Markov chains are a fundamental subject of study in mathematical probability and have found wide application in nearly every branch of science. Of particular interest are finite-state Markov chains; the representation of finite-state Markov chains by a transition matrix facilitates detailed analysis by linear algebraic methods. Previous methods of analyzing finite-state Markov chains have emphasized state events. In this thesis we develop the concept of a transition event and define two types of transition events: cumulative events and time-average events. Transition events generalize state events and provide a more flexible framework for analysis. We derive computable, closed-form expressions for the expectation of these two events, characterize the conditioning of transition events, provide an algorithm for computing the expectation of these events, and analyze the complexity and stability of the algorithm. As an application, we derive a construction of composite Markov chains, which we use to study competitive dynamics.

An activated sludge system that incorporates a sidestream anaerobic bioreactor, called the Cannibal process, was the focus of this study. A prior study of this process (Novak et al., 2007) found that this system generated about 60% less solids than conventional activated sludge without any negative effects on the effluent quality. Although that study showed substantial solids reduction, questions remain concerning the specific mechanism(s) that account for the solids loss. In this study, the mechanisms that account for the loss of biological solids was the focus of the investigation. The first part of this study was conducted to evaluate those effects in terms of the role of iron in the influent wastewater and feeding patterns on the performance of the Cannibal system. It was found that the Cannibal system with high iron in the influent produced less biological solids than the system receiving low iron. The data also showed that the Cannibal system operated under fast feed (high substrate pressure) produced much less solids than the system with slow feed (low substrate pressure). The high substrate pressure was achieved by feeding the influent wastewater to the Cannibal system over a short time period so that the substrate concentration would initially peak and then decline as degradation occurred. This is called "fast feed." For low substrate pressure, the influent was added slowly so the substrate concentration remained low at all times. This is called "slow feed." Later, an attempt to increase substrate pressure in the slow feed Cannibal system was conducted by either manipulating the aeration patterns or adding a small reactor in front of the main reactor (selector). It was found that either interrupting aeration in the aerobic reactor or providing a small aerobic reactor in front of the main reactor resulted in an increase in solids reduction. The second part of this study was to investigate the mechanisms of floc destruction in the fast and the slow feed Cannnibal systems. It was found that higher accumulation of biopolymers (proteins and polysaccharides) occurred in the fast feed system and this was associated with a greater solids reduction in the fast than the slow feed system. In addition, more protein hydrolysis and more Fe(III)-reducing microorganism activity in the fast feed environment were found to be factors in higher solids reduction. The last part of this study was to investigate the structure of the Cannibal sludge flocs generated under the fast and the slow feed conditions. It was found that the readily biodegradable (1 kDa.) protein is larger in the flocs from the fast feed than the slow feed Cannibal system. This resulted in higher floc destruction in the fast feed condition. / Ph. D.

