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    Physicochemical properties of nickel and cobalt sulphate solutions of hydrometallurgical relevance

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    Producing nickel and cobalt metal by high pressure acid leaching (HPAL) of nickel laterites is becoming one of Australia's largest mineral processing industries. However, the background chemical information for this process, including the fundamental physicochemical properties of acidic metal sulphate leachate solutions, is not well known. In order to improve the efficiency of current and future HPAL plants, high quality physicochemical and thermodynamic data will be necessary. This thesis reports measurements on the densities and heat capacities of nickel and cobalt sulphate solutions and their mixtures along with detailed studies of the nature of the species present and the thermodynamics of their interconversions. Densities and heat capacities of nickel and cobalt sulphate and perchlorate solutions and their ternary mixtures were measured using a vibrating tube densimeter and a flow microcalorimeter respectively. These data were used to calculate the apparent molal volumes and heat capacities of these solutions. Standard partial molal quantities were then obtained by appropriate extrapolation procedures, along with the volume and heat capacity changes of ion pair formation. A comparison has been made between experimental densities and heat capacities with those predicted by Young's rule. Good agreement was obtained except when the degree of complexation varied significantly in the mixtures. The various ion pair species in nickel and cobalt sulphate solutions, along with those of magnesium sulphate (which is a major impurity in HPAL leachates), were reinvestigated by dielectric relaxation spectroscopy. Doubly solvent separated ion pairs, solvent shared ion pairs and contact ion pairs were shown to exist simultaneously in solution and their concentrations were determined from dilute to near-saturated concentrations. Evidence for the possible existence of a triple ion, M2SO4 2+, was also obtained in highly concentrated solutions. The equilibrium constants of the stepwise reactions and the effective hydration numbers of ions and ion pairs were also calculated. The heats of complexation of nickel(II) and cobalt(II) sulphate were determined at different ionic strengths in sodium perchlorate media by titration calorimetry. These data were fitted to a specific ion interaction model to obtain the standard state values. The corresponding entropies of complexation were calculated and were found to be the major contributor to the stability of the complexes

    Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs

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    We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman and Nowak [Nature 441 (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for the magnitude of fixation probabilities of the underlying evolutionary game between cooperators and defectors. We view the Markov chains associated with the two updating mechanisms as voter model perturbations. Then we present a first-order approximation for fixation probabilities of general voter model perturbations on finite graphs subject to small perturbation in terms of the voter model fixation probabilities. In the context of regular graphs, we obtain algebraically explicit first-order approximations for the fixation probabilities of cooperators distributed as certain uniform distributions. These approximations lead to a rigorous proof that both of the rules of Ohtsuki et al. are valid and are sharp.Comment: Published in at http://dx.doi.org/10.1214/12-AAP849 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    On the Convergence and Consistency of the Blurring Mean-Shift Process

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    The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shift algorithm, which is one version of the mean-shift process that successively blurs the dataset. The analysis of the blurring mean-shift is relatively more complicated compared to the nonblurring version, yet the algorithm convergence and the estimation consistency have not been well studied in the literature. In this paper we prove both the convergence and the consistency of the blurring mean-shift. We also perform simulation studies to compare the efficiency of the blurring and the nonblurring versions of the mean-shift algorithms. Our results show that the blurring mean-shift has more efficiency.Comment: arXiv admin note: text overlap with arXiv:1201.197
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