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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
Does school participatory budgeting (SPB) increase students’ political efficacy? SPB, which is implemented in thousands of schools around the world, is a democratic process of deliberation and decision-making in which students determine how to spend a portion of the school’s budget. We examined the impact of SPB on political efficacy in one middle school in Arizona. Our participants’ (n = 28) responses on survey items designed to measure self-perceived growth in political efficacy indicated a large effect size (Cohen’s d = 1.46), suggesting that SPB is an effective approach to civic pedagogy, with promising prospects for developing students’ political efficacy.
ContributorsGibbs, Norman P. (Author) / Bartlett, Tara Lynn (Author) / Schugurensky, Daniel, 1958- (Author)
Created2021-05-01
Description
This thesis focuses on the theoretical work done to determine thermodynamic properties of a chalcopyrite thin-film material for use as a photovoltaic material in a tandem device. The material of main focus here is ZnGeAs2, which was chosen for the relative abundance of constituents, favorable photovoltaic properties, and good lattice matching with ZnSnP2, the other component in this tandem device. This work is divided into two main chapters, which will cover: calculations and method to determine the formation energy and abundance of native point defects, and a model to calculate the vapor pressure over a ternary material from first-principles. The purpose of this work is to guide experimental work being done in tandem to synthesize ZnGeAs2 in thin-film form with high enough quality such that it can be used as a photovoltaic. Since properties of photovoltaic depend greatly on defect concentrations and film quality, a theoretical understanding of how laboratory conditions affect these properties is very valuable. The work done here is from first-principles and utilizes density functional theory using the local density approximation. Results from the native point defect study show that the zinc vacancy (VZn) and the germanium antisite (GeZn) are the more prominent defects; which most likely produce non-stoichiometric films. The vapor pressure model for a ternary system is validated using known vapor pressure for monatomic and binary test systems. With a valid ternary system vapor pressure model, results show there is a kinetic barrier to decomposition for ZnGeAs2.
ContributorsTucker, Jon R (Author) / Van Schilfgaarde, Mark (Thesis advisor) / Newman, Nathan (Committee member) / Adams, James (Committee member) / Arizona State University (Publisher)
Created2011
Description
Electromigration in metal interconnects is the most pernicious failure mechanism in semiconductor integrated circuits (ICs). Early electromigration investigations were primarily focused on aluminum interconnects for silicon-based ICs. An alternative metallization compatible with gallium arsenide (GaAs) was required in the development of high-powered radio frequency (RF) compound semiconductor devices operating at higher current densities and elevated temperatures. Gold-based metallization was implemented on GaAs devices because it uniquely forms a very low resistance ohmic contact and gold interconnects have superior electrical and thermal conductivity properties. Gold (Au) was also believed to have improved resistance to electromigration due to its higher melting temperature, yet electromigration reliability data on passivated Au interconnects is scarce and inadequate in the literature. Therefore, the objective of this research was to characterize the electromigration lifetimes of passivated Au interconnects under precisely controlled stress conditions with statistically relevant quantities to obtain accurate model parameters essential for extrapolation to normal operational conditions. This research objective was accomplished through measurement of electromigration lifetimes of large quantities of passivated electroplated Au interconnects utilizing high-resolution in-situ resistance monitoring equipment. Application of moderate accelerated stress conditions with a current density limited to 2 MA/cm2 and oven temperatures in the range of 300°C to 375°C avoided electrical overstress and severe Joule-heated temperature gradients. Temperature coefficients of resistance (TCRs) were measured to determine accurate Joule-heated Au interconnect film temperatures. A failure criterion of 50% resistance degradation was selected to prevent thermal runaway and catastrophic metal ruptures that are problematic of open circuit failure tests. Test structure design was optimized to reduce resistance variation and facilitate failure analysis. Characterization of the Au microstructure yielded a median grain size of 0.91 ìm. All Au lifetime distributions followed log-normal distributions and Black's model was found to be applicable. An activation energy of 0.80 ± 0.05 eV was measured from constant current electromigration tests at multiple temperatures. A current density exponent of 1.91 was extracted from multiple current densities at a constant temperature. Electromigration-induced void morphology along with these model parameters indicated grain boundary diffusion is dominant and the void nucleation mechanism controlled the failure time.
ContributorsKilgore, Stephen (Author) / Adams, James (Thesis advisor) / Schroder, Dieter (Thesis advisor) / Krause, Stephen (Committee member) / Gaw, Craig (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.
ContributorsChoukulkar, Aditya (Author) / Calhoun, Ronald (Thesis advisor) / Mahalov, Alex (Committee member) / Kostelich, Eric (Committee member) / Huang, Huei-Ping (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis is a qualitative research study that focuses on siblings of children with Autistic Spectrum Disorder (ASD). Even though it is expected that having a child with ASD in the family will influence the whole family including siblings of the child with ASD, the sibling population is rarely included in research related to children with ASD, and there is only limited services available for them. This exploratory study (n=6) is aimed at better understanding the siblings' lives in their family settings in order to identify the siblings' unmet needs and determine how they have been influenced by the child with ASD. This study is also aimed at identifying the most appropriate support for the siblings to help them cope better. The study followed the Resiliency Model of Family Stress, Adjustment, and Adaptation and a narrative theory approach. An in-depth interview with the parents was conducted for the study, so the findings reflect the parents' perception of the siblings. All the themes emerged into two categories: life in the family setting and supports. The findings indicate that the families are striving for balance between the siblings and the children with ASD, but still tend to focus more on the children with ASD. Also, the families tend to have autonomous personal support systems. The parents tend to perceive that these personal support systems are good enough for the siblings; therefore, the parents do not feel that formal support for the siblings was necessary. As a result of the findings, recommendations are made for the organizations that work with individuals with ASD to provide more appropriate services for the families of children with ASD, including siblings. Also, recommendations are made for future studies to clarify more factors related to the siblings due to the limitation of this study; the siblings' lives were reflected vicariously via the parents.
