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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
My thesis is a creative project in which I designed, developed, marketed, and sold a mobile application on the iOS (iPhone) platform. In addition to developing a mobile application, I also formed a Limited Liability Company, Flem LLC, which I will own, manage, and operate for the duration of this project and beyond the thesis project. Flem LLC allows me to create a unique brand for my company, separate from myself, as well as providing legal protection for my personal assets. My initial application is titled "Derpy Calc". It is a basic calculator for iPhone capable of adding, subtracting, multiplying, dividing, and taking the square root of positive, negative, and decimal numbers. Derpy Calc is unique because before it will output an answer, Derpy, the calculator's personality, will make a remark or ask a question that is factual, random, or silly. This application is targeted at teenagers and young adults and the outputs Derpy gives will be targeted those demographic. The purpose of this application is to provide humor and spontaneity to the process of doing math and is currently the only iOS application with that focus. Derpy debuted on the Apple App store on March 1st 2013. As of March 27th, it is on Version 1.2, has had 457 advertisement views on 328 downloads. It has earned Flem LLC a total of $0.75 in advertising revenues.
ContributorsFleming, William Patrick (Author) / Peck, Sidnee (Thesis director) / Nemanich, Louise (Committee member) / Faucon, Christophe (Committee member) / Barrett, The Honors College (Contributor) / Department of Finance (Contributor) / School of Accountancy (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
Industrial design is the practice of creating solutions by studying people and businesses. Originally centered on development of goods, industrial design uses methods rooted in human behavioral study, human factors, and strategic problem solving. As our economy and professional practice shift away from manufacturing towards a service-dominant landscape, industrial design must align its profession to formally include service design. The small service business setting is a microcosm in which the value of design and branding in business is magnified. This research reinforces design's ties with services marketing and business and is dedicated to finding solutions for the backbone of our economy. Micro-businesses with fewer than 20 employees often lack the sophisticated management, marketing, and strategies that bring about success. Despite the fact that 70% to 80% of small and micro businesses are service based, little research is dedicated to unique strategies for these small service firms. Research has shown that using strategic business design increases small business success. Given high small business failure rates, it behooves entrepreneurs to use intuitive planning tools that are appropriate for the dynamic startup years. When put within reach and context of small business owners, the tools used in design draw a clear map of insights into the "design" of small businesses. Through a literature review, interviews, and a new workshop method, the needs of small business owners and the challenges they face are used to design and implement an accessible, actionable strategic toolkit for small service businesses. This simple, interdisciplinary toolkit was designed with the goal of increasing the efficacy and likelihood of ongoing strategic business planning through context-specific, instrumental activities. The tools are shown to help a business owner form pragmatic, iterative problem-solving approaches that allow the business owner to plan in the face of uncertainty and find insights into her own business, brand, and services.
ContributorsGrimes, Lynelle (Author) / Takamura, John (Thesis advisor) / Peck, Sidnee (Committee member) / Wolf, Peter (Committee member) / Arizona State University (Publisher)
Created2012
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
As part of the InnovationSpace program, interdisciplinary teams of five undergraduate students from the areas of business, engineering, graphic design, industrial design, and sustainability are responsible for creating a product idea that addresses a societal need. My team, Flo, was tasked with finding a product/service solution that will increase collaboration or creativity in a workplace environment. After deciding as a group how to define collaboration—working with others to achieve a common goal—and creativity—getting to an end goal in a different way than is expected—we spent the fall 2014 semester researching pain points and areas of interest for potential customers and users. We learned that one of the barriers to productivity for our target users in startups and mature corporations is that they often lack the right mix of private and collaborative spaces. From this insight, we created a product system called Trenz.
There are benefits and drawbacks to both collaboration and individual work. Trenz sits at the intersection of both work styles, thus aiming to negate the downsides of both and harness their benefits based on real-time user needs. Holistically, the corporate workplace furniture industry is stagnant, despite several trends that pave the way for future innovation. Even though studies are consistently released on the benefits of natural light, flexibility, and activity in the workplace, the furniture industry has not yet responded with a solution that successfully solves all three while keeping the user in mind. As such, Trenz is a product-service system with the potential to create a new segment in the market because of its user-centric design, the support of individual/group work dynamics, and its feature set that can accommodate a diverse group of users.
There are benefits and drawbacks to both collaboration and individual work. Trenz sits at the intersection of both work styles, thus aiming to negate the downsides of both and harness their benefits based on real-time user needs. Holistically, the corporate workplace furniture industry is stagnant, despite several trends that pave the way for future innovation. Even though studies are consistently released on the benefits of natural light, flexibility, and activity in the workplace, the furniture industry has not yet responded with a solution that successfully solves all three while keeping the user in mind. As such, Trenz is a product-service system with the potential to create a new segment in the market because of its user-centric design, the support of individual/group work dynamics, and its feature set that can accommodate a diverse group of users.
ContributorsDicicco, Ryan Paul (Author) / Peck, Sidnee (Thesis director) / Smith, Jacqueline (Committee member) / Barrett, The Honors College (Contributor) / Department of Supply Chain Management (Contributor) / Department of Finance (Contributor)
Created2015-05