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The n-body problem is the study of the motion of n-point masses in space governed by Newton’s equation. The twosingularities where Newton’s equation failed to describe the motions are where the distance between any bodies is at zero (collision) or at infinity. Many researchers studied the first case of singularity. In this dissertation, we studied the second case where the distances among the bodies approach infinity under the collinear setup. We will introduce a geometric object that can help us to understand the behavior not only at infinity but, more importantly, the behavior of the bodies when they are near infinity.

In this dissertation, we discuss two fundamental processes in the inner heliosphere: magnetic reconnection and turbulence. Understanding the two processes is crucial for a more complete description of the solar atmosphere and solar wind. Our studies are confined within magnetohydrodynamic (MHD) and Hall-MHD regimes. We employ methods of linear stability analysis, numerical simulation, as well as satellite data analysis. The main results of our studies are summarized as follows. (1) Through linear stability calculation and linear MHD simulations, we confirm that the inhomogeneous flow inside a reconnecting current sheet stabilizes the tearing instability. The threshold Lundquist number $S_c$ for stabilization is on the order of $10^4$. (2) Through nonlinear Hall-MHD simulations, we show that during the ``recursive'' reconnection process driven by tearing instability, the generation of secondary plasmoids is suppressed as the system scale approaches the ion inertial length. (3) We calculate the linear dispersion relation of the tearing instability under a generalized three-dimensional configuration with Hall effect and guide field. We show that the largest linear growth rate is in general found in parallel modes rather than oblique modes, regardless of the guide field strength. (4) We carry out high-resolution two-dimensional MHD simulations, based on expanding-box-model (EBM), of Alfv\'en waves propagating inside large-scale solar wind streams. We show that the stream structures significantly impact the evolution of Alfv\'enic turbulence properties, such as the cross helicity and residual energy. (5) Through the EBM simulations in combination with a superposed-epoch analysis using OMNI data set, we show that, around heliospheric current sheets (HCSs), the Alfv\'enicity of the solar wind turbulence is destroyed. (6) We analyze Parker Solar Probe (PSP) data of the first four orbits and carry out a statistical study of the turbulence properties in the young solar wind. A radial evolution of various turbulence properties is observed in the data.

Abstract: Interactions mechanisms of deformable air bubbles and liquid droplets play critical roles in many established and modern industrial processes. Understanding the interaction mechanisms of oil droplets and air bubbles is of fundamental and practical importance to solve many challenging issues, especially for oil industries. In this study, a state-of-art droplet probe atomic force microscopy (AFM) coupled with reflection interference contrast microscopy (RICM) was applied, for the first time in the world, to simultaneously quantify interaction forces and the spatiotemporal evolution of the thin water film between air bubbles and solid mica surfaces. The measured force results were analyzed using a theoretical model based on Reynolds lubrication theory and augmented Young-Laplace equation to elucidate the intrinsic interaction mechanisms. Stable films sustained by van der Waals force were always observed between air bubbles and hydrophilic mica surfaces, whereas bubbles were found to readily attach onto hydrophobized mica surfaces. An exponential equation was also developed to quantify the hydrophobic attraction involved in asymmetric systems involving deformable droplets and air bubbles. The validated AFM droplet probe technique and theoretical model were then applied to quantitatively study the interaction mechanisms of (1) oil droplets interacting in aqueous media in the presence or absence of asphaltenes, representing stabilization mechanism of oil-in-water emulsions (2) water droplets interaction in oil media with or without presence of asphaltenes, which represents the stabilization mechanism of water-in-oil emulsion, and (3) oil droplets interacting with solid surfaces in aqueous media, representing the bitumen and oil liberation processes. The force results between oil droplets in water revealed that the interaction between two pristine oil droplets in water could be described by the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Adsorption of asphaltenes at oil/water interface was found to result in more negative surface potential of the oil droplets and also induced steric repulsion, both of which inhibited coalescence of oil droplets and contributed to the stability of O/W emulsion. Lower pH could lead to less negative surface potential, and divalent ions (Ca2+) could disrupt the protection of interfacial asphaltenes and induce oil droplets coalescence. For water droplets in oil, rapid coalescence was observed between bare water droplets, while interfacially adsorbed asphaltenes sterically inhibited droplet coalescence and induced interfacial adhesion. The adhesion increased with asphaltenes concentration but drastically decreased after the concentration exceeded ~ 100 mg/L. The addition of poor solvent (heptane) strengthened the interfacial adhesion at low asphaltenes concentration, while the opposite trend was observed for high asphaltenes concentration. Pure heptane was found to destabilize asphaltenes-coated water droplets. Droplet probe AFM was also applied to directly measure the interaction force between oil droplets (i.e. toluene and heptol) with the addition of asphaltenes and mica surfaces with varying hydrophobicity in aqueous media to understand the wetting mechanisms of the oil/water/solid system. For hydrophilic mica surfaces, asphaltenes adsorbed at oil/water interface strengthened electrical double layer repulsion and induced steric repulsion, stabilizing water films and inhibiting oil droplet attachment on the surfaces. For hydrophobized mica surfaces, the hydrophobic attraction overcame the steric hindrance of interfacial asphaltenes, leading to rapid attachment and strong adhesion of oil droplet on the surfaces. This study provides a novel technique to study the interaction mechanisms of deformable droplets and air bubbles, with the capacity of synchronous measurements of the interaction forces and the drainage dynamics of thin liquid films. Results obtained using this technique for the systems in oil production also provide fundamental insights into the interaction mechanisms of oil and water droplets in complex solution conditions, with valuable implication on the stabilization mechanism of O/W and W/O emulsions and the wetting mechanisms of oil/water/solid systems in presence of asphaltenes.

