Since its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This study is divided into five Chapters and an Appendix. The first chapter is devoted to an introduction of the Adomian Decomposition method (ADM) with simple illustrations. The Second Chapter is devoted to the application of the ADM to generalized Blasius Equation and our result is compared to other published results when the parameter values are appropriately set. Chapter 3 presents the solution generated for the Falkner-Skan equation. Finally, the Orr-Sommerfeld equation is dealt with in the fourth Chapter. Chapter 5 is devoted to the findings and recommendations based on this study. The Appendix contains details of the solutions considered as well as an alternate solution for the generalized Blasius Equation using Bender's delta-perturbation method.

In this thesis, the perturbation-based decomposition technique developed by Szlavik [1] was used in an attempt to solve the inverse problem in EEG source localization. A set of dipole locations were forward modeled using a 4-layer sphere model of the head at uniformly distributed lead locations to form the vector basis necessary for the method. Both a two-dimensional and a pseudo-three-dimensional versions of the model were assessed with the two-dimensional model yielding decompositions with minimal error and the pseudo-three-dimensional version having unacceptable levels of error. The utility of interpolation as a method to reduce the number of data points to become overdefined was assessed as well. The approach was effective as long as the number of component functions did not exceed the number of data points and stayed relatively small (less than 77 component functions). This application of the method to a spatially variate system indicates its potential for other systems and with some tweaking to the least squares algorithm used, could be applied to multivariate systems.

No / The aim of this paper is to introduce the Systems State Flow Diagram as a structured approach to high level solution-independent function based decomposition of a complex multi-disciplinary system. The approach is discussed in the context of existing function modelling frameworks and in relation to current practice in industry. A generic case study is used to introduce the approach and to highlight the salient features, followed by an illustration on its application to the analysis of an electric vehicle powertrain. Experience with the practical application of the approach with engineering teams is discussed.

<p> A dissolved oxygen model for stratified lakes is developed and is verified for Lake Ontario. The processes affecting the dissolved oxygen budget of a lake including hydraulic inflow and outflow, production and decomposition, atmospheric reaeration, vertical transport across the thermocline, and sediment oxygen demand are analyzed and quantified. The production and decomposition oxygen fluxes are provided by a phosphorus model developed by others. These phosphorus-oxygen inter-relationships are quantified using stoichiometry developed for oceans. Nine years of temperature data for Lake Ontario are used to estimate the annual variations of epilimnetic temperatures, the rate of deepening of the epilimnion (i.e. thermocline depth vs time) and the vertical exchange coefficient. Dissolved oxygen data over a similar period are used to estimate lake-wide concentrations of DO. The vertical exchange and decomposition hypolimnetic oxygen fluxes are estimated from observed data. Model predictions of concentrations and fluxes compare favourably to the observed data. This provides some verification for the predictions of the oxygen model, the oxygen-phosphorus stoichiometry and the decomposition flux predicted by the phosphorus model.</p> / Thesis / Master of Engineering (MEngr)

We study a Ginzburg--Landau model for an inhomogeneous superconductor in the singular limit as the Ginzburg--Landau parameter tends to infinity. The inhomogeneity is represented by a potential term which vanishes when the order parameter equals a given smooth function, the pinning term, which is assumed to become negative in finitely many smooth subdomains, the ''normally included'' regions. For large exterior magnetic field, we study the Gamma-limit of this inhomogeneous Ginzburg-Landau functional. The vanishing of the given smooth function near the inner boundaries imply that the associated operators are strictly but not uniformly elliptic, leading to many questions to be resolved near the boundaries of the normal regions. The method we use is an extension of many techniques including the product estimate from Sandier-Serfaty, Jacobian estimates from Jerrard-Soner and an appropriate Hodge decomposition adapted to our problem. To resolve these problems, we first study the Gamma-limit in the simpler case when the pinning term is varying but bounded below by a positive constant. Second, we consider singular limits of the three-dimensional Ginzburg-Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain is multiply connected and has a small characteristic thickness, and we consider the simultaneous limit as the thickness tends to zero and the Ginzburg-Landau parameter to infinity. We do this when the applied field is strong in its components tangential to the film domain. Finally, we study the Gamma-limit of the inhomogeneous superconducting Ginzburg-Landau model with the pinning term vanishing on the boundary of the normal regions. / Thesis / Doctor of Science (PhD)

