Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

Wastewater Electrolysis Cell for Environmental Pollutants Degradation and Molecular Hydrogen Generation

This study proposes a wastewater electrolysis cell (WEC) for on-site treatment of human waste coupled with decentralized molecular H₂ production. The core of the WEC includes mixed metal oxides anodes functionalized with bismuth doped TiO₂ (BiO_x/TiO₂). The BiO_x/TiO₂ anode shows reliable electro-catalytic activity to oxidize Cl- to reactive chlorine species (RCS), which degrades environmental pollutants including chemical oxygen demand (COD), protein, NH4⁺, urea, and total coliforms. The WEC experiments for treatment of various kinds of synthetic and real wastewater demonstrate sufficient water quality of effluent for reuse for toilet flushing and environmental purposes. Cathodic reduction of water and proton on stainless steel cathodes produced molecular H2 with moderate levels of current and energy efficiency. This thesis presents a comprehensive environmental analysis together with kinetic models to provide an in-depth understanding of reaction pathways mediated by the RCS and the effects of key operating parameters. The latter part of this thesis is dedicated to bilayer hetero-junction anodes which show enhanced generation efficiency of RCS and long-term stability.

Chapter 2 describes the reaction pathway and kinetics of urea degradation mediated by electrochemically generated RCS. The urea oxidation involves chloramines and chlorinated urea as reaction intermediates, for which the mass/charge balance analysis reveals that N₂ and CO₂ are the primary products. Chapter 3 investigates direct-current and photovoltaic powered WEC for domestic wastewater treatment, while Chapter 4 demonstrates the feasibility of the WEC to treat model septic tank effluents. The results in Chapter 2 and 3 corroborate the active roles of chlorine radicals (Cl•/Cl₂^-•) based on iR-compensated anodic potential (thermodynamic basis) and enhanced pseudo-first-order rate constants (kinetic basis). The effects of operating parameters (anodic potential and [Cl^-] in Chapter 3; influent dilution and anaerobic pretreatment in Chapter 4) on the rate and current/energy efficiency of pollutants degradation and H₂ production are thoroughly discussed based on robust kinetic models. Chapter 5 reports the generation of RCS on Ir_0.7Ta_0.3O_y/Bi_xTi_1-xO_z hetero-junction anodes with enhanced rate, current efficiency, and long-term stability compared to the Ir_0.7Ta_0.3O_y anode. The effects of surficial Bi concentration are interrogated, focusing on relative distributions between surface-bound hydroxyl radical and higher oxide.

Physical, Metabolic, and Energetic Investigations of Methane-Metabolizing Microbial Communities

Understanding the roles of microorganisms in environmental settings by linking phylogenetic identity to metabolic function is a key challenge in delineating their broad-scale impact and functional diversity throughout the biosphere. This work addresses and extends such questions in the context of marine methane seeps, which represent globally relevant conduits for an important greenhouse gas. Through the application and development of a range of culture-independent tools, novel habitats for methanotrophic microbial communities were identified, established settings were characterized in new ways, and potential past conditions amenable to methane-based metabolism were proposed. Biomass abundance and metabolic activity measures – both catabolic and anabolic – demonstrated that authigenic carbonates associated with seep environments retain methanotrophic activity, not only within high-flow seep settings but also in adjacent locations exhibiting no visual evidence of chemosynthetic communities. Across this newly extended habitat, microbial diversity surveys revealed archaeal assemblages that were shaped primarily by seepage activity level and bacterial assemblages influenced more substantially by physical substrate type. In order to reliably measure methane consumption rates in these and other methanotrophic settings, a novel method was developed that traces deuterium atoms from the methane substrate into aqueous medium and uses empirically established scaling factors linked to radiotracer rate techniques to arrive at absolute methane consumption values. Stable isotope probing metaproteomic investigations exposed an array of functional diversity both within and beyond methane oxidation- and sulfate reduction-linked metabolisms, identifying components of each proposed enzyme in both pathways. A core set of commonly occurring unannotated protein products was identified as promising targets for future biochemical investigation. Physicochemical and energetic principles governing anaerobic methane oxidation were incorporated into a reaction transport model that was applied to putative settings on ancient Mars. Many conditions enabled exergonic model reactions, marking the metabolism and its attendant biomarkers as potentially promising targets for future astrobiological investigations. This set of inter-related investigations targeting methane metabolism extends the known and potential habitat of methanotrophic microbial communities and provides a more detailed understanding of their activity and functional diversity.