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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
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
This thesis focuses on the erotic depictions of Lucretia and Susanna in Renaissance art. Both noted for displaying exemplary chastity, Lucretia and Susanna gained popularity as Christian and secular role models for women in the late Middle Ages and Renaissance. My examination of the heroines addresses the seductive portrayal of these women in painting, which seemingly contradicts the essence of their celebrity. The images specifically analyzed in this thesis include: Lucas Cranach the Elder's Lucretia from 1525, Lucretia from 1533, and Venus from 1532 as well as Tintoretto's Susanna and the Elders and Annibale Carracci's Susanna and the Elders. The scope of my thesis includes both textual and visual analyses of the myths/figures and the disparity that arises between them. Employing Lucretia and Susanna as examples, my aim is to demonstrate a subtle subversion occurring within images of powerful women that ultimately strips them of their power.
ContributorsWilliamson, Jennifer Marie (Author) / Schleif, Corine (Thesis director) / Geschwind, Rachel (Committee member) / Pratt, Rebekah (Committee member) / Barrett, The Honors College (Contributor) / School of Social Transformation (Contributor) / School of Human Evolution and Social Change (Contributor) / School of Art (Contributor)
Created2013-05
Description
Science fiction themed video games, specifically Role Playing Games (RPGs) like Deus Ex: Human Revolution (DX:HR), that focus on an emerging technology, contain features that help to better inform anticipatory governance. In a game like DX:HR, players vicariously experience human-enhancement technology and its societal effects through their in-game character. Acting as the character, the player explores the topic of human-enhancement technology in various ways, including dialogue with non-player characters (NPCs) and decisions that directly affect the game's world. Because Deus Ex: Human Revolution and games similar to it, allow players to explore and think about the technology itself, the stances on it, and its potential societal effects, they facilitate the anticipatory governance process. In this paper I postulate a theory of anticipatory gaming, which asserts that video games inform the anticipatory governance process for an emerging technology. To demonstrate this theory I examine the parts of the anticipatory governance process and demonstrate RPG's ability to inform it, through a case study of Deus Ex: Human Revolution.
ContributorsShedd, Jesse Bernard (Author) / Wetmore, Jameson (Thesis director) / Fisher, Erik (Committee member) / McKnight, John Carter (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2013-05
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
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
This paper studies the change in social diversity and interaction space from the Classic to Postclassic periods in the Mimbres Valley and East Mimbres Area. Between the Classic and Postclassic periods the Mimbres region of the American Southwest exhibits an increase in diversity of ceramic wares. Previous research suggests that increased diversity of ceramics indicates a more diverse community, which could pose challenges to local social interaction (Nelson et al. 2011). I am interested in whether the architecture of plazas, focal points of communities' social structures, change in response to the growing social diversity. To examine this, I quantify the diversity of painted ceramics at Classic and Postclassic villages as well as the extent of the enclosure of plazas. I find that there is a definite shift towards greater plaza enclosure between the Classic and Postclassic periods. I conclude this paper with a discussion of possible interpretations of this trend regarding the social reactions of Mimbres communities to the changes which reshaped the region between the Classic and Postclassic periods.
ContributorsHarkness, Rebecca Jean (Author) / Nelson, Margaret (Thesis director) / Hegmon, Michelle (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution and Social Change (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor)
Created2015-05