential for the design and selection of solvents used from liquid- liquid extraction process. Abstract vi The separation of carboxylic acids from hydrocarbons and the alcohols from hydrocarbons is commercially lucrative consideration and is an important reason of this study. The separation of carboxylic acids or alcohols from hydrocarbons by extraction with sulfolane was found to be feasible as all selectivity values obtained are greater than 1. The modified Hlavatý, beta (β) and log equations were fitted to the experimental binodal data measured in this work. Hlavatý gave the best overall fit as compared to beta ( ) and log function. The NRTL (Non-Random, Two Liquid) and UNIQUAC Universal Quasichemical) model were used to correlate the experimental tie-lines and calculate the phase compositions of the ternary systems. The correlation work served three purposes:  to summarise experimental data  to test theories of liquid mixtures  prediction of related thermodynamics properties. The final part of the study was devoted to the determination of the excess molar volumes of mixtures of [sulfolane (1) + alcohol (2)] at T = 298.15 K, T = 303.15 K and T = 309.15 K. Density was used to determine the excess molar volumes of the mixtures of [sulfolane (1) + alcohols (2)]. Alcohol refers to methanol, ethanol, 1- propanol, 2-propanol, 1-butanol, 2-butanol, 2-methyl-1-propanol, 2-methyl-2-propanol. The work was done to investigate the effect of temperature on excess molar volumes of binary mixtures of alcohols and sulfolane, as well as to get some idea of interactions involved between an alcohol and sulfolane. The excess molar volume data for each binary mixture was fitted in the Redlich–Kister equation to correlate the composition dependence of the excess property. / National Research Foundation

Submitted in fulfilment of the academic requirements for the Masters Degree in Technology: Chemistry, Durban University of Technology, 2012. / National Research Foundation

Phase equilibrium data is vital for designing chemical separation equipment. Traditionally, such data is obtained through laboratory experiments by sampling and analysing each phase of an equilibrated chemical mixture. An alternative means of generating such data is via molecular simulations, which also gives insight into the microscopic structure of the phases. This project was undertaken due to the lack of work on molecular simulations in predicting vapour-liquid-liquid equilibrium (VLLE). Gibbs Ensemble Monte Carlo molecular simulations were performed in the isochoricisothermal (NVT) and isobaric-isothermal (NVT) ensembles to determine the ability and limitations of the Transferable Potentials for Phase Equilibria (United-Atom) and Extended Simple Point Charge (SPC-E) force fields in predicting three-phase fluid equilibrium for two binary and three ternary industrially relevant mixtures: n-hexane/water (1), ethane/ethanol (2), methane/n-heptane/water (3), n-butane/1-butene/water (4) and nhexane/ ethanol/water (5). The NPT ensemble proved inadequate for predicting VLLE for binary mixtures, as for both binary mixtures (1 and 2), the simulations reverted to two phases. This was due in part to the unlike-pair interactions between pseudoatoms in different molecules not being accurately predicted at the specified simulation conditions to reproduce experimental mixture densities and vapour pressures. It was also due to the sensitivity of the NPT ensemble to perturbations which probably removed the system from its three-phase trajectory in Gibbs phase space, since specifying even the correct pressure corresponding to the potential models was unsuccessful in obtaining stable VLLE. Furthermore, ternary VLLE could not be obtained for a mixture exhibiting an extremely narrow three-phase region (4) and simulations for a miscible, non-ideal mixture (5) gave mole fractions that were in poor agreement with experiment. Good results were obtained for mixture 3 which exhibits limited mutual solubilities and a large three phase region. The NVT ensemble overcame the shortcomings of the NPT ensemble by producing three stable phases for the binary mixtures, revealing that the three-phase pressures were shifted by as much as 12%. Also, the narrow three-phase region of mixture 4 was overcome by adjusting the total system volume, producing three stable phases. These were also the first successful binary VLLE simulations involving complex polyatomic molecules. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2008.