Herein are described some model problems, means of solution, and some properties of solutions for the equilibrium of self-gravitating isothermal gases in interstellar configurations, with magnetic field. The approach is from the viewpoint of the calculus of variations, with flux-freezing being modelled as well as flux loss through partial ionization. In this work such a treatment is presented for the first time, incorporating aspects of the physical problem as previously studied by authors Woltjer, Mouschovias, and others, and presenting a new application of recently developed variational methods, extending their previous applications from fluid dynamics and terrestrial plasma problems to the present situation. In this approach the problem is formulated and solved as a non-linear, free-boundary problem in variational form with linear and non-linear constraints. The full extent of the matter is considered, from model construction, through construction of solutions to dimensionless PDE, to interpretation of results and their physical and mathematical meaning. Computational methods for calculating the physical and mathematical meaning. Computational methods for calculating the solutions are applied. The construction and justification of this solution method forms the basis for a constructive proof of the existence of solutions. A foundation is prepared for complete analytical investigations of the model or prototype problem, as well as for computational investigation of important realistic physical situations.

Electrical discharge is a commonly used method to produce ions and radicals that can be used for degrading compounds as well as for chemical synthesis. Previously, the application of electrical discharges has been studied in liquids such as water and alcohols to produce hydrogen peroxide and hydrogen and to destroy organic compounds in the water and gas phases. Recently low power gas-liquid electric discharges have been employed to increase efficiency for hydrogen peroxide and oxidized products for synthesis or degradation. Determination and analysis of the intermediate radicals produced in the plasma has not been studied intensively for discharges at the gas-liquid interface such as aerosol sprays and thin liquid films. According to theoretical models based on reaction kinetics in plasma these radicals such as hydroxyl radicals play an important role in formation of hydrogen peroxide. However, there may be excess hydroxyl radicals formed and not involved in the formation of hydrogen peroxide. The main goal of this work is to characterize and identify key intermediate radicals and their reaction pathways in the liquid phase, gas phase, and at the interface of these aerosol droplets and thin film surfaces using various gases and liquid feeds. / A Dissertation submitted to the Department of Chemical and Biomedical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2015. / March 17, 2015. / advanced oxidation processes, electrical discharge, Fenton reaction, hydrogen peroxide, hydroxyl radical, plasma / Includes bibliographical references. / Bruce R. Locke, Professor Directing Dissertation; Igor Alabugin, University Representative; Ravindran Chella, Committee Member; Rufina Alamo, Committee Member.

1a. Two model porous media and a precise drying protocol are employed in numerical simulation of fluid configurations in partially saturated porous media. Over a substantial range of partial saturation $N\sb{L},$ the liquid-vapor configurations are inhomogeneous on a length scale that is a sensitive function of $N\sb{L}.$ Several measures of the characteristics of fluid configurations are developed. Details of the fluid configurations are found in the study of $p(x;\ell,N\sb{L}),$ the probability density for a porous medium of partial saturation $N\sb{L}$ to contain a piece of material of size $\ell\sp{d}$ having partial saturation x. This probability density is a gauge of inhomogeneity and appears importantly in NMR studies of porous media. 1b. The equations governing magnetization evolution in fluid filled pore systems are developed. In pore systems with a range of pore sizes (and/or decay rates) the magnetization evolution is described exactly by a spectrum of decay rates, leading to multiple exponential decay. We study this spectrum of decay rates as a function of coupling strength between pores using perturbation theory, effective medium theory, and matrix diagonalization. The spectrum of decay rates evolves from the individual pore decay rate distribution, at zero coupling, to a delta function distribution, at infinite coupling. The effect of coupling between pores is important in NMR studies of temperature dependence of characteristic decay rates in porous media. 2. The equation of motion describing a borehole elastic system (BES) is studied in the form of a perturbation problem, i.e. as the sum of terms describing a model elastic system (MES) and terms describing the departure of the BES being studied from the MES. The MES is chosen such that the departure terms in the BES equation of motion are small. The Green tensor for an infinite, azimuthally symmetric borehole is developed. As an illustration of the perturbation technique, the consequences of a mudcake layer on the borehole wall are explored. Comparison of first order perturbation calculations confirms the perturbation method is a valid technique for probing small changes to a model elastic system.

The central purpose of this thesis is to explore the behavior of the numerical solution of the Cold- Ion model with shock forming conditions in one and two dimensions. In the one dimensional case, a comparison between the numerical solution of the Vlasov equation is made. It is observed that the Cold-Ion model is no longer representative of the cold-ion limit of the Vlasov-Poisson equation when a spike forms in the solution. It was found that the lack of a spike in the solution of the Cold-Ion model does not necessarily mean that a bifurcation has not formed in the solution of the Vlasov-Poisson equation. It was also determined that the spike present in the solution of the one dimensional problem appears again in the two dimensional simulation. The findings presented in this thesis opens up the question of determining which initial and boundary conditions of the Cold-Ion model causes a shock to form in the solution. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2014. / October 15, 2014. / Cold-Ion, Plasma, Shocks, Vlasov-Poisson / Includes bibliographical references. / Max Gunzburger, Professor Directing Thesis; Janet Peterson, Committee Member; Sachin Shanbhag, Committee Member.

