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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
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
Since the introduction of the common school in the United States (US), education has constantly been in a state of reform. Given the importance of student learning to the future state of our nation, it is important to understand how positive educational reform can be achieved. This ethnographic case study aims to try to understand how a reform effort works as an educational and a sociocultural process, and what the important contributing factors to actualizing school reform are, as well as the challenges of effective implementation. Specifically, this study focuses on a school-wide reform effort based upon Stephen Covey's Seven Habits (1989). Qualitative research methods were used to address the research questions in this study. The researcher drew upon interviews, observations, and artifact and field note collection to tell the story of an elementary school engaged in year three of a school-wide reform initiative from the viewpoint of 10 teachers involved. Three recurring themes emerged from the data. First, data indicate that school reform is most effective when a school culture is created that supports the activation of teacher voice, efficacy, and coparticipation. Second, time and support are factors impacting implementation. Third, teachers reported that the common language from the reform has impacted the culture of the school. The evolution of a school culture is not simple and is demonstrated in the different ways the teachers experience the reform. Questions of authenticity arise when the reform effort changes from a grassroots, bottom-up initiative to a more top-down, bureaucratized business model.
ContributorsLamp, Michelle (Author) / Mccarty, Teresa (Thesis advisor) / Schugurensky, Daniel, 1958- (Committee member) / Powers, Jeanne (Committee member) / Arizona State University (Publisher)
Created2013
Description
Providing nutrition information at point of sale at restaurants has gained in popularity in recent years and will soon become a legal requirement. Consumers are using this opportunity to become more informed on the nutritional quality of the foods they consume in an effort to maintain healthfulness. Prior research has confirmed the utility of this information in adult populations. However, research on adolescents in school environments has resulted in mixed findings. This study investigated the effect of exposure to calorie and fat information on student purchases at lunchtime in a high school cafeteria. Additionally, it explored other factors that may contribute to students' food selections during school lunches. The research methods included analysis of changes in cafeteria food sales in one school, surveys, and focus groups. Analysis of cafeteria food sales during lunch did not show any significant change in the average number of calories and fat purchased per student between pre and post intervention. However, information gathered from focus group questioning demonstrated how students used the nutrition information to change their behavior after they have purchased their food.
ContributorsFresques, Audrey Delfina (Author) / Schugurensky, Daniel, 1958- (Thesis advisor) / Barnett, Joshua (Committee member) / Cruz, Heather (Committee member) / Arizona State University (Publisher)
Created2013
Description
The purpose of this study is to examine the influence of neoliberalism on the occurrence and intervention of genocide, particularly the ability to create othered groups through a process of dehumanization that desensitizes those in power to the human condition. I propose Social Externalization Theory as paradigm that explains how neoliberalism can be used as a means social control to create subjects vulnerable to political and collective violence that is justified as the externalized cost of economic growth, development, and national security. Finally, the conflict in Darfur (2003 - 2010) serves as a case study to analyze the influence of neoliberal policies on the resistance of the International community to recognize the violence as genocide. Analysis of the case study found that some tenets of neoliberalism produce results that fit within the ideologies of genocide and that some aspects of neoliberalism assume a genocidal mentality. In this case, those in positions power engage in daily activities that justify some suffering as acceptable, thus desensitizing them to the harm that their decisions generate.
ContributorsCalleja, Robert J (Author) / Romero, Mary (Thesis advisor) / Swadener, Beth Blue (Committee member) / Schugurensky, Daniel, 1958- (Committee member) / Arizona State University (Publisher)
Created2013
Description
Woody plant encroachment is a worldwide phenomenon linked to water availability in semiarid systems. Nevertheless, the implications of woody plant encroachment on the hydrologic cycle are poorly understood, especially at the catchment scale. This study takes place in a pair of small semiarid rangeland undergoing the encroachment of Prosopis velutina Woot., or velvet mesquite tree. The similarly-sized basins are in close proximity, leading to equivalent meteorological and soil conditions. One basin was treated for mesquite in 1974, while the other represents the encroachment process. A sensor network was installed to measure ecohydrological states and fluxes, including precipitation, runoff, soil moisture and evapotranspiration. Observations from June 1, 2011 through September 30, 2012 are presented to describe the seasonality and spatial variability of ecohydrological conditions during the North American Monsoon (NAM). Runoff observations are linked to historical changes in runoff production in each watershed. Observations indicate that the mesquite-treated basin generates more runoff pulses and greater runoff volume for small rainfall events, while the mesquite-encroached basin generates more runoff volume for large rainfall events. A distributed hydrologic model is applied to both basins to investigate the runoff threshold processes experienced during the NAM. Vegetation in the two basins is classified into grass, mesquite, or bare soil using high-resolution imagery. Model predictions are used to investigate the vegetation controls on soil moisture, evapotranspiration, and runoff generation. The distributed model shows that grass and mesquite sites retain the highest levels of soil moisture. The model also captures the runoff generation differences between the two watersheds that have been observed over the past decade. Generally, grass sites in the mesquite-treated basin have less plant interception and evapotranspiration, leading to higher soil moisture that supports greater runoff for small rainfall events. For large rainfall events, the mesquite-encroached basin produces greater runoff due to its higher fraction of bare soil. The results of this study show that a distributed hydrologic model can be used to explain runoff threshold processes linked to woody plant encroachment at the catchment-scale and provides useful interpretations for rangeland management in semiarid areas.
