<p>Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|y-x|<\gamma (t), t>0} |u(y,t)|= + \infty$$ for all $x \in \RR$. This theorem was proved by choosing $$\widehat{f}(\xi )=\widehat{f_a}(\xi )= | \xi | ^{-n} (\log | \xi |)^{-3/4} \sum_{j=1}^{\infty} \chi _j(\xi)e^{- i( x_{n_j} \cdot \xi + t_j | \xi | ^a)}, \, a=2,$$ where $\chi_j$ is the characteristic function of shells $S_j$ with the inner radius rapidly increasing with respect to $j$. The purpose of this essay is to explain the proof given by Sjögren and Sjölin, by first showing that the theorem is true for $\gamma (t)=t$, and to investigate the result when we use $$S^a f_a (x, t)= (2 \pi)^{-n}\int_{\RR} {e^{i x\cdot \xi}e^{it |\xi|^a}\widehat{f_a}(\xi)}\, d \xi$$ instead of $u$.</p>

A multi-scale approach was used to investigate the occurrence and physical characteristics of viral surrogates in water systems. This approach resulted in a methodology to quantify the dynamics and physical parameters of viral surrogates, including bacteriophages and nanoparticles. Physical parameters impacting the occurrence and survival of viruses can be incorporated into models that predict the levels of viral contamination in specific types of water. Multiple full-scale water systems (U.S., Italy and Australia) were tested including surface water, drinking water, stormwater and wastewater systems. Water quality parameters assessed included viral markers (TTV, polyomavirus, microviridae and adenovirus), bacteriophages (MS2 and ΦX-174), and coliforms (total coliforms and E. coli). In this study, the lack of correlations between adenovirus and that of bacterial indicators suggests that these bacterial indicators are not suitable as indicators of viral contamination. In the wastewater samples, microviridae were correlated to the adenovirus, polyomavirus, and TTV. While TTV may have some qualities which are consistent with an indicator such as physical similarity to enteric viruses and occurrence in populations worldwide, the use of TTV as an indicator may be limited as a result of the detection occurrence. The limitations of TTV may impede further analysis and other makers such as coliphages, and microviridae may be easier to study in the near future. Batch scale adsorption tests were conducted. Protein-coated latex nanospheres were used to model bacteriophages (MS2 and ΦX-174) and includes a comparison of the zeta potentials in lab water, and two artificial groundwaters with monovalent and divalent electrolytes. This research shows that protein-coated particles have higher average log10 removals than uncoated particles. Although, the method of fluorescently labeling nanoparticles may not provide consistent data at the nanoscale. The results show both that research on viruses at any scale can be difficult and that new methodologies are needed to analyze virus characteristics in water systems. A new dynamic light scattering methodology, area recorded generalized optical scattering (ARGOS) method, was developed for observing the dynamics of nanoparticles, including bacteriophages MS2 and ΦX-174. This method should be further utilized to predict virus fate and transport in environmental systems and through treatment processes. While the concentration of MS2 is higher than ΦX-174 as demonstrated by relative total intensity, the RMSD shows that the dynamics are greater and have more variation in ΦX-174 than MS2 and this may be a result of the hydrophobic nature of ΦX-174. Relationships such as these should be further explored, and may reflect relationships such as particle bonds or hydrophobicity.

Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t&gt;0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|y-x|&lt;\gamma (t), t&gt;0} |u(y,t)|= + \infty$$ for all $x \in \RR$. This theorem was proved by choosing $$\widehat{f}(\xi )=\widehat{f_a}(\xi )= | \xi | ^{-n} (\log | \xi |)^{-3/4} \sum_{j=1}^{\infty} \chi _j(\xi)e^{- i( x_{n_j} \cdot \xi + t_j | \xi | ^a)}, \, a=2,$$ where $\chi_j$ is the characteristic function of shells $S_j$ with the inner radius rapidly increasing with respect to $j$. The purpose of this essay is to explain the proof given by Sjögren and Sjölin, by first showing that the theorem is true for $\gamma (t)=t$, and to investigate the result when we use $$S^a f_a (x, t)= (2 \pi)^{-n}\int_{\RR} {e^{i x\cdot \xi}e^{it |\xi|^a}\widehat{f_a}(\xi)}\, d \xi$$ instead of $u$.

