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無 / We derive the MacLaurin series for the moments of the idle time with respect to the parameters in the service time and interarrival time distributions for a GI/G/I queue. The light traffic derivatives are obtained to investigate the quality of a well-known MacLaurin series. The coefficients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The result for the idle period is easily taken as input to the calculation of other performance measures of the system, e.g., interdeparture time distributions. Numerical examples are given to illustrate these results.

Micro-reactors, enabling continuous processes at small scales, have been of growing interest due to their advantage over batch. These advantages include better scaling, as well as improved mass and heat transfer, though many new challenges arise due to the small scales involved such as non-negligible entrance effects and significant pressure drops. The flow in coils, rectangular channel serpentine plates, mix-and-reside plates, and complex liquid-liquid mixing plates was investigated and characterized using residence time distribution (RTD) tests. A pulse test was used to determine the RTD curve shape of these reactors at flowrates ranging from 20 to 100 g/min. A semi-empirical, multi-parameter model was used to describe the asymmetrical curves, while the axial dispersion model was used to describe the symmetrical ones. The Peclet number is given in function of the Reynolds number for the liquid-liquid plates that were found to be near-plug flow (Pe > 100). In a continuous mixing plate, the Pe ranged from 190 to 475 with Pe increasing as Re increased. The effect of straight channel sections in micro-reactors is also evaluated. Longer straight segments between micromixers resulted in the development of unidirectional flow and the occurrence of tailing in the RTD. Finally, the suitability of a liquid-liquid plate for a reactive liquid-solid system is evaluated. The plugging is determined visually and by measuring pressure increase; pressure started to increase after 5 minutes and the experiment had to be halted after 10 minutes due to plugging. Parallels between the particle size distribution and the residence time distribution curves are drawn. The particle size distribution of silver chloride at low flow rates is much wider than at high flowrates. The average particle size at high flowrates was also much lower (≈69nm) than at low flowrates (≈112nm).

The potential for improved selectivity has made column flotation cells a popular choice for upgrading fine coal. Unfortunately, recent production data from full-scale column plants indicate that many industrial installations have failed to meet original expectations in terms of clean coal recovery. Theoretical studies performed using a simple dispersion model showed that this inherent shortcoming could be largely minimized by reconfiguring the columns to operate in series as a cell-to-cell circuit. Follow-up field data showed that this low-cost modification increased flotation recovery as predicted by the dispersion model. This study presents the key findings obtained from the field investigation and provides generic guidelines for designing multi-stage column circuits. / Master of Science

This thesis establishes residence time distribution (RTD) as a key tool for the investigation of water treatment systems. RTD software for tracer data modelling and interpretation is developed and validated for problem solving purposes in water treatment systems. The technique focuses on the systematic interpretation of RTD data using a tanks-in-series based model and an indicator, flushing time (tf ). This approach removes the subjectivity often associated with RTD interpretation and is tested extensively using experimental and numerical data. The influence of design elements, intended to enhance hydraulic efficiency, is also addressed. For this purpose, both numerical modelling (Mike 21) and the proposed approach are employed. Results reveal that the interpretive provides valuable information, facilitating a greater understanding of the hydraulic effects of changes to geometry and inlet/outlet configuration than other techniques alone. The approach was shown to be particularly successful at interpreting RTD curves from stormwater treatment systems due to their susceptibility to stagnation. However, it was shown to have limited applicability in systems with complex flow characteristics (such as large bioreactor vessels) or those susceptible to extensive short-circuiting. The approach was also found to be unsuitable for evaluating the impact of deviations from ideal flow on pollutant removal in systems governed by complex biokinetic reactions.

In this work the relationship between physical properties, such as physical aging and relaxation time distributions, and chemical structure for a variety of polymeric systems were investigated. Although there is a vast amount of physical aging data for polymers, most of these studies do not attempt to correlate structure with physical aging. Therefore, a set of engineering thermoplastics was examined with the goal of relating certain of their characteristic molecular dimensions to their mechanical and volumetric physical aging attributes.Another series of polymeric materials, based on a poly(ether sulfone) backbone, and having various endgroups differing in size, was also studied to determine physical aging rates and relaxation time distributions. Furthermore, it was concluded that the density of the poly(ether sulfones) increased while the glass transition temperature decreased as the endgroup became smaller.Thermoplastic toughened epoxies were also examined to clarify the importance of covalent bonds between toughener and epoxy on physical aging, relaxation time distributions and fracture toughness. In these studies the covalently bonded tougheners differed from their non-reactive counterparts in the rates of volumetric physical aging at high temperatures for the difunctional epoxy. The solvent resistance of the reactive thermoplastic toughened tetrafunctional epoxy was higher than the non-reactive thermoplastic toughened system. The tetrafunctional epoxies with the reactive toughener also had higher toughener glass transition temperatures. / Ph. D.