Rotor (helicopter/wind turbine) blades are typically slender structures that can be modeled as beams. Beam modeling, however, involves a substantial mathematical formulation that ultimately helps save computational costs. A beam theory for rotor blades must account for (i) initial twist and/or curvature, (ii) inclusion of composite materials, (iii) large displacements and rotations; and be capable of offering significant computational savings compared to a non-linear 3D FEA (Finite Element Analysis). The mathematical foundation of the current effort is the Variational Asymptotic Method (VAM), which is used to rigorously reduce the 3D problem into a 1D or beam problem, i.e., perform a cross-sectional analysis, without any ad hoc assumptions regarding the deformation. Since its inception, the VAM based cross-sectional analysis problem has been in a constant state of flux to expand its horizons and increase its potency; and this is precisely the target at which the objectives of this work are aimed. The problems addressed are the stress-strain-displacement recovery for spanwise non-uniform beams, analytical verification studies for the initial curvature effect, higher fidelity stress-strain-displacement recovery, oblique cross-sectional analysis, modeling of thin-walled beams considering the interaction of small parameters and the analysis of plates of variable thickness. The following are the chief conclusions that can be drawn from this work: 1. In accurately determining the stress, strain and displacement of a spanwise non-uniform beam, an analysis which accounts for the tilting of the normal and the subsequent modification of the stress-traction boundary conditions is required. 2. Asymptotic expansion of the metric tensor of the undeformed state and its powers are needed to capture the stiffnesses of curved beams in tune with elasticity theory. Further improvements in the stiffness matrix can be achieved by a partial transformation to the Generalized Timoshenko theory. 3. For the planar deformation of curved laminated strip-beams, closed-form analytical expressions can be generated for the stiffness matrix and recovery; further certain beam stiffnesses can be extracted not only by a direct 3D to 1D dimensional reduction, but a sequential dimensional reduction, the intermediate being a plate theory. 4. Evaluation of the second-order warping allows for a higher fidelity extraction of stress, strain and displacement with negligible additional computational costs. 5. The definition of a cross section has been expanded to include surfaces which need not be perpendicular to the reference line. 6. Analysis of thin-walled rotor blade segments using asymptotic methods should consider a small parameter associated with the wall thickness; further the analysis procedure can be initiated from a laminated shell theory instead of 3D. 7. Structural analysis of plates of variable thickness involves an 8×8 plate stiffness matrix and 3D recovery which explicitly depend on the parameters describing the thickness, in contrast to the simplistic and erroneous approach of replacing the thickness by its variation.

A Comparison of Solvent and Water-Borne Alkyd Coatings Abstract Conventional solvent based alkyd coatings have gone out of favor due to concerns over volatile organic compound (VOC) content. However, due to recent focus on renewable raw materials, alkyds are making a comeback in waterborne form. Water based alkyd coatings are known to have poor shelf stability and corrosion resistance, as well as other problems during the formulation process. This project focused on comparing solvent borne to two types of water-borne alkyds, water reducible alkyds and alkyds emulsions. The purpose was to understand the differences between the three types of alkyds in terms of their production and final properties. It was ultimately hoped that the formulations used for this project would prove to solve the problems normally experienced by waterborne alkyds. After testing several chemical and physical properties, it was determined that the solvent borne alkyd coatings performed better than both water based systems in corrosion resistance, accelerated weathering, and shelf stability but the water reducible and emulsion alkyd coatings performed similarly to the solvent borne alkyd in gloss, contrast ratio, and durability. The VOC emissions for all three alkyd types were as expected; the solvent borne had the highest emission at 253 g/L, followed by water reducible with 166 g/L, and emulsion with 34 g/L. The History of VOC Regulations in the United States Abstract In another solvent based alkyd coating focused project within my research group, the question of the how volatile organic compound (VOC) regulation in the United States (U.S.) evolved came up. It quickly became apparent that no comprehensive answer to this question existed. Part two of this project is an attempt to answer this question in a comprehensive manner. VOC regulations started in California in the late 1970s, and paints and coatings became a nationally regulated emission source by the 1990s. The U.S. government limited harmful emissions, such as smog and compounds contributing to ozone depletion, through Clean Air Acts. The first Clean Air Act was enacted in 1965, but it wasn’t until the Clean Air Act of 1990 that VOC emissions became a focus. VOCs are not inherently hazardous but are a source of concern because they serve as a precursor to the formation of damaging ground level ozone. The Environmental Protection Agency (EPA) has established the minimum VOC emission limits in the Architectural and Industrial Maintenance (AIM) federal rule, but each state or state subdivision can enforce stricter limits within their borders. The strictest limits are set by the South Coast Air Quality Management District (SCAQMD) in Southern California, but other entities exist. This report thoroughly documents the history of VOC regulation in the United States by collecting, combining, organizing, and summarizing information gathered from various industries and government publications, agency members, and industrial and academic professionals.

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No description available.

