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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
Surveys have shown that several hundred billion weather forecasts are obtained by the United States public each year, and that weather news is one of the most consumed topics in the media. This indicates that the forecast provides information that is significant to the public, and that the public utilizes details associated with it to inform aspects of their life. Phoenix, Arizona is a dry, desert region that experiences a monsoon season and extreme heat. How then, does the weather forecast influence the way Phoenix residents make decisions? This paper aims to draw connections between the weather forecast, decision making, and people who live in a desert environment. To do this, a ten-minute survey was deployed through Amazon Mechanical Turk (MTurk) in which 379 respondents were targeted. The survey asks 45 multiple choice and ranking questions categorized into four sections: obtainment of the forecast, forecast variables of interest, informed decision making based on unique weather variables, and demographics. This research illuminates how residents in the Phoenix metropolitan area use the local weather forecast for decision-making on daily activities, and the main meteorological factors that drive those decisions.
ContributorsMarturano, Julia (Author) / Middel, Ariane (Thesis director) / Schneider, Florian (Committee member) / School of Geographical Sciences and Urban Planning (Contributor, Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
A new analytical method is proposed for measuring the deuterium to hydrogen ratio (D/H) of non-stoichiometric water in hydrous minerals via pyrolysis facilitated gas-chromatography - isotope ratio mass spectrometry (GC-IRMS). Previously published analytical methods have reported a poorly understood nonlinear dependence of D/H on sample size, for which any accurate correction is difficult. This sample size effect been variously attributed to kinetic isotope fractionation within the mass spectrometer and peripheral instruments, ion source linearity issues, and an unstable H_3^+-factor or incorrect H_3^+-factor calculations. The cause of the sample size effect is here identified by examinations of individual chromatograms as well as bulk data from chromatographic peaks. It is here determined that it is primarily an artifact of the calculations employed by the manufacturer's computer program, used to both monitor the functions of the mass spectrometer and to collect data. Ancillary causes of the sample size effect include a combination of persistent background interferences and chromatographic separation of the isotopologues of molecular hydrogen. Previously published methods are evaluated in light of these findings. A new method of H_3^+-factor and D/H calculation is proposed which makes portions of the Isodat software as well as other published calculation methods unnecessary. Using this new method, D/H is measured in non-stoichiometric water in chert from the Cretaceous Edwards Group, Texas, as well as the Precambrian Kromberg Formation, South Africa, to assess hydrological conditions as well as to estimate the maximum average surface temperature during precipitation of the chert. Data from Cretaceous chert are consistent with previously published data and interpretations, based upon conventional analyses of large samples. Data from Precambrian chert are consistent with maximum average surface temperatures approaching 65°C during the Archean, instead of the much lower temperatures derived from erroneous methods of sample preparation and analysis. D/H is likewise measured in non-stoichiometric water in silicified basalt from the Precambrian Hooggenoeg Complex, South Africa. Data are shown to be consistent with D/H of the Archean ocean similar to present day values.
ContributorsSheehan, Michael Robert (Author) / Knauth, Leroy P (Thesis advisor) / Anbar, Ariel (Committee member) / Farmer, Jack (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
Harsh environments have conditions that make collecting scientific data difficult with existing commercial-off-the-shelf technology. Micro Electro Mechanical Systems (MEMS) technology is ideally suited for harsh environment characterization and operation due to the wide range of materials available and an incredible array of different sensing techniques while providing small device size, low power consumption, and robustness. There were two main objectives of the research conducted. The first objective was to design, fabricate, and test novel sensors that measure the amount of exposure to ionizing radiation for a wide range of applications including characterization of harsh environments. Two types of MEMS ionizing radiation dosimeters were developed. The first sensor was a passive radiation-sensitive capacitor-antenna design. The antenna's emitted frequency of peak-intensity changed as exposure time to radiation increased. The second sensor was a film bulk acoustic-wave resonator, whose resonant frequency decreased with increasing ionizing radiation exposure time. The second objective was to develop MEMS sensor systems that could be deployed to gather scientific data and to use that data to address the following research question: do temperature and/or conductivity predict the appearance of photosynthetic organisms in hot springs. To this end, temperature and electrical conductivity sensor arrays were designed and fabricated based on mature MEMS technology. Electronic circuits and the software interface to the electronics were developed for field data collection. The sensor arrays utilized in the hot springs yielded results that support the hypothesis that temperature plays a key role in determining where the photosynthetic organisms occur. Additionally, a cold-film fluidic flow sensor was developed, which is suitable for near-boiling temperature measurement. Future research should focus on (1) developing a MEMS pH sensor array with integrated temperature, conductivity, and flow sensors to provide multi-dimensional data for scientific study and (2) finding solutions to biofouling and self-calibration, which affects sensor performance over long-term deployment.
ContributorsOiler, Jonathon (Author) / Yu, Hongyu (Thesis advisor) / Anbar, Ariel (Committee member) / Hartnett, Hilairy (Committee member) / Scannapieco, Evan (Committee member) / Timmes, Francis (Committee member) / Arizona State University (Publisher)
Created2013
Description
The presence of a number of extinct radionuclides in the early Solar System (SS) is known from geochemical and isotopic studies of meteorites and their components. The half-lives of these isotopes are short relative to the age of the SS, such that they have now decayed to undetectable levels. They can be inferred to exist in the early SS from the presence of their daughter nuclides in meteoritic materials that formed while they were still extant. The extinct radionuclides are particularly useful as fine-scale chronometers for events in the early SS. They can also be used to help constrain the astrophysical setting of the formation of the SS because their short half-lives and unique formation environments yield information about the sources and timing of delivery of material to the protoplanetary disk. Some extinct radionuclides are considered evidence that the Sun interacted with a massive star (supernova) early in its history. The abundance of 60Fe in the early SS is particularly useful for constraining the astrophysical environment of the Sun's formation because, if present in sufficient abundance, its only likely source is injection from a nearby supernova. The initial SS abundance of 60Fe is poorly constrained at the present time, with estimates varying by 1-2 orders of magnitude. I have determined the 60Fe-60Ni isotope systematics of ancient, well-preserved meteorites using high-precision mass spectrometry to better constrain the initial SS abundance of 60Fe. I find identical estimates of the initial 60Fe abundance from both differentiated basaltic meteorites and from components of primitive chondrites formed in the Solar nebula, which suggest a lower 60Fe abundance than other recent estimates. With recent improved meteorite collection efforts there are more rare ungrouped meteorites being found that hold interesting clues to the origin and evolution of early SS objects. I use the 26Al-26Mg extinct radionuclide chronometer to constrain the ages of several recently recovered meteorites that sample previously unknown asteroid lithologies, including the only know felsic meteorite from an asteroid and two other ungrouped basaltic achondrites. These results help broaden our understanding of the timescales involved in igneous differentiation processes in the early SS.
ContributorsSpivak-Birndorf, Lev (Author) / Wadhwa, Meenakshi (Thesis advisor) / Hervig, Richard (Committee member) / Timmes, Francis (Committee member) / Williams, Lynda (Committee member) / Anbar, Ariel (Committee member) / Arizona State University (Publisher)
Created2012
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