Dissolving multicomponent NAPL as a source of contamination in subsurface water is considered. In particular, two processes are analyzed with regard to how they alter inter-species concentration ratios at remote monitoring locations relative to inter-species molar ratios in the NAPL: nonlinear dissolution governed by Raoult’s Law and differential sorption during subsurface transport. An analytic solution for Raoult’s Law-governed dissolution is presented. Separately, it is shown how a variety of 1D analytic transport models for simple boundary conditions may be adapted to use arbitrary time-varying concentrations by use of some properties of Laguerre series. This is combined with the analytic solution so that Raoult’s Law-governed multicomponent NAPL dissolution may be employed as the boundary condition for analytic transport models. A new computer model implementing this technique in an environment of discrete, parallel fractures is presented, and its accuracy verified for specific conditions against an existing code. The new code is applied to a parametric study on the plume separation of PAH and phenolic compounds from the dissolution of creosote. Narrow fracture spacing as well as significant values of matrix organic carbon are seen as particularly conducive to separation of these types of plumes, which in some circumstances may be entirely disjoint. Concentration ratios downgradient are shown largely unrelated to concentration ratios at the source. Finally, a study of PCB speciation is undertaken in fractured rock with known parameters, for which a rigorous, least squares speciation approach is developed. Even at distances of 5 m from the source, given perfect information about the subsurface, it is found not possible to chemically fingerprint a source PCB mixture from a list of three absent a model of the weathering of the NAPL. Both the PCB and creosote studies demonstrate that forensic inference of source compositions from field data is unreliable and the need for coupled dissolution and transport models like the one developed here. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2012-09-25 21:43:29.04

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Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this thesis, two novel entropy measures are developed based on using coarse quantization to classify and compare dynamical features within a time series; quantized dynamical entropy (QDE) and a quantized approximation of sample entropy (QASE). Following this, comprehensive guidelines for the quantification of complexity are presented based on a detailed investigation of the performance characteristics of the two developed measures and three existing measures; permutation entropy, sample entropy and fuzzy entropy. The sensitivity of the considered entropy measures to changes in dynamics was assessed using the case study of characterizing bipedal walking gait dynamics. Based on the analysis conducted, it was found that sample entropy and fuzzy entropy, while computationally inefficient, provide the best overall performance. In instances where computational efficiency is vital, QDE and QASE serve as viable alternatives to existing methods.

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Primarily because of its low cost and ease of implementation, analogue control has been the dominant control strategy in modern switch-mode power supply designs. The 'on/off' nature of power switches is essentially digital, which makes it tempting for power elec- tronics engineers to combine the emerging capability of digital technologies with existing switch-mode power supply designs. Whereas an analogue controller is usually cheaper to implement, it lacks the flexibility and capacity to implement the complex control func- tions which a digital controller can offer. The research presented in this thesis addresses the practical implementation of a digi- tal controller for a Series-Loaded Resonant Converter (SLR). The resonant frequency of the SLR converter is around 60 kHz, and the switching frequency varies up to around 80 kHz to regulate the 12V dc output voltage across a 100W, variable resistive load, from a variable 46.6V 60.2V input voltage. This provides a fair challenge for digital waveform generators as the digital processor needs to have a high clock rate to produce high speed, high resolution and linearly varying frequency square waves, to regulate the output volt- age with adequate resolution. Digital compensation algorithms also need to be efficient to minimise the phase lag caused by the instruction overhead. In order to completely understand the control needs of the SLR converter, an analogue controller was constructed using a UC3863N. The feedback compensation consists of an error amplifier in an integrator configuration. Digital control is accomplished with a TMS320F2812 Digital Signal Processor (DSP). Its high throughput of 150 MIPS provides sufficient resolution to digitally generate linearly varying frequency switching signals util- ising Direct Digital Synthesis (DDS). Time domain analysis of the switching signals, shows that the DDS generated square iv ABSTRACT waves display evidence of jitter to minute variations in pulse-widths caused by the digi- tisation process, while in the frequency domain, this jitter displays itself as additional sidebands that deteriorate the fundamental frequency of the switching signal. Overall, DDS generated square waves are shown experimentally to be adequate as control signals for the MOSFET power switches. Experiments with step load changes show the digi- tal controller is able to regulate the output voltage properly, with the drawback of the settling time being a little longer than the analogue counterpart, possibly caused by the unpredictable damping effects of switching signal jitter. Variations in input voltage shows that the digital controller excels at operating under noisier conditions, while the analogue controlled output has slightly greater noise as input voltage is increased. As the digital technology continues to improve its speed, size and capacity, as well as becoming more affordable, it will not be long before it becomes the leading form of control circuitry in power supplies.

The study of formal power series is an area of interest that spans many areas of mathematics. We begin by looking at single-variable formal power series with coefficients from a field. By restricting to those series which are invertible with respect to formal composition we form a group. Our focus on this group focuses on the classification of elements having finite order. The notion of a semi-cyclic group comes up in this context, leading to several interesting results about torsion subgroups of the group. We then expand our focus to the composition of multivariate formal power series, looking at similar questions about classifying elements of finite order. We end by defining a natural automorphism on this group induced by a group action of the symmetric group.

A mathematical method is developed for the analysis of the electrostatic fields existing within finite, three-dimensional, cylindrically shaped regions which do not contain the axis of revolution. The derived method defines the potential field within such a region provided that the potentials are known at the boundaries, that the insulating media has homogeneous, linear, and isotropic characteristics, and that the region is charge free. The general solution for the potential field involves forms of both the Fourier and the Fourier Bessel series, and the resulting series solution is shown to be uniformly convergent . It is also shoran that this potential field series solution can be integrated and differentiated to yield series solutions for electric fiend and capacitance and that these solutions are also uniformly convergent.