This dissertation focuses on the development and implementation of a new method to solve the time-dependent form of the linear Boltzmann transport equation for reactor transients. This new method allows for a stable solution to the fully explicit form of the transport equation with delayed neutrons by employing an error-controlled, adaptive Runge-Kutta-Fehlberg (RKF) method to differentiate the time domain. Allowing for the time step size to vary adaptively and as needed to resolve the time-dependent behavior of the angular flux and neutron precursor concentrations. The RKF expansion of the time domain occurs at each point and is coupled with a Source Iteration to resolve the spatial behavior of the angular flux at the specified point in time. The decoupling of the space and time domains requires the application of a quasi-static iteration between solving the time domain using adaptive RKF with error control and resolving the space domain with a Source Iteration sweep. The research culminated with the development of the 1-D Adaptive Runge-Kutta Time-Dependent Transport code (ARKTRAN-TD), which successfully implemented the new method and applied it to a suite of reactor transient benchmarks.

Application of polymer matrix composites in engineering structures has been steadily increasing over the past five decades. Multidirectional polymer composites are one class of continuous fiber reinforced polymer matrix composites used in aerospace structures, where the desired mechanical performance outweighs the cost. Their modulus and strength degrade with time (known as creep and creep rupture) during the service, owing to the viscos-elasticity of the polymer matrix. Additional contribution to this degradation comes from various damage modes developed in the plies of the composite with time and identified in this thesis as TDD (Time Dependent Damage). These damage modes may also develop due to process-induced residual stresses, and during loading to the service load, identified as TID (Time Independent Damage). TID influences the TDD, the creep and the creep rupture. The objective of this thesis is to develop a model to predict the evolution of TID and TDD in multiple plies of a laminate and their influence on creep. The predominant damage mode, transverse cracking, is modeled in this study. The model consists of four modules, PIS, QSL, SL, and VA. The PIS, QSL, and SL moduli predict changes in ply stresses for incremental change in temperature, stress, and time respectively, using lamination theory and assuming linear elastic behavior of the plies during an incremental step. In parallel, each module predicts the stored elastic energy in each ply after each incremental step and compares it with a critical stored elastic energy criterion to determine if a ply would crack. If fracture is predicted, the VA module based on variational analysis, is invoked to determine the crack density and the perturbation in ply stresses due to cracking. The perturbation stresses are used by the module that invoked the VA module to determine the ply stresses after cracking during the current incremental step. The model predictions for a [±45/90]s laminate, at two test temperatures (80C and 180C) and four stresses in the range of 20–54 MPa, compare very well with experimental results validating the model.

Application of polymer matrix composites in engineering structures has been steadily increasing over the past five decades. Multidirectional polymer composites are one class of continuous fiber reinforced polymer matrix composites used in aerospace structures, where the desired mechanical performance outweighs the cost. Their modulus and strength degrade with time (known as creep and creep rupture) during the service, owing to the viscos-elasticity of the polymer matrix. Additional contribution to this degradation comes from various damage modes developed in the plies of the composite with time and identified in this thesis as TDD (Time Dependent Damage). These damage modes may also develop due to process-induced residual stresses, and during loading to the service load, identified as TID (Time Independent Damage). TID influences the TDD, the creep and the creep rupture. The objective of this thesis is to develop a model to predict the evolution of TID and TDD in multiple plies of a laminate and their influence on creep. The predominant damage mode, transverse cracking, is modeled in this study. The model consists of four modules, PIS, QSL, SL, and VA. The PIS, QSL, and SL moduli predict changes in ply stresses for incremental change in temperature, stress, and time respectively, using lamination theory and assuming linear elastic behavior of the plies during an incremental step. In parallel, each module predicts the stored elastic energy in each ply after each incremental step and compares it with a critical stored elastic energy criterion to determine if a ply would crack. If fracture is predicted, the VA module based on variational analysis, is invoked to determine the crack density and the perturbation in ply stresses due to cracking. The perturbation stresses are used by the module that invoked the VA module to determine the ply stresses after cracking during the current incremental step. The model predictions for a [±45/90]s laminate, at two test temperatures (80C and 180C) and four stresses in the range of 20–54 MPa, compare very well with experimental results validating the model.