The following Thesis is comprised of two separate and individual parts, both of which relate to the disposal of hydrogen sulfide. Section One is an investigation into the possibility of developing a hydrogen sulfide decomposition process which would produce both hydrogen and elemental sulfur. Section Two deals with the speciation study of a catalyst used in a traditional process which converts hydrogen sulfide gas into elemental sulfur. / Section 1: <p> The disposal of hydrogen sulfide by electrolysis to produce both hydrogen and sulfur appears to an interesting alternative to the conventional Claus process which wastes the hydrogen content of hydrogen sulfide. The electrolysis at room temperature has been reported in the literature, however, the investigation was somewhat limited by the low conductivity displayed by the electrolysis solution (pyridine/hydrogen sulfide mixture). </p> <p> The primary goal of this research was to construct a suitable apparatus and carry out a series of conductivity measurements of liquid hydrogen sulfide at room temperature with and without the addition of possible electrolytes. The objective was to determine if an electrolyte could be found that would increase the conductivity to a suitably high level to warrant the further investigation of the electrolysis process. </p> <p> Of the six possible electrolytes, only tetrapropyl ammonium iodide increased the conductivity to a desirable level. A 0.4034 M solution of this alkyl ammonium iodide in liquid hydrogen sulfide increased the conductivity (at 23 C) from 7.00 X 10-8 ohm-1cm-1 for the pure solvent to 1.13 X 10-2 ohm-1cm-1. This increase was attributed to the formation of the corresponding hydrogen sulfide adduct and its subsequent dissociation in liquid hydrogen sulfide. </p> </p> Now that it has clearly been established that appropriately high conducting solutions of hydrogen sulfide can be prepared, the further investigation of the electrolysis of hydrogen sulfide as a viable industrial process is warranted. </p> Section 2: <p> This section deals with the investigation of species present in vanadium(IV): citrate solutions over a wide range of pH values. Various spectroscopic methods (UV/VIS, ESR, vanadium Sl FT-NMR) were used to probe this specific system. The accumulated spectroscopic data were rationalized on the basis of thirteen vanadium(IV) containing species, four of which were proposed to be vanadium(IV): citrate species. Based on the observed spectroscopic data an equilibrium diagram was prepared which illustrates the vanadium(IV) species present as a function of pH. </p> / Thesis / Master of Science (MSc)

<p> This thesis presents an experimental study of the decomposition of the four isomers of butyl acetate over charcoal catalyst in a fixed bed reactor. The research attempts to determine the kinetics and mechanism of butyl acetate decomposition over a high surface area, non-selective catalyst, and to compare the catalyzed reactions of butyl acetates with their gas-phase reactions. When interpreting the experimental kinetic data it is hypothesized that each of the butyl acetates follows the same mechanism when reacting on charcoal. The best theoretical equation for expressing the rate of butyl acetate reaction was selected from the Langmuir-Hinshelwood equations.</p> / Thesis / Doctor of Philosophy (PhD)

This thesis comprises three chapters involving the analysis of the body mass index (BMI) in health economics. The first chapter evaluates two correction models that aim to address measurement error in self-reported (SR) BMI in survey data. This chapter is an addition to the literature as it utilizes two separate Canadian datasets to evaluate the transportability of these correction equations both over time and across different datasets. Our results indicate that the older method remains competitive and that when BMI is used as an independent variable, correction may even be unnecessary. The second chapter measures the relationship between long-term physician costs and BMI. The results show that obesity is associated with higher longterm physician costs only at older ages for males, but at all ages for females. We find that accounting for existing health conditions that are often associated with obesity does not explain the increase in long-term physician costs as BMI increases. This indicates that there is an underlying relationship between the two that we could not account for in our econometric models. Finally, the third chapter decomposes the differences in BMI distributions of Canada and the US. The results show that the differences between BMI levels, both over time and across countries, are increasing with BMI; meaning the highest difference is observed at the right tail of the two distributions. In analysis comparing two points in time, these differences are solely due to differences in the returns from attributes and the omitted variables that we cannot account for in our models. In cross-country analysis, there is evidence that the differences observed below the mean can be explained by the differences in characteristics of the two populations. The differences observed above the mean are again due to those in returns and the omitted variables. / Dissertation / Doctor of Philosophy (PhD)

WHY:”Making is the most powerful way we solve problems, express ideas and shape our world. What and how we make defines who we are, and communicates who we want to be.”-Daniel Charny. My vision of this semesters has been to embrace the joy of making. Since I got a fear inside of my body, that the act of making will be lost in the upcoming working life, in front of a computer. Design is a verb, it is an act of doing, it is making. WHAT:To design a primitive cabin small enough for me to hide from society for short times. The reason of the small scale is the opportunity to decompose every part of the building, every single layer.  The semester has been decided in three part:  1. The act of making: reference project Hermits Cabin (6.2 square meters) by Mats Theselius (warm up phase of model making in the scale 1.10) 2. The act of reflecting : triggerpoints of model making + theory (Gottfried Semper- Bekleiding) 3. The act of designing : result of design in a small scale cabin (Model 1.10 + drawings as representation of the model) HOW:The project has been driven by the principle of dressing. Inspired by the German architect Gottfried Semper´s theory of “bekleidung”. Were he argues for the German word “wand” (wall) as the envelope of space and ”gewand” (garment) as the clothing of the body. Buildings and humans require a similar kind of coating: people are dressed and buildings are cladded to either protect or decorate the bodies. What happens if the design of a small scale cabin is driven by the theory of dressing?

