In [ASTW] it was given a Gröbner reduction based division formula for entire functions by polynomial ideals. Here we give degree bounds where the input function can be truncated in order to compute approximations of the coeffcients of the power series appearing in the division formula within a given precision. In addition, this method can be applied to the approximation of the value of the remainder function at some point.

In [ASTW] it was given a Gröbner reduction based division formula for entire functions by polynomial ideals. Here we give degree bounds where the input function can be truncated in order to compute approximations of the coeffcients of the power series appearing in the division formula within a given precision. In addition, this method can be applied to the approximation of the value of the remainder function at some point.

In this study, we numerically explore methods of coupling sensitivity analysis to the reduced model in order to increase the accuracy of a proper orthogonal decomposition (POD) basis across a wider range of parameters. Various techniques based on polynomial interpolation and basis alteration are compared. These techniques are performed on a 1-dimensional reaction-diffusion equation and 2-dimensional incompressible Navier-Stokes equations solved using the finite element method (FEM) as the full scale model. The expanded model formed by expanding the POD basis with the orthonormalized basis sensitivity vectors achieves the best mixture of accuracy and computational efficiency among the methods compared. / Master of Science

Controlled and selective electrochemical CO2 reduction to hydrocarbons and oxygenates utilizing energy from renewables such as solar energy is a promising alternative approach to store energy in chemical bonds while simultaneously close the anthropogenic carbon cycle, thus to address the twin problems of fossil fuels depletion and environmental challenges. Copper-based electrocatalysts have been demonstrated promising performance for CO2 reduction. However, Cu usually converts CO2 into a mixture, where more than 16 different species have been identified, and the selective yield of any product is limited by the competing reactions. Other major bottlenecks of Cu electrochemical catalyzed CO2 reduction reaction include the competition of hydrogen evolution reaction (HER), high overpotentials needed towards desired product, and lack of high-value products. In this dissertation, we addressed these three issues via surface modification, sulfurization, and coupling cathodic/anodic reactions, respectively. Specifically, (1) we developed a benzimidazole (BIMH)-modified copper foil catalyst, where the formed Cu(BIM)x complexes on Cu surfaces can enhance the Faradaic efficiency (FE) of C2/C3 products. The overall FE for CO2 reduction reaches 92.1% and the undesired hydrogen evolution reaction (HER) is lowered to 7% at -1.07 VRHE. (2) We demonstrated that Cu2S nanoarrays enable the selective CO2 reduction to formate starting at a very low overpotential (~ 120 mV), with high current density (over -20 mA/cm2 at -0.89 VRHE), and good Faradaic efficiency (>75%) over a broad potential window (-0.7 VRHE to -0.9 VRHE). Further- more, Cu2S catalysts show excellent durability without deactivation following more than 15 cycles (1h per cycle) of operation. The notable reactivity toward CO2 reduction to formate achieved by Cu2S nanoarrays may be ascribed to their ability to facilitate CO2 activation by stabilizing the CO2•− intermediate more effectively than pristine Cu foil. (3) We reported that direct electrochemical conversion of CO2 to 2-bromoethanol, a valuable pharmaceutical intermediate, is enabled by coupling the anodic and cathodic reactions with the presence of potassium bromide electrolyte in a membraneless electrochemical cell. The maximum Faradaic Efficiency of converting CO2 to 2-bromoethanol that we achieved is 40 % at -1.01 VRHE with its partial current density of -19 mA cm-2.