A dynamic momentum compaction factor, also referred to as a dynamic $\Delta\gamma\sb{t}$, lattice for the FNAL Antiproton Source Debuncher Storage Ring is studied, both theoretically and experimentally, for the purpose of improving stochastic precooling, and hence, improving the global antiproton production and stacking performance. A dynamic $\Delta\gamma\sb{t}$ lattice is proposed due to the competing requirements inherent within the Debuncher storage ring upon $\gamma\sb{t}$. Specifically, the Debuncher storage ring performs two disparate functions, (i) accepting and debunching a large number of ps/pulse at the outset of the production cycle, which would perform ideally with a large value of $\gamma\sb{t}$, and (ii) subsequently employing stochastic cooling throughout the remainder of the p production cycle for improved transfer and stacking efficiency into the Accumulator, for which a small value $\gamma\sb{t}$ is ideal in order to reduce the diffusive heating caused by the mixing factor. In the initial design of the Debuncher optical lattice, an intermediate value of $\gamma\sb{t}$ was chosen as a compromise between the two functional requirements. The goal of the thesis is to improve stochastic precooling by changing $\gamma\sb{t}$ between two desired values during each p production cycle. In particular, the dynamic $\Delta\gamma\sb{t}$ lattice accomplishes a reduction in $\gamma\sb{t}$, and hence the mixing factor, through an uniform increase to the dispersion throughout the arc sections of the storage ring. Experimental measurements of cooling rates and system performance parameters, with the implementation of the dynamic $\Delta\gamma\sb{t}$ lattice, are in agreement with theoretical predictions based upon a detailed integration of the stochastic cooling Fokker Planck equations. Based upon the consistency between theory and experiment, predictions of cooling rates are presented for future operational parameters of the Antiproton Source with the dynamic $\Delta\gamma\sb{t}$.

The first large-scale study of magnetically-confined plasma for the production of fusion energy is scheduled to begin this decade and will answer many questions. Two critical issues are: (1) how to control and prevent non-axisymmetric magnetic perturbations that may drive harmful current and plasma energy into the surrounding walls, and (2) how to understand the relationship between plasma rotation, plasma confinement, and plasma stability. To address both, this dissertation reports research with biasable electrode arrays in the HBT-EP tokamak. This work conducts systematic studies of driven current and achieves the first active control of plasma rotation and rotating magnetic instabilities with a toroidal electrode array. Electrode-driven current impacts the plasma in several ways. First, it can increase, decrease, and reverse plasma rotation as measured by Mach probes, which results in an altered radial electric field. By controlling the electrode voltage with an active feedback system, plasma rotation is controlled between 4 and 8 kHz. Second, by modulating the driven electrode current at fixed frequencies, spontaneous magnetic perturbations develop at the plasma’s edge. These distortions are field aligned, do not rotate, and match the magnetic helicity of the scrape-off-layer (SOL). Direct measurement of SOL current to collectors mounted on the wall, show that the SOL current is field-aligned with a filamentary structure. When a naturally-occurring rotating m=2 mode is present, magnetic measurements show that the two structures are superimposed with no obvious indication of coupling. Third, when the electrode current is driven at the natural frequency of rotating magnetic perturbations, the plasma’s proportional response increases, indicating a resonance at 9 kHz. Resonance is observed in the radial electric field, floating potential profile, plasma rotation, and magnetic measurements. Finally, when the electrode array is biased in quadrature and actively controlled, driven currents modify the rotation and amplitude of the long-wavelength rotating magnetic modes. When the quadrature electrode array is phase locked to the n=1 mode rotation, mode amplitudes are suppressed by as much as 50%. Suppression shows a clear dependence on a phase between the rotating mode and the driven current. These experiments show that the structure of SOL currents are field-aligned and demonstrate a clear relationship between biased-electrode driven current and the rotation and amplitude of helical magnetic perturbations.