This work offers a well-developed understanding of the mixing process inside Jet- Stirred Reactors (JSR’s) with different geometries. Due to the difficulty of manufacturing these JSR’s made in quartz, existing JSR configurations were assessed with certain modifications and optimal operating conditions were suggested for each reactor. The effect of changing the reactor volume, the nozzle diameter and shape on mixing were both studied. Two nozzle geometries were examined in this study, a crossed shape nozzle and an inclined shape nozzle. Overall, six reactor configurations were assessed by conducting tracer experiments - using the state-of-art technologies of high-speed cameras and laser absorption spectroscopy- and Computational Fluid Dynamics (CFD) simulations. The high-speed camera tracer experiment gives unique qualitative information – not present in the literature – about the actual flow field. On the other hand, when using the laser technique, a more quantitative analysis emerges with determining the experimental residence time distribution (RTD) curves of each reactor. Comparing these RTD curves with the ideal curve helped in eliminating two cases. Finally, the CFD simulations predict the RTD curves as well as the mixing levels of the JSR’s operated at different residence times. All of these performed studies suggested the use of an inclined nozzle configuration with a reactor diameter D of 40mm and a nozzle diameter d of 1mm as the optimal choice for low residence time operation. However, for higher residence times, the crossed configuration reactor with D=56mm and d=0.3mm gave a nearly perfect behavior.

Consider a sequence (Formula presented.) of i.i.d. uniform random variables taking values in the alphabet set {1, 2,…, d}. A k-superpattern is a realization of (Formula presented.) that contains, as an embedded subsequence, each of the non-order-isomorphic subpatterns of length k. We focus on the (non-trivial) case of d = k = 3 and study the waiting time distribution of (Formula presented.). Our restricted set-up leads to proofs that are very combinatorial in nature, since we are essentially conducting a string analysis.

This dissertation is a collection of papers on anomalous phenomena in physics, biology, and sociology. These phenomena are primarily analyzed in terms of their temporal and spatiotemporal statistical properties. The analysis is based on both numerical simulations and, in some cases, real-world physiological and sociological data. The primary methods of analysis are diffusion entropy analysis, power spectral analysis, multifractal analysis, and survival (or waiting-time) analysis.

For many aggregate mining facilities, the stockpile is the preferred method of storing rock. In many aggregate mines, as well as other mines using stockpiling techniques, understanding the timing and flow of particles through a stockpile is important for correctly timing samples, making proper process adjustments and overall stockpile safety. Because much of the research of today lacks important information regarding actual interior particle movement within a stockpile, a series of Real Time Distribution (RTD) analyses and stockpile flow models have been prepared and analyzed for this study in order to better understand the flow characteristics of a stockpile. A series of three RTD analyses performed on three separate stockpiles provides information leading to the assumption that stockpiles tend to operate similar to a plug flow system. While conveyor loading techniques may lead to separation of rocks prior to traveling through the stockpile, the majority of the rock particles entering the pile remain near the point of entry, or within the "action" area, and will travel through the pile in a plug flow, rather than a mixed flow, manner. High Peclet number results for each analysis prove this assumption to be accurate. A series of models on three separate stockpiles have been created using PFC3d. Mainly, the simulations prove PFC3d is capable of showing how stockpile particles move in three dimensions while monitoring specific particles within the pile. In addition, these models provide simulation results similar to the results obtained within the RTD analyses. Results show that particles located directly above the discharge point, or "action" area, travel through the pile at a faster rate than particles surrounding this area. Velocity results obtained from the simulations show particles accelerating as they get closer to the discharge points while also providing evidence of "arching" during the simulation process. These findings provide a better understanding of internal flow within the stockpile and ways to possibly predict future stockpile flow issues that may be encountered. / Master of Science