Coastal regions are the most densely populated regions of the world. The populations of these regions continue to grow which has created a high demand for water that stresses existing water resources. Coastal aquifers provide a source of water for coastal populations and are generally part of a larger system where freshwater aquifers are hydraulically connected with a saline surface-water body. They are characterized by salinity variations in space and time, sharp freshwater/saltwater interfaces which can lead to dramatic density differences, and complex groundwater chemistry. Mismanagement of coastal aquifers can lead to saltwater intrusion, the displacement of fresh water by saline water in the freshwater regions of the aquifers, making them unusable as a freshwater source. Saltwater intrusion is of significant interest to water resource managers and efficient simulators are needed to assist them. Numerical simulation of saltwater intrusion requires solving a system of flow and transport equations coupled through a density equation of state. The scale of the problem domain, irregular geometry and heterogeneity can require significant computational resources. Also, modeling sharp transition zones and accurate flow velocities pose numerical challenges. Discontinuous Galerkin (DG) finite element methods (FEM) have been shown to be well suited for modeling flow and transport in porous media but a fully coupled DG formulation has not been applied to the variable density flow and transport model. DG methods have many desirable characteristics in the areas of numerical stability, mesh and polynomial approximation adaptivity and the use of non-conforming meshes. These properties are especially desirable when working with complex geometries over large scales and when coupling multi-physics models (e.g. surface water and groundwater flow models). In this dissertation, we investigate a new combined local discontinuous Galerkin (LDG) and non-symmetric, interior penalty Galerkin (NIPG) formulation for the non-linear coupled flow and solute transport equations that model saltwater intrusion. Our main goal is the formulation and numerical implementation of a robust, efficient, tightly-coupled combined LDG/NIPG formulation within the Department of Defense (DoD) Proteus Computational Mechanics Toolkit modeling framework. We conduct an extensive and systematic code and model verification (using established benchmark problems and proven convergence rates) and model validation (using experimental data) to verify accomplishment of this goal. Lastly, we analyze the accuracy and conservation properties of the numerical model. More specifically, we derive an a priori error estimate for the coupled system and conduct a flow/transport model compatibility analysis to prove conservation properties. / text

Hydroxyapatite (HA, Ca₁₀(PO₄)₆(OH)₂) is one of the most abundant materials in mammal bone. It crystallizes in an aqueous environment within spaces between tropocollagen protein chains. However, despite its abundance and possible usefulness in the medical field this complex physical system remains poorly understood to date. We present a theoretical study of the energetics of hydroxyapatite, its electronic, mechanical and thermodynamic properties. Our mechanical and thermodynamic properties from first principles are in excellent agreement with the rare available experimental data. The monoclinic and hexagonal phases are lowest in energy. A comparison of the phonon dispersions of these two phases reveals that a phase transition occurs due to a difference in vibrational free energy. The transition is of order-disorder type. Our calculated phase transition temperature is 680 K, in decent agreement with the experimentally determined 470 K. An alternative theoretical model yields 882 K. The phase transition is mediated by OH libration modes. We also report for the first time on a peculiarity in the phonon spectrum of hexagonal and monoclinic HA. When studying the Lyddane-Sachs-Teller shifts in the spectrum close to the [Gamma]-point we identify two vibration modes showing a systematically increasing Lyddane-Sachs-Teller shift in frequency with decreasing dielectric constant. In experiment, the dielectric constant varies between 5 and 20 depending on the Ca/P ratio in the sample. The frequency shifts in the affected modes are as large as 20 cm⁻¹ as one spans the range of the dielectric constant. Thus, a simple spectroscopic analysis of a sample of bone may determine the quality of the sample in a physiological sense. We also identify the chemically stable low energy surface configurations as function of the OH, PO₄ and Ca concentration. In the experimentally relevant OH-rich regime we find only two surfaces competing for lowest energy. The surface most stable over almost the entire OH-rich regime is OH-terminated, and is currently being investigated in the presence of water and atomic substitutions on the HA surface. / text

Profiles for electron density and temperature were determined in a self-consistent way using line emission spectroscopy and collisional radiative models for neutral and singly ionized Argon (Ar I and Ar II) in the Texas Helimak. Neutral Argon density profiles were calculated using a kinetic gas model. Electron-impact excitation and Ionization rates were corrected to account for the electron velocity distribution deviating slightly from a true Maxwellian distribution due to inelastic electron-neutral collisions. Results show an electron temperature which roughly agrees with probe diagnostics. This method gives an electron density that is about twice as high, which may be possible from a power balance perspective. / text

