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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
Hispanic youth have the highest risk for obesity, making this population a key priority for early childhood interventions to prevent the development of adult obesity and its consequences. Involving parents in these interventions is essential to support positive long-term physical activity and nutrition habits. Interventions in the past have engaged parents by providing information about nutrition and fruit and vegetable intake through written materials or text such as newsletters and text messages. The Sustainability via Active Garden Education (SAGE) intervention used gardening and interactive activities to teach preschool children ages 3-5 about healthy eating and physical activity. It aimed to increase physical activity and fruit and vegetable intake in preschool children as well as improve related parenting practices. The intervention utilized newsletters to engage parents by promoting opportunities to increase physical activity and fruit and vegetable intake for their children at home. The newsletters also encouraged parents to discuss what was learned during the SAGE lessons with their children. The purpose of this paper is to describe the content of the newsletters and determine the parent perception of the newsletters through parent survey responses. This can help inform future childhood obesity interventions and parent engagement.
ContributorsVi, Vinny (Author) / Lee, Rebecca (Thesis director) / Martinelli, Sarah (Committee member) / Edson College of Nursing and Health Innovation (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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
Acne scarring can negatively affect individuals’ lives long after active acne has resolved. An online survey analyzed the public’s acne history and knowledge of acne scar prevention to determine acne scar risk factors and public awareness of acne scar prevention and yielded 209 complete data sets. Though types of acne scars vary in how long they persist on one’s skin, all forms were found to be equal in the negative psychological impact they inflict. Acne severity, acne duration, individual age, and family history of scarring were found to have associations with atrophic scarring The findings suggest a need for implementing a structured and standardized way for communicating acne scar prevention information to the general public. Practical implications of these findings are discussed further for increasing public awareness of acne scarring and prevention knowledge.
ContributorsJone, Jillian Louise (Author) / Lee, Rebecca (Thesis director) / Redden, Tamara (Committee member) / Edson College of Nursing and Health Innovation (Contributor) / College of Health Solutions (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Cultural Perceptions of Leisure and Well-being in Rock Climbing Communities of Peru and Arizona, USA
Description
In December of 2015, I made my way to rural Peru for a few weeks, my first visit to South America. While I was there, I observed a devotion to family and leisure activity, topics that were not heavily prioritized in my experience in Arizona. Upon my return, I became more involved in leisure activities, particularly running, hiking, yoga, and climbing. These involvements noticeably benefitted my health and well-being. The way the Peruvians I met prioritized these subjects fascinated me, and I wanted to study this difference between Arizona and Peru. In July of 2017, I returned to Peru for a semester abroad with my bags packed and the following research questions: 1) Are differences in motivation for rock climbing between Arizona and Peruvian climbers associated with cultural values? 2) Do leisure activities and the amount of time spent on them have an effect on quality of life? 3) Does the degree of climbing specialization impact perceptions of well-being? 4) What characteristics impact perceptions of quality of life among climbers? Are these characteristics affected by country of origin? My prediction was that Peruvians had higher quality of life due to their emphasis on leisure. Through this study, I learned that this conclusion was not as simple as I anticipated.
ContributorsMatta, Samantha Tania (Author) / Hultsman, Wendy (Thesis director) / Sampson, David (Committee member) / Lee, Rebecca (Committee member) / College of Integrative Sciences and Arts (Contributor) / School of Molecular Sciences (Contributor) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This study confirms that there is stigma attached to how Somali-Americans perceive mental and emotional impairments compared to the perception of physical disabilities and impairments. More Somali-Americans are willing to seek help regarding their mental and physical health which is a positive step in improving the perceptions of Somali-Americans towards mental or emotional impairments and physical disabilities. Findings can contribute to the knowledge of health care professionals (i.e. nurses) in caring for patients identifying as Somali to promote culturally competent care.
