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Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
A novel concept for integration of flame-assisted fuel cells (FFC) with a gas turbine is analyzed in this paper. Six different fuels (CH4, C3H8, JP-4, JP-5, JP-10(L), and H2) are investigated for the analytical model of the FFC integrated gas turbine hybrid system. As equivalence ratio increases, the efficiency of the hybrid system increases initially then decreases because the decreasing flow rate of air begins to outweigh the increasing hydrogen concentration. This occurs at an equivalence ratio of 2 for CH4. The thermodynamic cycle is analyzed using a temperature entropy diagram and a pressure volume diagram. These thermodynamic diagrams show as equivalence ratio increases, the power generated by the turbine in the hybrid setup decreases. Thermodynamic analysis was performed to verify that energy is conserved and the total chemical energy going into the system was equal to the heat rejected by the system plus the power generated by the system. Of the six fuels, the hybrid system performs best with H2 as the fuel. The electrical efficiency with H2 is predicted to be 27%, CH4 is 24%, C3H8 is 22%, JP-4 is 21%, JP-5 is 20%, and JP-10(L) is 20%. When H2 fuel is used, the overall integrated system is predicted to be 24.5% more efficient than the standard gas turbine system. The integrated system is predicted to be 23.0% more efficient with CH4, 21.9% more efficient with C3H8, 22.7% more efficient with JP-4, 21.3% more efficient with JP-5, and 20.8% more efficient with JP-10(L). The sensitivity of the model is investigated using various fuel utilizations. When CH4 fuel is used, the integrated system is predicted to be 22.7% more efficient with a fuel utilization efficiency of 90% compared to that of 30%.
ContributorsRupiper, Lauren Nicole (Author) / Milcarek, Ryan (Thesis director) / Wang, Liping (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School for Engineering of Matter,Transport & Enrgy (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
Meteorology is an uncommon term rarely resonating through elementary classrooms. However, it is a concept found in both fourth and sixth grade Arizona science standards. As issues involving the environment are becoming more pertinent, it is important to study and understand atmospheric processes along with fulfilling the standards for each grade level. This thesis project teaches the practical skills of weather map reading and weather forecasting through the creation and execution of an after school lesson with the aide of seven teen assistants.
ContributorsChoulet, Shayna (Author) / Walters, Debra (Thesis director) / Oliver, Jill (Committee member) / Balling, Robert (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Plants are essential to human life. They release oxygen into the atmosphere for us to breathe. They also provide shelter, medicine, clothing, tools, and food. For many people, the food that is on their tables and in their supermarkets isn't given much thought. Where did it come from? What part of the plant is it? How does it relate to others in the plant kingdom? How do other cultures use this plant? The most many of us know about them is that they are at the supermarket when we need them for dinner (Nabhan, 2009) (Vileisis, 2008).
ContributorsBarron, Kara (Author) / Landrum, Leslie (Thesis director) / Swanson, Tod (Committee member) / Pigg, Kathleen (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
DescriptionBased on previous research and findings it is proven that a non-profit class to create awareness will be beneficial in the prevention of eating disorders. This analysis will provide significant research to defend the proposed class.
ContributorsAllen, Brittany (Author) / Chung, Deborah (Author) / Fey, Richard (Thesis director) / Peck, Sidnee (Committee member) / Mazurkiewicz, Milena (Committee member) / Barrett, The Honors College (Contributor) / W. P. Carey School of Business (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Restraint stress is the most commonly used laboratory stressor. It is difficult to characterize as psychological or physical, because past studies show psychological features, but the nature of confinement adds a physical dimension. This was the first study to investigate how experience with restraint stress affects brain response to the next stress without a physical burden. Pair-housed adult male rats were transported to a novel context and restrained or left undisturbed (6hr). The next day, rats were returned to the same context and were either restrained or left undisturbed in the context (n=8/group). After 90min, rats were euthanized to determine functional activation in limbic structures using Fos immunohistochemistry and to measure HPA axis reactivity through blood serum corticosterone levels. Regardless of day 1 experience, context exposure on day 2 enhanced Fos expression in CA1 and CA3 of the hippocampus, basolateral amygdala, and central amygdala. Conversely, other regions and corticosterone levels demonstrated modulation from the previous day's experience. Specifically, rats that were placed back into the restraint context but not restrained on day 2 showed enhanced Fos expression in the dentate gyrus suprapyramidal blade (DGSup), and infralimbic cortex (IL). Also Fos expression was attenuated in rats that received two restraint exposures in the IL and medial amygdala (MEA), suggesting habituation. Only the DG infrapyramidal blade (DGInf) showed enhanced Fos expression to restraint on day 2 without influence of the previous day. While context predominately directed Fos activation, prior experience with restraint influenced Fos expression in the DGSup, IL, MEA and corticosterone levels to support restraint having psychological components.