Für einen R^d-wertigen stochastischen Prozess X auf R bezeichne X_t den Segmentprozess X_t:={X(t+u): u = 0. Es wird folgende affine stochastische Differentialgleichung mit unendlichem Gedächtnis betrachtet: dX(t)=L(X_t)dt + dW(t) für t >= 0, X_0=F, (A) wobei L:B -> R^d ein lineares stetiges Funktional, W einen Wiener-Prozess mit Werten in R^d sowie B einen semi-normierten linearen Unterraum von {f:(-00, 0] -> R^d} bezeichnen. Die Anfangsbedingung F ist eine B-wertige Zufallsvariable. Die Lösung X der Gleichung (A) lässt sich mittels einer Formel der Variation der Konstanten darstellen. Für die Existenz einer stationären Lösung werden hinreichende und notwendige Bedingungen vorgestellt. Für eine spezielle Klasse von Funktionalen L kann Gleichung (A) auf ein System gewöhnlicher stochastischer Gleichungen ohne Gedächtnis reduziert werden. Diese Reduktion wird im Detail untersucht, insbesondere gewinnt man hierdurch ein einfaches äquivalentes Kriterium für die Existenz stationärer Lösungen von Gleichungen mit Funktionalen L dieser Klasse. Durch Einbettung der Gleichung (A) in den Bidualraum B** gelingt die Bestimmung der Lyapunov-Exponenten der Lösung. Hierzu wird ein neuer Zusammenhang der Lösung der sogenannten adjungierten Gleichung von (A) und einer Spektralzerlegung des Raumes B benutzt. Die Untersuchung der stetigen Abhängigkeit der Lösung von dem Funktional L und der Anfangsbedingung F ermöglicht die Behandlung anwendungsorientierter Aspekte. In Verbindung mit den Ergebnissen über reduzierbare Gleichungen wird ein Verfahren zur Approximation der Lösung von Gleichung (A) durch Ornstein-Uhlenbeck-Prozesse vorgestellt. Eine allgemeine Klasse von Ito-Differentialgleichungen mit nichtlinearen vergangenheitsabhängigen Drift- und Dispersionskoeffizienten wird eingeführt, in der die Gleichung (A) als eine spezielle affine Gleichung verstanden werden kann. Für diese allgemeinen Gleichungen wird ein Existenz- und Eindeutigkeitssatz nachgewiesen. / For an R^d-valued stochastic process X denote the segment process by X_t:={X(t+u): u = 0. We consider the following affine stochastic differential equation with infinite delay: dX(t)=L(X_t)dt + dW(t) for t >= 0, X_0= F, (A) where L:B -> R^d denotes a linear continuous functional, W denotes a Wiener process with values in R^d and B is a semi-normed linear subspace of {f: (-00, 0] -> R^d}. The initial condition F is a B-valued random variable. The solution X of equation (A) can be represented by a variation of constants formula. We provide sufficient and necessary conditions for the existence of a stationary solution. For a special class of functionals L the equation (A) can be reduced to a system of ordinary stochastic differential equations without memory. This reduction is studied in detail. In particular, we deduce a simple equivalent condition for the existence of stationary solutions of equations with functionals L in this class. The embedding of equation (A) into the bidualspace B** enables us to calculate the Lyapunov exponents of the solution. For this purpose we exploit a new connection between the solution of the so-called adjoint equation of (A) and a spectral decompositon of the space B. By considering the continuous dependence of the solution on the functional L and the initial condition F we obtain results useful in applications. In conjunction with results on reducible equations we establish an approximation scheme for the solution of equation (A) by Ornstein-Uhlenbeck processes. Moreover, we introduce a general class of Ito differential equations with non-linear drift and dispersion hereditary coefficients. We deduce a result on the existence of unique solutions for this general class of equations. Equation (A) can be regarded as a special affine equation in this class.

