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Thermonuclear burning of hydrogen on white dwarfs (WDs) is an inevitable occurence for accreting WDs in binary systems. After the onset of thermally-unstable nuclear burning, the WD rapidly expands and ejects much of its hydrogen-rich matter. Once it regains thermal equilibrium, it contracts and becomes a luminous source of supersoft X-rays. This supersoft phase can last anywhere from days (for novae on massive WDs) to millions of years (for persistent supersoft sources). In this dissertation, we explore how the supersoft phase of accreting WDs proceeds and what observations of it reveal about the underlying WD. We present stellar models of persistent supersoft sources and novae. We then use these models to explain the isothermal nature of the ejecta as observed in the radio. We also use these models to test the efficacy of g-modes excited in the burning layer as an explanation of observed oscillations in the supersoft phase of novae. While we find excited modes, their periods are too short to account for the observed oscillations.

The work contained in thesis represents our efforts towards a fundamental understanding of gold in the context of redox cycling. The use of late transition metals in catalysis typically relies on two or more readily accessible oxidation states for bond breaking and bond forming events. However, the heaviest coinage metal does not enjoy such a wealth of reactivity and has been comparatively unexplored.Chapter 1 summarizes the research by our group and others in advancing the concept of redox active gold catalysis. Two strategies that differ on the use sacrificial oxidants to affect catalysis are described, as well as our efforts to improve on the performance of bimetallic gold catalysts through a ligand design approach. A brief survey of fundamental reactivity of Au(I) towards oxidative addition is also presented, to provide context for our studies as described in the subsequent chapters.Chapter 2 describes our studies on the C(sp2)–C(sp2) reductive elimination of biaryls from Au(III). Low temperature NMR studies revealed and characterized an unexpectedly rapid process that is mechanistically distinct from previous studies on C(sp3)–C(sp3) reductive elimination from Au(III). In addition, our preliminary efforts towards the development of a gold-catalyzed biaryl cross-coupling were informed by these studies on reductive elimination.Chapter 3 focuses on our investigations of a photochemical oxidative addition of CF3I to Au(I) complexes. This type of transformation was initially described for the oxidation of phosphine-supported Au(I) alkyl complexes; however the use of phosphine-supported Au(I) aryl complexes allows for the isolation and characterization of organometallic Au(III) complexes containing the –CF3 moiety. These complexes are also capable of C(sp2)–CF3 bond forming reductive elimination upon halide abstraction at low temperature and represent a unique class of compound in this regard.Chapter 4 builds on the results from chapter 3 and focuses on the effects of halide ligands on the C(sp2)–CF3 reductive elimination from Au(III) at elevated temperature. A series of Au(III) complexes containing each member of the halide family (I, Br, Cl, and F) were prepared and the effects of these ancillary ligands on the selectivity of C(sp2)–CF3 vs. C(sp2)–X (X = halide) elimination from Au(III) were characterized. The selectivity can be tuned by choice of halide ligand, and this phenomenon is attributed to increasing Au–X bond strengths which correlate with an increase in selectivity for C(sp2)–CF3 elimination.

Travelling-wave problems, due to their sizeable Kolmogorov n-width, have brought critical challenges to conventional model reduction techniques. This study aims to provide new insights into this problem by exploiting the Radon cumulative distribution transform (R-CDT) [1] emerged in the sector of computer vision science. The core lies in the unique property of the nonlinear in-vertible R-CDT that renders both travelling and scaling components into amplitude modulations. In contrast to the physical space, a substantial model-reduction is achieved in the R-CDT space while sustaining high accuracy. The method is parameter-free and data-driven that lends itself to problems regardless of the dimensions or boundary conditions. Examples start with one-dimensional Burger's equation subject to non-periodic boundary conditions, where both travelling and diffusion dominate the physics. Further in higher-dimensional problems, we show the model reduction of travelling Gaussian solitons. In addition to foreseeable motions, the proposed method is capable of handling random travelling with a non-differentiable trajectory.