ContributorsJeong, Seong Hae (Author) / Marsiglia, Flavio F (Thesis advisor) / Ayers, Stephanie (Committee member) / Adams, James (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation investigates the condition of skeletal muscle insulin resistance using bioinformatics and computational biology approaches. Drawing from several studies and numerous data sources, I have attempted to uncover molecular mechanisms at multiple levels. From the detailed atomistic simulations of a single protein, to datamining approaches applied at the systems biology level, I provide new targets to explore for the research community. Furthermore I present a new online web resource that unifies various bioinformatics databases to enable discovery of relevant features in 3D protein structures.
ContributorsMielke, Clinton (Author) / Mandarino, Lawrence (Committee member) / LaBaer, Joshua (Committee member) / Magee, D. Mitchell (Committee member) / Dinu, Valentin (Committee member) / Willis, Wayne (Committee member) / Arizona State University (Publisher)
Created2013
Description
While exercising mammalian muscle increasingly relies on carbohydrates for fuel as aerobic exercise intensity rises above the moderate range, flying birds are extraordinary endurance athletes and fuel flight, a moderate-high intensity exercise, almost exclusively with lipid. In addition, Aves have long lifespans compared to weight-matched mammals. As skeletal muscle mitochondria account for the majority of oxygen consumption during aerobic exercise, the primary goal was to investigate differences in isolated muscle mitochondria between these species and to examine to what extent factors intrinsic to mitochondria may account for the behavior observed in the intact tissue and whole organism. First, maximal enzyme activities were assessed in sparrow and rat mitochondria. Citrate synthase and aspartate aminotransferase activity were higher in sparrow compared to rat mitochondria, while glutamate dehydrogenase activity was lower. Sparrow mitochondrial NAD-linked isocitrate dehydrogenase activity was dependent on phosphate, unlike the mammalian enzyme. Next, the rate of oxygen consumption (JO), electron transport chain (ETC) activity, and reactive oxygen species (ROS) production were assessed in intact mitochondria. Maximal rates of fat oxidation were lower than for carbohydrate in rat but not sparrow mitochondria. ETC activity was higher in sparrows, but no differences were found in ROS production between species. Finally, fuel selection and control of respiration at three rates between rest and maximum were assessed. Mitochondrial fuel oxidation and selection mirrored that of the whole body; in rat mitochondria the reliance on carbohydrate increased as the rate of oxygen consumption increased, whereas fat dominated under all conditions in the sparrow. These data indicate fuel selection, at least in part, can be modulated at the level of the mitochondrial matrix when multiple substrates are present at saturating levels. As an increase in matrix oxidation-reduction potential has been linked to a suppression of fat oxidation and high ROS production, the high ETC activity relative to dehydrogenase activity in avian compared to mammalian mitochondria may result in lower matrix oxidation-reduction potential, allowing fatty acid oxidation to proceed while also resulting in low ROS production in vivo.
ContributorsKuzmiak, Sarah (Author) / Willis, Wayne T (Thesis advisor) / Mandarino, Lawrence (Committee member) / Sweazea, Karen (Committee member) / Harrison, Jon (Committee member) / Gadau, Juergen (Committee member) / Arizona State University (Publisher)
Created2012
Description
This report will review the mechanical and microstructural properties of the refractory element rhenium (Re) deposited using Laser Additive Manufacturing (LAM). With useable structural strength over 2200 °C, existing applications up to 2760 °C, very high strength, ductility and chemical resistance, interest in Re is understandable. This study includes data about tensile properties including tensile data up to 1925 °C, fracture modes, fatigue and microstructure including deformation systems and potential applications of that information. The bulk mechanical test data will be correlated with nanoindentation and crystallographic examination. LAM properties are compared to the existing properties found in the literature for other manufacturing processes. The literature indicates that Re has three significant slip systems but also twins as part of its deformation mechanisms. While it follows the hcp metal characteristics for deformation, it has interesting and valuable extremes such as high work hardening, potentially high strength, excellent wear resistance and superior elevated temperature strength. These characteristics are discussed in detail.
ContributorsAdams, Robbie (Author) / Chawla, Nikhilesh (Thesis advisor) / Adams, James (Committee member) / Krause, Stephen (Committee member) / Arizona State University (Publisher)
Created2012
Description
In 2022, integrated circuit interconnects will approach 10 nm and the diffusion barrier layers needed to ensure long lasting devices will be at 1 nm. This dimension means the interconnect will be dominated by the interface and it has been shown the interface is currently eroding device performance. The standard interconnect system has three layers - a Copper metal core, a Tantalum Adhesion layer and a Tantalum Nitride Diffusion Barrier Layer. An alternate interconnect schema is a Tantalum Nitride barrier layer and Silver as a metal. The adhesion layer is removed from the system along with changing to an alternate, low resistivity metal. First principles are used to assess the interface of the Silver and Tantalum Nitride. Several stoichiometric 1:1 Tantalum Nitride polymorphs are assessed and it is found that the Fe2P crystal structure is actually the most stable crystal structure which is at odds with the published phase diagram for ambient crystal structure. The surface stability of Fe2P-TaN is assessed and the absorption enthalpy of Silver adatoms is calculated. Finally, the thermodynamic stability of the TaN-Ag interconnect system is assessed.
ContributorsGrumski, Michael (Author) / Adams, James (Thesis advisor) / Krause, Stephen (Committee member) / Alford, Terry (Committee member) / Arizona State University (Publisher)
Created2012