Global concerns of climate change, increased greenhouse gas emissions and security of energy supply have accelerated the search for alternative energy sources both indeveloped and developing countries. Developing countries are now embracingutilization of biogas as a renewable energy option to meet some of their cooking andlighting needs. In Uganda, despite the introduction of biogas in the 1950’s, thetechnology has not received considerable acceptance and as a result its penetrationhas remained relatively low.  Several installed biogas plants have failed and those working are not working to theexpectation of the technicians and their owners. This research presents results of thestudy carried out to establish the performance of farm based biogas systems so as toassess the challenges faced by the users and to identify the possible causes of failurefor the non-operational systems.  A survey of 144 biogas plants was carried out after which performance monitoring ofselected digesters in the districts of Luwero, Kampala, Wakiso, Mbale, Jinja andMukono. It was found that 55% of the surveyed  biogas  plants  were  not  operational and  others  not  performing  to  the  users expectations. Most of the plants monitoredwere operating in the temperature range of 18°C-25°C with the gas quality rangingbetween 50-60% methane. Most digesters showed evidence of high organic loadingrates indicated by traces of biogas at the expansion chamber. The identified  causes of  failure  were  poor  system  maintenance, poor workmanship during constructionworks, poor  operation  practices, availability of other cheap fuel alternatives, lazinessand lack of interest amongst  the users, lack of alternative sources of feedstock andsystem blockages. Furthermore, there is need to sensitize people on the need for using alternativesources of energy such as biogas and improved cooking stoves for fuel saving as mostof them use wood and charcoal as supplementary fuels. This would reduce globalwarming through reduced deforestation and bring about environmental sustainabilityas a whole.

The objective of this thesis was the design of a regeneratively cooled, high temperature, clean gas plasma generator facility. This facility was desired to extend the high temperature research capabilities of the Department of Mechanical Engineering.

The Comparison of Climate Change Rates in Rural versus Urban Areas in Tennessee An analysis of climate data was performed in three counties in Tennessee. The goal of this study is to identify the different rates of climate change in counties of varying urbanization levels. Davidson County, which contains the city of Nashville, is used as the most urban county. Two counties outside Nashville, Sumner and Dickson Counties, are used as a moderately urban county and a rural county, respectively. The level of urbanization was adopted from Tennessee Advisory Commission on Intergovernmental Relations' Index of Relative Rurality. Yearly average temperature and daily mean temperature for the warm season (May through October) were collected on each county from the years of 1960-2020 via the PRISM Climate Group at Oregon State University. A Mann-Kendall (MK) trend test was used for each individual county’s data to determine if the series had a monotonic upward trend, meaning overall temperature increase. The hypothesis of this analysis is that the most urban county will have the highest rate of warming due to the urban heat island (UHI) effect. The analysis of the yearly average temperature data for the three counties showed that Davidson and Sumner had higher Sen’s slopes and Kendall’s Taus, which were the prominent factors examined to determine the extent of climate change. Comparatively, Dickson County was found to have a lower Sen’s slope and Kendall’s Tau, which implies a lower overall rate of warming. Significance was found within all the results, since P-values were α Laina Caywood: Environmental Health, East Tennessee State University. Ying Li: Environmental Health, East Tennessee State University. Andrew Joyner: Department of Geosciences, East Tennessee State University.

Fossil resources provide the raw materials for manufacturing a majority of commodity chemicals and fuels, but the release of this buried carbon accelerates environmental crises related to rising levels of atmospheric CO2. Engineering direct and energy-efficient pathways to synthesize chemicals and fuels from sustainable reagents and using CO2-free renewable energy could mitigate these challenges. Promising strategies for developing such reaction processes utilize non-precious metal catalysts to address kinetic challenges and non-thermal plasma activation to circumvent thermodynamic constraints. Non-precious bimetallic catalysts were employed to selectively convert CO2 with H2 to the building block chemical CO, and in situ X-ray and infrared techniques revealed the properties of the catalytic components. Significant oxygen exchange between the ceria catalyst support material and gas-phase CO2 was quantified under reaction conditions, and NiFe bimetallic catalysts tuned the reaction selectivity while maintaining high activity. In order to eliminate H2 as a reagent, ethane (an underutilized shale gas fraction) was reacted with CO2 to produce alcohols. This reaction is not thermodynamically feasible under mild conditions, so non-thermal/non-equilibrium plasma activation was implemented in order to achieve a one-step, H2-independent process to synthesize alcohols and other oxygenates under ambient temperature and pressure. The ability to use non-thermal plasma to activate N2 at mild conditions introduces the possibility of moving beyond the carbon-based paradigm for chemicals and fuels. Non-thermal plasma has been used to synthesize ammonia under mild conditions, but the dearth of fundamental understanding of plasma-catalyst interactions handicaps the development of plasma catalytic N2 conversion processes. Therefore, an in situ FTIR reactor was employed to identify the surface reaction intermediates during plasma catalytic ammonia synthesis. These results provide the first direct evidence of catalytic surface reactions under plasma activation and reveal the presence of reaction pathways that are distinct from analogous thermocatalytic reactions. Finally, an energy-based analysis evaluates the environmental and economic outlook for plasma-activated nitrogen fixation processes.