ContributorsPierini, Nicole A (Author) / Vivoni, Enrique R (Thesis advisor) / Wang, Zhi-Hua (Committee member) / Mays, Larry W. (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation explores the unique role schools play in contributing toward a sustainable future for their communities. This was undertaken by first conducting a thorough review and analysis of the literature on the current utilization of schools as agents of sustainable development, along with an evaluation of schools engaging in this model around the United States. Following this, a framework was developed to aid in the assessment of school-community engagements from the perspective of social change. Sustainability problem solving tools were synthesized for use by schools and community stakeholders, and were tested in the case study of this dissertation. This case study combined methods from the fields of sustainable development, transition management, and social change to guide two schools in their attempts to increase community sustainability through addressing a shared sustainability problem: childhood obesity. The case study facilitated the creation of a sustainable vision for the Phoenix Metropolitan Area without childhood obesity, as well as strategic actions plans for each school to utilize as they move forward on addressing this challenge.
ContributorsLawless, Tamara Hope (Author) / Golub, Aaron (Thesis advisor) / Redman, Charles (Committee member) / Schugurensky, Daniel, 1958- (Committee member) / Arizona State University (Publisher)
Created2013
Description
Sustainability challenges with severe local to global impacts require fundamental shifts in what industrial societies aspire to, generate, consume, and represent, as well as how they function. Transition governance is a promising framework to support these transformational efforts. A key component of transition governance is the construction of transition strategies, i.e., action schemes for how to transition from the current state to a sustainable one. Despite accomplishments in building theory and methodology for transition governance, the concepts of what transition strategies entail and how they relate to specific interventions are still underdeveloped. This dissertation further develops the concept of transition strategies, and explores how different stakeholder groups and allies can develop and test transition strategies across different scales, in the specific context of urban sustainability challenges. The overarching research question is: How can cities build and implement comprehensive transition strategies across different urban scales, from the city to the organizational level? The dissertation comprises four studies that explore the dynamic between transition strategies and experiments at the city, neighborhood, and organizational levels with empirical examples from Phoenix, Arizona. The first study reviews and compares paradigms of intentional change, namely transition governance, backcasting, intervention research, change management, integrated planning, and adaptive management in order to offer a rich set of converging ideas on what strategies for intentional change towards sustainability entail. The second study proposes a comprehensive concept of transition strategies and illustrates the concept with the example of sustainability strategies created through a research partnership with the City of Phoenix. The third study explores the role of experiments in transition processes through the lens of the neighborhood-level initiative of The Valley of the Sunflowers. The fourth study examines the role organizations can play in initiating urban sustainability transitions using exemplary strategies and experiments implemented at a local high school. The studies combined contribute to the further development of transition theory and sustainable urban development concepts. While this research field is at a nascent stage, the thesis provides a framework and empirical examples for how to build evidence-based transition strategies in support of urban sustainability.
ContributorsKay, Braden Ryan (Author) / Wiek, Arnim (Thesis advisor) / Loorbach, Derk (Committee member) / Schugurensky, Daniel, 1958- (Committee member) / Tiger, Fern (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
Description
In this thesis, we present the study of several physical properties of relativistic mat- ters under extreme conditions. We start by deriving the rate of the nonleptonic weak processes and the bulk viscosity in several spin-one color superconducting phases of quark matter. We also calculate the bulk viscosity in the nonlinear and anharmonic regime in the normal phase of strange quark matter. We point out several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. In the corresponding study, we take into account the interplay between the non- leptonic and semileptonic weak processes. The results can be important in order to relate accessible observables of compact stars to their internal composition. We also use quantum field theoretical methods to study the transport properties in monolayer graphene in a strong magnetic field. The corresponding quasi-relativistic system re- veals an anomalous quantum Hall effect, whose features are directly connected with the spontaneous flavor symmetry breaking. We study the microscopic origin of Fara- day rotation and magneto-optical transmission in graphene and show that their main features are in agreement with the experimental data.
ContributorsWang, Xinyang, Ph.D (Author) / Shovkovy, Igor (Thesis advisor) / Belitsky, Andrei (Committee member) / Easson, Damien (Committee member) / Peng, Xihong (Committee member) / Vachaspati, Tanmay (Committee member) / Arizona State University (Publisher)
Created2013