ContributorsAden, Amina (Author) / Hosley, Brenda (Thesis director) / Lee, Rebecca (Committee member) / Lyles, Annmarie (Committee member) / Arizona State University. College of Nursing & Healthcare Innovation (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
ContributorsCole, Alexandra Shea (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / School of International Letters and Cultures (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Research supports that music therapy can be used in multiple aspects of care for patients living within different environments. There is a gap in the literature when it comes to the impact of music sessions for older adults who do not have a diagnosed disease, therefore this study analyzes this population specifically. This study examines music therapy and its effects on anxiety and depression in adults aged 65 or older living in independent living homes. The adults participated in a mixed-methods study over the span of one month examining music as an intervention to decrease anxiety and depression. Each subject consented into the study, completed a demographic survey, answered open-ended questions regarding their experience with anxiety/sadness and ways to cope, as well as Profile of Moods Scale (POMS) during the first session. On the last week of the study, the participants were asked to fill out the same POMS scale to evaluate whether music influenced anxiety and depression. There was limited evidence found in this study to support the use of music therapy as an intervention to decrease anxiety and depression in adults over the age of 65.
ContributorsWolfus, Sarah Ilyssa (Author) / Lee, Rebecca (Thesis director) / Larkey, Linda (Committee member) / Arizona State University. College of Nursing & Healthcare Innovation (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The Centers for Disease Control and Prevention in the United States announced that there has been roughly a 50% increase in the prevalence of food allergies among people between the years of 1997 - 2011. A food allergy can be described as a medical condition where being exposed to a certain food triggers a harmful immune response in the body, known as an allergic reaction. These reactions can range from mild to fatal, and they are caused mainly by the top 8 major food allergens: dairy, eggs, peanuts, tree nuts, wheat, soy, fish, and shellfish. Food allergies mainly plague children under the age of 3, as some of them will grow out of their allergy sensitivity over time, and most people develop their allergies at a young age, and not when they are older. The rise in prevalence is becoming a frightening problem around the world, and there are emerging theories that are attempting to ascribe a cause. There are three well-known hypotheses that will be discussed: the Hygiene Hypothesis, the Dual-Allergen Exposure Hypothesis, and the Vitamin-D Deficiency Hypothesis. Beyond that, this report proposes that a new hypothesis be studied, the Food Systems Hypothesis. This hypothesis theorizes that the cause of the rise of food allergies is actually caused by changes in the food itself and particularly the pesticides that are used to cultivate it.
ContributorsCromer, Kelly (Author) / Lee, Rebecca (Thesis director) / MacFadyen, Joshua (Committee member) / Sanford School of Social and Family Dynamics (Contributor) / Dean, W.P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
Traditional Reinforcement Learning (RL) assumes to learn policies with respect to reward available from the environment but sometimes learning in a complex domain requires wisdom which comes from a wide range of experience. In behavior based robotics, it is observed that a complex behavior can be described by a combination of simpler behaviors. It is tempting to apply similar idea such that simpler behaviors can be combined in a meaningful way to tailor the complex combination. Such an approach would enable faster learning and modular design of behaviors. Complex behaviors can be combined with other behaviors to create even more advanced behaviors resulting in a rich set of possibilities. Similar to RL, combined behavior can keep evolving by interacting with the environment. The requirement of this method is to specify a reasonable set of simple behaviors. In this research, I present an algorithm that aims at combining behavior such that the resulting behavior has characteristics of each individual behavior. This approach has been inspired by behavior based robotics, such as the subsumption architecture and motor schema-based design. The combination algorithm outputs n weights to combine behaviors linearly. The weights are state dependent and change dynamically at every step in an episode. This idea is tested on discrete and continuous environments like OpenAI’s “Lunar Lander” and “Biped Walker”. Results are compared with related domains like Multi-objective RL, Hierarchical RL, Transfer learning, and basic RL. It is observed that the combination of behaviors is a novel way of learning which helps the agent achieve required characteristics. A combination is learned for a given state and so the agent is able to learn faster in an efficient manner compared to other similar approaches. Agent beautifully demonstrates characteristics of multiple behaviors which helps the agent to learn and adapt to the environment. Future directions are also suggested as possible extensions to this research.
ContributorsVora, Kevin Jatin (Author) / Zhang, Yu (Thesis advisor) / Yang, Yezhou (Committee member) / Praharaj, Sarbeswar (Committee member) / Arizona State University (Publisher)
Created2021