ContributorsAnouti, P. Danya (Author) / Conrad, D. Cheryl (Thesis director) / Hammer, Ronald (Committee member) / Hoffman, N. Ann (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Production from a high pressure gas well at a high production-rate encounters the risk of operating near the choking condition for a compressible flow in porous media. The unbounded gas pressure gradient near the point of choking, which is located near the wellbore, generates an effective tensile stress on the porous rock frame. This tensile stress almost always exceeds the tensile strength of the rock and it causes a tensile failure of the rock, leading to wellbore instability. In a porous rock, not all pores are choked at the same flow rate, and when just one pore is choked, the flow through the entire porous medium should be considered choked as the gas pressure gradient at the point of choking becomes singular. This thesis investigates the choking condition for compressible gas flow in a single microscopic pore. Quasi-one-dimensional analysis and axisymmetric numerical simulations of compressible gas flow in a pore scale varicose tube with a number of bumps are carried out, and the local Mach number and pressure along the tube are computed for the flow near choking condition. The effects of tube length, inlet-to-outlet pressure ratio, the number of bumps and the amplitude of the bumps on the choking condition are obtained. These critical values provide guidance for avoiding the choking condition in practice.
ContributorsYuan, Jing (Author) / Chen, Kangping (Thesis advisor) / Wang, Liping (Committee member) / Huang, Huei-Ping (Committee member) / Arizona State University (Publisher)
Created2013
Description
Food system and health characteristics were evaluated across the last Waorani hunter-gatherer group in Amazonian Ecuador and a remote neighboring Kichwa indigenous subsistence agriculture community. Hunter-gatherer food systems like the Waorani foragers may not only be nutritionally, but also pharmaceutically beneficial because of high dietary intake of varied plant phytochemical compounds. A modern diet that reduces these dietary plant defense phytochemicals below levels typical in human evolutionary history may leave humans vulnerable to diseases that were controlled through a foraging diet. Few studies consider the health impact of the recent drastic reduction of plant phytochemical content in the modern global food system, which has eliminated essential components of food because they are not considered "nutrients". The antimicrobial and anti-inflammatory nature of the food system may not only regulate infectious pathogens and inflammatory disease, but also support beneficial microbes in human hosts, reducing vulnerability to chronic diseases. Waorani foragers seem immune to certain infections with very low rates of chronic disease. Does returning to certain characteristics of a foraging food system begin to restore the human body microbe balance and inflammatory response to evolutionary norms, and if so, what implication does this have for the treatment of disease? Several years of data on dietary and health differences across the foragers and the farmers was gathered. There were major differences in health outcomes across the board. In the Waorani forager group there were no signs of infection in serious wounds such as 3rd degree burns and spear wounds. The foragers had one-degree lower body temperature than the farmers. The Waorani had an absence of signs of chronic diseases including vision and blood pressure that did not change markedly with age while Kichwa farmers suffered from both chronic diseases and physiological indicators of aging. In the Waorani forager population, there was an absence of many common regional infectious diseases, from helminthes to staphylococcus. Study design helped control for confounders (exercise, environment, genetic factors, non-phytochemical dietary intake). This study provides evidence of the major role total phytochemical dietary intake plays in human health, often not considered by policymakers and nutritional and agricultural scientists.
ContributorsLondon, Douglas (Author) / Tsuda, Takeyuki (Thesis advisor) / Beezhold, Bonnie L (Committee member) / Hruschka, Daniel (Committee member) / Eder, James (Committee member) / Arizona State University (Publisher)
Created2012
Description
Tesla turbo-machinery offers a robust, easily manufactured, extremely versatile prime mover with inherent capabilities making it perhaps the best, if not the only, solution for certain niche applications. The goal of this thesis is not to optimize the performance of the Tesla turbine, but to compare its performance with various working fluids. Theoretical and experimental analyses of a turbine-generator assembly utilizing compressed air, saturated steam and water as the working fluids were performed and are presented in this work. A brief background and explanation of the technology is provided along with potential applications. A theoretical thermodynamic analysis is outlined, resulting in turbine and rotor efficiencies, power outputs and Reynolds numbers calculated for the turbine for various combinations of working fluids and inlet nozzles. The results indicate the turbine is capable of achieving a turbine efficiency of 31.17 ± 3.61% and an estimated rotor efficiency 95 ± 9.32%. These efficiencies are promising considering the numerous losses still present in the current design. Calculation of the Reynolds number provided some capability to determine the flow behavior and how that behavior impacts the performance and efficiency of the Tesla turbine. It was determined that turbulence in the flow is essential to achieving high power outputs and high efficiency. Although the efficiency, after peaking, begins to slightly taper off as the flow becomes increasingly turbulent, the power output maintains a steady linear increase.
ContributorsPeshlakai, Aaron (Author) / Phelan, Patrick (Thesis advisor) / Trimble, Steve (Committee member) / Wang, Liping (Committee member) / Arizona State University (Publisher)
Created2012