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To combat the escalating environmental challenges and alleviate the current energy crisis, CO2 conversion to fuels and chemical feedstocks provides a reliable approach to mitigate the devastating impact of greenhouse emissions on climate change. CO2 conversion/reduction could be carried out by several methods; however, the electrochemical CO2 reduction (CO2R) approach has coupled several advantages. For instance, CO2R occurs in near-ambient reaction conditions and could be driven through the employment of renewable energy resources (wind or solar) to generate electricity. However, this reaction has a large energy barrier which requires a catalyst to facilitate its pathway. In this context, various catalyst designs were developed and investigated during the last decades, such as heterogenous (metal and metal oxide) and homogenous (organic molecules) catalysts. A new class of materials – atomically dispersed metal nitrogen–doped carbon support (M–N–C)– has emerged recently and showed remarkable enhancement for CO2R compared to the state-of-the-art. In particular, Ni–N–C catalysts have demonstrated an improved selectivity toward CO production compared to precious metal catalysts. Researchers have postulated this superior performance to the high atomic utilization (theoretically 100%) of the metal sites under reaction conditions and the enhanced electronic properties. In addition, intermetallic carbides have been included as a promising class of catalysts for CO2R due to their unique physical and chemical characteristics. These catalysts could be synthesized using different precursors; among them, MOFs are currently one of the most promising platforms that generate several catalyst designs. It was demonstrated that MOF’s unique characteristics, such as high surface area and porosity, would be transitioned to the derived catalysts. In this thesis, two MOF architectures (ZIF-8 and MOF-74) were initially selected to be employed as precursors for deriving atomically dispersed Ni–N–C catalysts. Both MOF-derived catalysts were evaluated for CO2R using a customized electrochemical cell (E-cell) with a 3–electrode configuration. The derived Ni–N–C catalysts using ZIF-8 and MOF-74 have achieved enhanced CO selectivity with Faradaic efficiencies (FE) > 90% at less negative applied potentials, –0.68 and –0.76 V vs RHE, respectively. Further, various synthetic conditions were explored in these studies, such as the role of the Ni content and the pyrolysis temperature on the resulted catalyst structure, and the electrocatalytic performance during CO2 electrolysis. Subsequently, one of the MOF topologies – ZIF-8 – was further utilized to develop other designs of electrocatalysts by introducing different synthetic conditions. This has resulted in generating various moieties that are able to produce CO during CO2R. For example, one derived catalyst design consists of homogenously distributed atomically dispersed dual Ni–Zn–NX/C sites. Whereas the other design demonstrated a heterogenous structure of Ni3ZnC-based particles anchored on atomically dispersed dual Ni–Zn–NX/C sites. Both electrocatalyst designs were integrated into a gas diffusion electrode (GDE) and evaluated for CO2R using an MEA-based electrolyzer. Our findings revealed that the co-existence of Ni3ZnC particles and dual Ni–Zn–NX/C active sites in a heterogenous structure has boosted the electrocatalytic activity towards CO production, achieving near unity CO FE at 448 mA/cm2 at an overall cell voltage of 3.1 V. Aside from the electrocatalytic performance, the nature of active sites in the developed catalyst designs has been studied using in-situ and ex-situ X-ray absorption spectroscopy. Other analytical techniques such as transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), powder X-ray diffraction (PXRD), and X-ray photoelectron spectroscopy (XPS) have also been used to identify the catalysts’ composition and morphology. / Thesis / Doctor of Philosophy (PhD) / This PhD thesis aims to develop and implement a sustainable technology that tackles increased CO2 emissions in the atmosphere and mitigates the greenhouse effect on climate change. The approach of this thesis focuses on developing efficient catalyst designs for CO2 electroreduction (CO2R) to CO as a beneficial chemical feedstock, and then pursues the practical implementation of these catalysts in an industrially relative reactor design in the form of a membrane electrode assembly (MEA)-type electrolyzer. This study selected atomically dispersed metal-doped nitrogen-carbon (M–N–C) and intermetallic carbide electrocatalysts as promising materials for CO2R. Among different precursors, metal-organic frameworks (MOFs) have been employed to synthesize the desired electrocatalysts due to their unique geometric structure and high surface area. On a fundamental level, our findings demonstrated that all MOF-derived catalysts have exhibited high selectivity towards CO during CO2 R. However, the conversion rates were governed by the nature of the active sites and the implemented electrochemical systems.

<p> The kinetics of the hematite to rnagnetite reduction have been studied in H2-H2O, and H2-H2O-N2 gas mixtures, using natural as well as synthetic specimens. The reactivity of hematite was found to be related to the structural defects formed during the preparation of the specimens. The type of defects formed and their effect on reactivity are discussed. Kinetic studies are performed on the specimens with reproducible properties. Rate expressions based upon suitable reaction mechanisms are derived and their validity checked with the experimental data. Reaction rate parameters for the expressions accurately interpreting the experimental results are evaluated, and the effect of nitrogen is separately established. Values of enthalpies and entropies for the mechanistic steps a.re calculated from the temperature dependence of these parameters, which reasonably support the proposed mechanism. </p> / Thesis / Doctor of Philosophy (PhD)

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