South African metropolitan areas are experiencing rapid growth and require an increase in network infrastructure. Increased congestion negatively impacts both public and freight transport costs. The concept of City Logistics is concerned with the mobility of cities, and entails the process of optimizing urban logistics activities by concerning the social, environmental, economic, financial, and energy impacts of urban freight movement. In a costcompetitive environment, freight transporters often use sophisticated vehicle routing and scheduling applications to improve fleet utilization and reduce the cost of meeting customer demands. In this thesis, the candidate builds on the observation that vehicle routing and scheduling algorithms are inherent problem specific, with no single algorithm providing a dominant solution to all problem environments. Commercial applications mostly deploy a single algorithm in a multitude of environments which would often be better serviced by various different algorithms. This thesis algorithmically implements the ability of human decision makers to choose an appropriate solution algorithm when solving scheduling problems. The intent of the routing agent is to classify the problem as representative of a traditional problem set, based on its characteristics, and then to solve the problem with the most appropriate solution algorithm known for the traditional problem set. A not-so-artificially-intelligent-vehicle-routing-agent™ is proposed and developed in this thesis. To be considered intelligent, an agent is firstly required to be able to recognize its environment. Fuzzy c-means clustering is employed to analyze the geographic dispersion of the customers (nodes) from an unknown routing problem to determine to which traditional problem set it relates best. Cluster validation is used to classify the routing problem into a traditional problem set. Once the routing environment is classified, the agent selects an appropriate metaheuristic to solve the complex variant of the Vehicle Routing Problem. Multiple soft time windows, a heterogeneous fleet, and multiple scheduling are addressed in the presence of time-dependent travel times. A new initial solution heuristic is proposed that exploits the inherent configuration of customer service times through a concept referred to as time window compatibility. A high-quality initial solution is subsequently improved by the Tabu Search metaheuristic through both an adaptive memory, and a self-selection structure. As an alternative to Tabu Search, a Genetic Algorithm is developed in this thesis. Two new crossover mechanisms are proposed that outperform a number of existing crossover mechanisms. The first proposed mechanism successfully uses the concept of time window compatibility, while the second builds on an idea used from a different sweeping-arc heuristic. A neural network is employed to assist the intelligent routing agent to choose, based on its knowledge base, between the two metaheuristic algorithms available to solve the unknown problem at hand. The routing agent then not only solves the complex variant of the problem, but adapts to the problem environment by evaluating its decisions, and updating, or reaffirming its knowledge base to ensure improved decisions are made in future. / Thesis (PhD (Industrial Engineering))--University of Pretoria, 2007. / Industrial and Systems Engineering / PhD / unrestricted

Survival models are used in analysing time-to-event data. This type of data is very common in medical research. The Cox proportional hazard model is commonly used in analysing time-to-event data. However, this model is based on the proportional hazard (PH) assumption. Violation of this assumption often leads to biased results and inferences. Once non-proportionality is established, there is a need to consider time-varying effects of the covariates. Several models have been developed that relax the proportionality assumption making it possible to analyse data with time-varying effects of both baseline and time-updated covariates. I present various approaches for handling time-varying covariates and time-varying effects in time-to-event models. They include the extended Cox model which handles exogenous time-dependent covariates using the counting process formulation introduced by cite{andersen1982cox}. Andersen and Gill accounts for time varying covariates by each individual having multiple observations with the total-at-risk follow up for each individual being further divided into smaller time intervals. The joint models for the longitudinal and time-to-event processes and its extensions (parametrization and multivariate joint models) were used as it handles endogenous time-varying covariates appropriately. Another is the Aalen model, an additive model which accounts for time-varying effects. However, there are situations where all the covariates of interest do not have time-varying effects. Hence, the semi-parametric additive model can be used. In conclusion, comparisons are made on the results of all the fitted models and it shows that choice of a particular model to fit is influenced by the aim and objectives of fitting the model. In 2002, an AntiRetroviral Treatment (ART) service was established in the Cape Town township of Gugulethu, South Africa. These models will be applied to an HIV/AIDS observational dataset obtained from all patients who initiated ART within the programme between September 2002 and June 2007.