The current generation of climate models in the Coupled Model Intercomparison Project Phase 5 (CMIP5) is used to assess the future changes in daily precipitation and its extremes. The simple average of all the models, i.e. the multi-model ensemble mean (MMEM), has been widely used due to its simplicity and better performance than most individual models. Weighting techniques are also proposed to deal with the systematic biases within the models. However, both methods are designed to reduce the uncertainties for the study of climate mean state. They will induce problems when the climate extremes are of interest. We utilize a Bayesian weighting method to investigate the rainfall mean state and perform a probability density function based assessment of daily rainfall extremes. Satellite measurement is used to evaluate the short historical period. The weighting method can be only applied to regions rather than hemispheric scale, and thus three tropical regions including the Amazon, Congo, and Southeast Asia are studied. The method based on the Gamma distribution for daily precipitation is demonstrated to perform much better than the MMEM with respect to the extreme events. A use of the Kolmogorov-Smirnov statistic for the distribution assessment indicates the method is more applicable in three tropical wet regions over land mentioned above. This is consistent with previous studies showing the Gamma distribution is more suitable for daily rainfall in wet regions. Both methods provide consistent results. The three regions display significant changes at the end of the 21st century. The Amazon will be drier, while the Congo will not have large changes in mean rainfall. However, both of the Amazon and Congo will have large rainfall variability, implying more droughts and floods. The Amazon will have 7.5% more little-rain days (defined as > 0.5 mm/d) and 4.5 mm/d larger 95th percentile for 2092-2099, and the Congo will have 2.5% more little-rain days and 1 mm/d larger 95th percentile. Southeast Asia will be dryer in the western part and wetter in the eastern part, which is consistent with the different changes in the 5th percentile. It will also experience heavier rainfall events with much larger increases in the 95th percentile. The future changes, especially the increase in rainfall extremes, are very likely associated with the strengthening of hydrological cycle. / text

published_or_final_version / Physics / Master / Master of Philosophy

Silicon (Si)-based materials have recently emerged as a promising candidate for anodes in lithium-ion batteries because they exhibit much higher energy-storage capacities than the conventional graphite anode. However, the practical use of Si is hampered by its poor cycleability; during lithiation, Si forms alloys with Li and undergoes significant structural and volume changes, which can cause severe cracking/pulverization and consequent capacity fading arising from the loss of electrical contacts. To overcome these drawbacks, many innovative approaches have been explored with encouraging results; however, many fundamental aspects of the lithiation behavior remain ambiguous. Hence, the focus of this work is to develop a better understanding of the lithiation process at the atomistic scale using quantum mechanical calculations. In addition, based on the improved understanding, we attempt to address the fundamental mechanisms behind the successful approaches to enhance the anode performance. To lay a foundation for the investigation of alloy-type anodes, in Chapter 3, we first examine how lithiation occurs in Si and the formation of crystalline and amorphous LixSi alloys (0 ≤ x ≤ 4); followed by assessing the lithiation-induced changes in the energetics, atomic structure, electronic and mechanical properties, and Li diffusivity. The same approach is then extended to analyze the lithiation behavior of germanium (Ge) and tin (Sn) for developing a generalized understanding on the Group IV alloy-type anodes. Along this comparative study, we notice a few distinguishing features pertain only to Si (or Ge), such as the facile Li diffusion in Ge and facet-dependent lithiation in Si, which are discussed in Chapter 4. Beyond the fundamental research, we also look into factors that may contribute to the improved anode performance, including (i) finetuning of the oxidation effects in Si-rich oxides, [alpha] -SiO [subscript 1/3] (Chapter 5), (ii) maximizing the surface effects through nano-engineered structures (Chapters 6 & 7), and finally (iii) the role of interface in Si-graphene (carbon) composites (Chapter 8).

A rejection algorithm, called ``transformed density rejection", is presented. It uses a new method for constructing simple hat functions for a unimodal density $f$. It is based on the idea of transforming $f$ with a suitable transformation $T$ such that $T(f(x))$ is concave. The hat function is then constructed by taking the pointwise minimum of tangents which are transformed back to the original scale. The resulting algorithm works very well for a large class of distributions and is fast. The method is also extended to the two- and multidimensional case. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

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In electronic structure calculations the computational cost is of great importance because large systems can contain a huge number of electrons. One effective method to make such calculations is by density matrix purification. Although, the cost for this method is relatively low compared to other existing methods there is room for improvements. In this paper one method proposed by Emanuel Rubensson and one method proposed by Jaehoon Kim & Yousung Jung was compared to each other with respect to efficiency, simplicity and robustness. Both are improved methods to compute the density matrix by accelerated polynomial expansion. Rubensson’s method consists of two different algorithms and results showed that both performed better than Kim & Jung’s method in terms of efficiency, which is the property both methods directs their main focus on. The major differences between them was identified in terms of adaptivity. The methods require different inputs that demands separate levels of knowledge about the system. Kim & Jung’s method which require less knowledge can however benefit efficiency-wise from more information in order to optimize the algorithm for the system. Results also showed that both methods were stable, but since they only were tested with arbitrarily assumed input arguments no conclusion about their general stability could be drawn.