Improved agricultural productivity due to use of fertilizers over the last century has resulted in yield of cash crops, such as corn (Zea mayes L), to be increased on a per hectare basis. Consequently, inadequate fertilizer management such as improper timing or over application has led to infiltration into aquatic environments which can be detrimental to the ecology of such systems. Agricultural systems within the Mississippi River Basin have contributed to large-scale eutrophication in the Gulf of Mexico through surface and dissolved fertilizer loading in upstream tributaries. In response to these concerns, nutrient loss reduction strategies (NLRS), have developed in order to minimize these contributions of eutrophication to aquatic environments. Among adjustments in agricultural practices, one solution is the implementation of cover crops at the end of the cash crop growing season. The primary purpose of cover crops is to increase retention of nutrients during the fall and spring through soil stabilization and nutrient uptake which can prevent erosion and dissolved pathways to fertilizer loading in aquatic environments. Common types of cover crops able to achieve these goals are categorized as winter cereal cover crops (WCCC) and namely, winter cereal rye (Secale cereale) (WCR) is preferred in the state of Illinois. Using WCR has provides addition potential benefits such as cold hardiness establishment, carbon sequestration, weed suppression, and altering hydrological conditions before or during the cash crop. Although there are a variety of benefits from WCR, there are documented tradeoffs due to the presence of WCR, namely, reduced corn yields due to diminished stand population and decreased nitrogen availability through the process of immobilization which results from a carbon to nitrogen ration (C:N) which is greater than 25:1. Our research centered around solutions to maximize benefits of WCR while minimizing negative tradeoffs to the subsequent corn. We hypothesized that reduced seeding rate and higher quality cultivars of WCR would lead to quicker decomposition of biomass (Chapter 1) and would result in corn yields (Chapter 2) that were higher than the alternative treatments of high seeding rates and typical cultivars of WCR. Additionally, we hypothesized that selecting alternative cover crop species such as crimson clover (Trifolium incarnatum), integrating crimson clover with WCR, and reducing seeding rate through precision planting of cover crops off of the corn row would lead to quicker decomposition and result in higher corn yields than the WCR treatment planted normally (Chapter 3). All research was conducted with two site-years for each study. Chapter 1 consisted of two studies (Study A and Study B) where WCR seeding rate was modified and consisted of five treatments of 0, 34, 56, 84, and 112 kg ha-1 of WCR (Study A), and where WCR seeding rate as well as cultivar was modified and consisted of five treatments (Study B). Treatments consisted of an initial no cover crop control and two cultivars, one typical rye considered as “normal” and a hybrid variety (KWS) considered as “hybrid” that were planted at rates of 67 kg ha-1, considered as “low”, and 100 kg ha-1, considered as “high”. The objective of both studies in Chapter 1 was to evaluate the influence of seeding rate (Study A) as well as seeding rate × cultivar had on (i) WCR biomass and nutrient composition, (ii) decomposition and C:N dynamics, and (iii) soil nitrogen dynamics during the growing season in 2021 (Year 1) and 2022 (Year 2). In Study A, it was found that overall biomass was higher as seeding rate increased linearly (R2 = .94) over the two years from 34, 56, 84, to 112 kg ha-1 (2810.43, 3022.14, 3179.89, 3416.52 kg ha-1, respectively). The seeding rate did not influence the rate at which WCR biomass decomposed due to similarities in carbon and nitrogen concentrations within WCR. Fluctuations in C:N ranged from a high of 37:1 at the beginning of the decomposition phase to a minimum of 21:1 by the end of the decomposition phase. Soil NO3-N and NH4-N measured lowest in the 112 kg ha-1 treatment at 15-30 cm in Year 1. Treatments with no cover crop had the highest soil NO3-N from 0-30 cm in Year 2. Overall biomass of WCR was consistently higher during both years in the hybrid WCR treatments at both seeding rates compared to the normal rye of the respective seeding rate. The ratio of carbon to nitrogen was higher in hybrid varieties (42:1) in Year 1 but not in Year 2. The decomposition rate of all WCR in Study B were similar and not influenced by the various treatments. Fluctuations of C:N ranged from a high of 42:1 in the beginning of decomposition to a minimum of 17:1 by the end of the decomposition phase. Estimated N release of all treatments were similar. Both NO3-N and NH4-N were higher in the no cover crop treatment at the end of the season from 0-30 cm during Year 1, while there was no end of year difference in Year 2. In conjunction with the results of Chapter 