This thesis examines sulfide oxidation in 4 physically and mineralogically diverse acid sulfate soil (ASS) materials collected from coastal floodplain sites in north-eastern New South Wales. The aim of this study is to gain further understanding of the process of sulfide oxidation in ASS materials, which will allow improved and more effective management strategies to be applied to these materials. The process of sulfide oxidation was examined using laboratory incubation experiments. The oxidation of pyrite was the primary cause of initial acidification of the ASS materials studied. Although the acid volatile sulfur fraction increased in concentration by an order of magnitude over the initial 8 days of incubation, the subsequent oxidation of this fraction did not result in substantial acidification. Sulfate (SO42-) was the dominant sulfur species produced from sulfide oxidation, however, water-soluble SO42- was a poor indicator of the extent of sulfide oxidation. The sulfoxyanion intermediates thiosulfate (S2O32-) and tetrathionate(S4O62-) were only detected in the early stages of incubation, and their relative abundance appeared to be pH dependent. The diminishing presence of these 2 sulfur species as oxidation progressed was indicative that ferric iron (Fe3+) and bacterial catalysis were driving the oxidation processes. The rate of sulfide oxidation, and consequent rate of acidification, was highly dependent on the soil pH and oxygen availability. Accelerated sulfide oxidation was only observed at low pH (i.e. pH < 4.0) when oxygen availability was not limited. The application of sub-optimal amounts of neutralising agents prevented severe soil acidification in the short-term (i.e. up to 2 months), but had little effect on decreasing the rate of sulfide oxidation and acidification in the long-term. Sub-optimal amounts of CaCO3 accelerated sulfide oxidation and acidification of the peaty marcasitic ASS material resulting in elevated soluble Fe and Al concentrations. For some of the ASS materials, sub-optimal applications of seawater-neutralised bauxite refinery residue (SNBRR) also resulted in elevated soluble Al concentrations. The response of partially-oxidised ASS materials to the exclusion of oxygen was variable. The rate of sulfide oxidation, acidification and the production of soluble oxidation products generally decreased markedly when subjected to anoxia. However, especially in highly acidic ASS materials (i.e. pH < 3.5), sulfide oxidation and acidification generally occurred (albeit at much slower rates), most probably due to oxidation by Fe3+. Rapid sulfide re-formation occurred in the peat ASS material that had been oxidised for 63 days, with 0.47% reduced inorganic sulfur (SCR) formed over 60 days of anoxia. Biogeochemical sulfide formation consumes acidity, however, sulfide re-formation was ineffective in reversing acidification under the conditions of this experiment. The peroxide oxidation methods examined were method dependent and substantially underestimated peroxide oxidisable sulfur, sulfidic acidity and net acidity. The precipitation of jarosite during peroxide oxidation was a major factor contributing to the underestimation in these ASS materials. Clay mineral dissolution may contribute towards the underestimation of both sulfidic and net acidity using peroxide oxidation methods. The atmospheric loss of sulfur and acidity was also identified as a possible additional interference. This study has shown that the initial pH of an ASS material is a useful indicator (additional to those already used) of the potential environmental hazard of an ASS material when oxygen is expected to be non-limiting, such as when ASS materials are excavated and stockpiled. The recommended action criteria need to be reassessed as the data indicate that the current criteria are conservative for alkaline and neutral ASS materials, but should be lowered for all acidic ASS materials (i.e. pH < 5.5) to 0.03% sulfide regardless of texture. Alternative strategies are necessary for the management of ASS materials that are subject to oxidation when the addition of optimal rates of neutralising materials cannot be ensured. The treatment of sites containing actual ASS materials by management strategies that rely on oxygen exclusion need to be accompanied by strategies that include either acid neutralisation or containment in order to reduce acid export from the site. The peroxide oxidation methods examined were subject to substantial interferences, and consequently are unable to reliably provide accurate measurements of the reduced inorganic sulfur fraction, sulfidic acidity, and net acidity in ASS materials.