Slender marine risers used in deepwater applications often experience vortex-induced vibration (VIV). Fatigue damage associated with VIV is of great concern to offshore engineers; however, it has proven difficult to predict this fatigue damage using existing semi-empirical tools. Similarly, approaches based on theoretical and computational fluid dynamics (CFD) generally rely on simplified assumptions on the fluid flow fields and response characteristics. To gain an understanding of VIV and associated fatigue damage, full-scale field monitoring campaigns as well as reduced-scale laboratory experiments are often carried out, wherein the riser response in the form of strains and/or accelerations is recorded using an array of a limited number of sensors distributed over the length of the riser. Simultaneously, current velocities at a proximate location are also recorded. Such measurements generally reveal complex characteristics of the dynamic response of a riser undergoing VIV, including the presence of multiple vibration harmonics, non-stationary behavior, and the existence of sustained or intermittent traveling wave patterns. Such complex features, often not accounted for in some semi-empirical and theoretical approaches, are critical to take into consideration for accurate fatigue damage estimation. In this study, several empirical methods are employed to first reconstruct the response of an instrumented riser and, then, estimate fatigue damage rates over the entire span of the riser based on a limited number of discrete measurements. The methods presented employ the measured data in different ways. One method, referred to as ``weighted waveform analysis'' relies on expressing the riser response as a summation of several weighted waveforms or riser modes; the mode shapes are ``assumed'' and time-varying weights for each mode are estimated directly from the measurements. The riser response over the entire span is reconstructed based on these assumed mode shapes and estimated modal weights. Other methods presented extract discrete mode shapes from the data directly. With the help of interpolation techniques, continuous mode shapes are formed, and the riser response is again reconstructed. Fatigue damage rates estimated based on the reconstructed strains obtained using the various empirical methods are cross-validated by comparing predictions against direct measurements available at the same locations (but not used in the analyses). Results show that the empirical methods developed here may be employed to accurately estimate fatigue damage rates associated with individual recorded segments of measurements. Finally, a procedure for prediction of long-term fatigue damage rates of an instrumented marine riser is presented that relies on combining (multiplying) the fatigue damage rates associated with short recorded segments for specific current profile types, with the relative likelihood of different incident current profiles, and integration over all current profiles. It should be noted that the empirical approaches to fatigue damage estimation presented in this study are based only on measured data; also, they explicitly account for different riser response characteristics and for site-specific current profiles developed from metocean studies. Importantly, too, such estimation procedures can easily accommodate additional data that become available in any ongoing field monitoring campaign to improve and update long-term fatigue damage prediction.

In this study, an attempt was made to understand the type and amounts of metastable intermediates formed when perfluoropropane was placed under electrical stress by adding small amoutns of organic compounds such as thiophene, isopropyl mercaptan, ethyl methyl sulfide, dimethyl disulfide, carbon disulfide, and nitrobenzene. The sulfur compounds were chose because fluorine was reported to react with thiophene to form sulfur hexafluoride. It was thought that if fluorine were formed from perfluorocarbons in the corona, it might be advantageous to remove this metastable species. Nitrobenzene was used because of its known free radical inhibitor characteristic in polymerization reactions. The hope was that these additive compounds might be effective in reducing corona or inhibiting breakdown by removing metastable intermediates formed in the gas by the electrical stress. It was also hoped that the study of the decomposition products and the nature of effectiveness of the additives might provide an insight into the relationship of chemical structure and dielectric strength. Evidence was obtained that the stable decomposition products of perfluoropropane after exposure to electrical stress do not in themselves begin to tell the story of the chemical changes taking place during the exposure process.