1, our objectives in Chapter 2 were to see how treatments from Study A and B influenced (i) corn grain yield, (ii) corn stand count, near difference vegetation index (NDVI), leaf area index (LAI), corn N uptake, corn ear composition, as well as end of year N balance, and (iii) to analyze how those components related to overall corn yield. We additionally included how the treatments’ influence on corn could impact soil N dynamics. In Study A, overall corn yield was influenced by WCR seeding rate (p < .05) as the no cover crop and 34 kg ha-1 treatment (11.57, 11.61 Mg ha-1, respectively) were significantly different from the 112 kg ha-1 treatment (10.73 Mg ha-1). Stand count for corn was also influenced by WCR seeding rate (p < .05) as it linearly decreased with increasing seeding rate (R2 = .90) from 70,0009 to 62,552 plants ha-1. The seeding rate influenced the NDVI reading as it was lower in the 84 and 112 kg ha-1 treatments, indicating greater potential soil N immobilization. It was found that yield was most strongly correlated with corn stand count and 1000 kernel weight. In Study B, corn stand count was the only variable influenced by treatment, which was highest in the no cover crop treatment and was lower in the hybrid WCR when compared to the normal WCR at their respective seeding rates. Yield, kernel weight, number, N uptake were all higher in Year 1 and N balance was lower in Year 1. Chapter 3 investigated how cover crop selection, integration, and planting method influenced all of the aforementioned objectives from Chapter 1 and 2. One study made up Chapter 3 (Study C) and consisted of six treatments which were a no cover crop control, WCR monoculture planted at a rate of 67 kg ha-1, crimson clover monoculture planted normally (CNP) at a rate of 28 kg ha-1, crimson clover monoculture precision planted off of the subsequent corn row (CPP) at a rate of 20 kg ha-1, a mixture of the WCR and crimson clover planted normally (RCNP) at a rate of 33 and 22 kg ha-1, respectively, and a mixture of WCR and crimson clover precision planted with crimson clover on the subsequent corn row (RCPP) at a rate of 50 and 7 kg ha-1, respectively. It was observed that overall biomass was driven by presence of WCR but was not significantly different from the mixture treatments in either year. The biomass of crimson clover was not impacted by precision planting, indicating the ability to lower seeding rate. Presence of crimson clover was responsible for the C:N ratio of the treatment as all crimson clover monoculture treatments, aside from Year 1 CNP due to presence of weeds biomass, were lower in C:N (17:1) than all other treatments. Decomposition rate was influenced by cover crop selection as CPP had the highest decay rate of all treatments in both years (-0.00111, -0.00118 in Year 1 and 2, respectively) and RCPP treatment decomposed quicker than WCR in Year 2. The ratio of carbon to nitrogen was lowest for crimson clover monoculture treatments, followed by mixture treatments. By the end of the decomposition phase in Year 1, all treatments had similar C:N ratios indicating biomass decomposition and higher N content in WCR. Year 2 had a lower amount of N concentration in all treatments which influenced C:N ratio of WCR associated treatments. Estimated N release was higher in the mixture treatments as their N content was higher than the WCR monoculture with more biomass than the crimson clover monocultures. Over the two years of the study, crimson clover monoculture treatments resulted in the highest yields (10.16 and 10.11 Mg ha-1 for CNP and CPP, respectively) which were significantly different than the RCPP and WCR treatments, resulting in higher N balances in the RCPP and WCR treatments. Year 2 had lower corn stand count, yield, kernel weight, kernel number, NDVI. Yield was strongly correlated with CSD (.81), diameter (.91) and length (-.91). During both years, soil NO3-N and NH4-N were similar in all treatments by the end of the season indicating uptake by corn. We conclude that in Southern Illinois it may not be fiscally responsible for a grower to use seeding rates over 34 kg ha-1 or hybrid cultivars if their intention is to use WCR as a cover crop before corn in their cropping system. Although the biomass was higher, decomposition was not quicker than lower seeding rate of WCR or typical varieties of WCR. Integrating WCR with crimson clover did not result in lower biomass which may be a practical solution to lowering C:N in the cover crop system, aiding in decomposition so the biomass associated N is able to accessed by corn without being loss to early in the growing season through leaching. Precision planting of cover crops did not impede biomass accumulation which indicates seeding rates and planting design possibilities for WCR, and crimson clover cover cropping systems. Corn stand density was highly impacted by the presence of WCR which indicates the need for adjusting rate and cover crop selection in order to minimize yield reduction in corn.