This thesis examines sulfide oxidation in 4 physically and mineralogically diverse acid sulfate soil (ASS) materials collected from coastal floodplain sites in north-eastern New South Wales. The aim of this study is to gain further understanding of the process of sulfide oxidation in ASS materials, which will allow improved and more effective management strategies to be applied to these materials. The process of sulfide oxidation was examined using laboratory incubation experiments. The oxidation of pyrite was the primary cause of initial acidification of the ASS materials studied. Although the acid volatile sulfur fraction increased in concentration by an order of magnitude over the initial 8 days of incubation, the subsequent oxidation of this fraction did not result in substantial acidification. Sulfate (SO42-) was the dominant sulfur species produced from sulfide oxidation, however, water-soluble SO42- was a poor indicator of the extent of sulfide oxidation. The sulfoxyanion intermediates thiosulfate (S2O32-) and tetrathionate(S4O62-) were only detected in the early stages of incubation, and their relative abundance appeared to be pH dependent. The diminishing presence of these 2 sulfur species as oxidation progressed was indicative that ferric iron (Fe3+) and bacterial catalysis were driving the oxidation processes. The rate of sulfide oxidation, and consequent rate of acidification, was highly dependent on the soil pH and oxygen availability. Accelerated sulfide oxidation was only observed at low pH (i.e. pH < 4.0) when oxygen availability was not limited. The application of sub-optimal amounts of neutralising agents prevented severe soil acidification in the short-term (i.e. up to 2 months), but had little effect on decreasing the rate of sulfide oxidation and acidification in the long-term. Sub-optimal amounts of CaCO3 accelerated sulfide oxidation and acidification of the peaty marcasitic ASS material resulting in elevated soluble Fe and Al concentrations. For some of the ASS materials, sub-optimal applications of seawater-neutralised bauxite refinery residue (SNBRR) also resulted in elevated soluble Al concentrations. The response of partially-oxidised ASS materials to the exclusion of oxygen was variable. The rate of sulfide oxidation, acidification and the production of soluble oxidation products generally decreased markedly when subjected to anoxia. However, especially in highly acidic ASS materials (i.e. pH < 3.5), sulfide oxidation and acidification generally occurred (albeit at much slower rates), most probably due to oxidation by Fe3+. Rapid sulfide re-formation occurred in the peat ASS material that had been oxidised for 63 days, with 0.47% reduced inorganic sulfur (SCR) formed over 60 days of anoxia. Biogeochemical sulfide formation consumes acidity, however, sulfide re-formation was ineffective in reversing acidification under the conditions of this experiment. The peroxide oxidation methods examined were method dependent and substantially underestimated peroxide oxidisable sulfur, sulfidic acidity and net acidity. The precipitation of jarosite during peroxide oxidation was a major factor contributing to the underestimation in these ASS materials. Clay mineral dissolution may contribute towards the underestimation of both sulfidic and net acidity using peroxide oxidation methods. The atmospheric loss of sulfur and acidity was also identified as a possible additional interference. This study has shown that the initial pH of an ASS material is a useful indicator (additional to those already used) of the potential environmental hazard of an ASS material when oxygen is expected to be non-limiting, such as when ASS materials are excavated and stockpiled. The recommended action criteria need to be reassessed as the data indicate that the current criteria are conservative for alkaline and neutral ASS materials, but should be lowered for all acidic ASS materials (i.e. pH < 5.5) to 0.03% sulfide regardless of texture. Alternative strategies are necessary for the management of ASS materials that are subject to oxidation when the addition of optimal rates of neutralising materials cannot be ensured. The treatment of sites containing actual ASS materials by management strategies that rely on oxygen exclusion need to be accompanied by strategies that include either acid neutralisation or containment in order to reduce acid export from the site. The peroxide oxidation methods examined were subject to substantial interferences, and consequently are unable to reliably provide accurate measurements of the reduced inorganic sulfur fraction, sulfidic acidity, and net acidity in ASS materials.

No description available.