The oral route of administration is the most widely used mode of drug administration due to advantages such as the convenience of oral drug administration, patient choice, cost-effectiveness, and ease of generating oral dosage forms on a large scale. How effectively an oral drug is absorbed and made accessible to the target organ depends on a variety of factors. Poor absorption from the absorption site, excessive metabolism in the gut and liver, and pharmacokinetic drug-drug (PK-DDI) interactions can all contribute to inadequate therapy. The PK-DDI may result in greater than anticipated bioavailability and toxicity due to irreversible enzyme inhibition including time-dependent inactivation (TDI) of the intestinal enzymes.There are different in vitro models available to predict the fraction escaping gut metabolism (Fg), which is a major determinant of intestinal bioavailability. On the other hand, using pre-clinical species, Fg can be extrapolated in humans using allometric scaling, but there has been significant discordance due to the variable intestinal metabolism in humans vs. pre-clinical species. A number of absorption models have been developed over the years to predict oral drug absorption, and intestinal TDI can be incorporated into many of those models. In this study, the continuous intestinal absorption model has been refined, including the intestinal metabolism model, to predict the oral absorption of midazolam and nicardipine in both humans and rats. This absorption model was also used to predict the Fg of these drugs in those two species. The in vitro metabolic characteristics of the model drugs were investigated using both human and rat microsomes. The kinetic profiles of their metabolic conversion in rats and humans were developed using numerical techniques. The continuous absorption model explains how drug concentration changes with time and distance. A physiologically based pharmacokinetic (PBPK) model describes the intestine. The physiological inputs to the model, as well as the structure of the gastrointestinal tract, vary depending on the species. Rats and humans have different lengths of the small intestine's regions, such as the jejunum, and absorptive surface area amplifiers, such as the villi and microvilli. Along with the metabolic characteristics established through in vitro metabolic investigations, physiological aspects (applied to both rats and humans) and physicochemical drug characteristics were also added to the model. To estimate the absorption characteristics of midazolam and nicardipine, this model was further connected to the traditional compartmental model that represents the rest of the body. Chapter one details the background and importance concerning this project, along with the hypothesis and goals. Chapter two involves developing and validating bioanalytical methods for the drugs of interest. Chapters three and four detail the in vitro metabolic studies in rat and human microsomes (both intestinal and liver). Chapter five represents the TDI studies which were finally excluded from the absorption modeling in this thesis. Finally, chapter six illustrates the prediction of the oral PK profile of midazolam and nicardipine in rats and humans, rendering predicted values of Fg of these drugs in both species. Finally, chapter seven presents the significance, summary, and some directions to take this research further down the future. / Pharmaceutical Sciences

This is Part A. / <p> Effects in 19 element CANDU fuel bundles containing ThO2 and UO2, located in thermonuclear reactor blankets, have been examined for a variety of blanket designs. The buildup in time of nuclides derived from Th232 by neutron capture was studied. The essential CTR (Controlled Thermonuclear Reactor) blanket features that were examined were tritium breeding in the blanket (the fusion reaction of interest was the DT reaction resulting in the production of a 14.1 MeV neutron and a 3.5 MeV alpha particle), neutron multiplication in the blanket and the U233 production. Means of optimizing these features were also examined. Some conclusions concerning the use and influence of the CANDU bundle are made.</p> <p> It is of interest to study the details of the buildup of U233 in the bundles with the view of perhaps transferring bundles directly from the CTR blanket into a core of a fission power reactor. As such, it would be necessary to convert approximately 3% of the initial thorium present to U233 before transferral. This report examines time steps over which this could be achieved and looks at the performance of the blanket as a whole when such changes occur. The production of unwanted radioactive isotopes is looked at with suggestions of how to minimize this production without harming the rest of the blanket's basic functions.</p> <p> Procedures outlined in the preliminary report "Bench-Mark Neutronic Calculations for Fusion Reactor Designs" by S.A. Kushneriuk and P.Y. Wong form a basis for all of the calculations made in this report. Based on the findings of that report, it is expected that values presented here do reflect, to a fair degree of accuracy, conditions encountered in the CTR blankets studied.</p> / Thesis / Master of Engineering (MEngr)