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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
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
Like individual organisms, complex social groups are able to maintain predictable trajectories of growth, from initial colony foundation to mature reproductively capable units. They do so while simultaneously responding flexibly to variation in nutrient availability and intake. Leafcutter ant colonies function as tri-trophic systems, in which the ants harvest vegetation to grow a fungus that, in turn, serves as food for the colony. Fungal growth rates and colony worker production are interdependent, regulated by nutritional and behavioral feedbacks. Fungal growth and quality are directly affected by worker foraging decisions, while worker production is, in turn, dependent on the amount and condition of the fungus. In this dissertation, I first characterized the growth relationship between the workers and the fungus of the desert leafcutter ant Acromyrmex versicolor during early stages of colony development, from colony foundation by groups of queens through the beginnings of exponential growth. I found that this relationship undergoes a period of slow growth and instability when workers first emerge, and then becomes allometrically positive. I then evaluated how mass and element ratios of resources collected by the ants are translated into fungus and worker population growth, and refuse, finding that colony digestive efficiency is comparable to digestive efficiencies of other herbivorous insects and ruminants. To test how colonies behaviorally respond to perturbations of the fungus garden, I quantified activity levels and task performance of workers in colonies with either supplemented or diminished fungus gardens, and found that colonies adjusted activity and task allocation in response to the fungus garden size. Finally, to identify possible forms of nutrient limitation, I measured how colony performance was affected by changes in the relative amounts of carbohydrates, protein, and phosphorus available in the resources used to grow the fungus garden. From this experiment, I concluded that colony growth is primarily carbohydrate-limited.
ContributorsClark, Rebecca, 1981- (Author) / Fewell, Jennifer H (Thesis advisor) / Mueller, Ulrich (Committee member) / Liebig, Juergen (Committee member) / Elser, James (Committee member) / Harrison, Jon (Committee member) / Arizona State University (Publisher)
Created2011
Description
The repression of reproductive competition and the enforcement of altruism are key components to the success of animal societies. Eusocial insects are defined by having a reproductive division of labor, in which reproduction is relegated to one or few individuals while the rest of the group members maintain the colony and help raise offspring. However, workers have retained the ability to reproduce in most insect societies. In the social Hymenoptera, due to haplodiploidy, workers can lay unfertilized male destined eggs without mating. Potential conflict between workers and queens can arise over male production, and policing behaviors performed by nestmate workers and queens are a means of repressing worker reproduction. This work describes the means and results of the regulation of worker reproduction in the ant species Aphaenogaster cockerelli. Through manipulative laboratory studies on mature colonies, the lack of egg policing and the presence of physical policing by both workers and queens of this species are described. Through chemical analysis and artificial chemical treatments, the role of cuticular hydrocarbons as indicators of fertility status and the informational basis of policing in this species is demonstrated. An additional queen-specific chemical signal in the Dufour's gland is discovered to be used to direct nestmate aggression towards reproductive competitors. Finally, the level of actual worker-derived males in field colonies is measured. Together, these studies demonstrate the effectiveness of policing behaviors on the suppression of worker reproduction in a social insect species, and provide an example of how punishment and the threat of punishment is a powerful force in maintaining cooperative societies.
ContributorsSmith, Adrian A. (Author) / Liebig, Juergen (Thesis advisor) / Hoelldobler, Bert (Thesis advisor) / Gadau, Juergen (Committee member) / Johnson, Robert A. (Committee member) / Pratt, Stephen (Committee member) / Arizona State University (Publisher)
Created2011
Description
Over the past century in the southwestern United States human actions have altered hydrological processes that shape riparian ecosystems. One change, release of treated wastewater into waterways, has created perennial base flows and increased nutrient availability in ephemeral or intermittent channels. While there are benefits to utilizing treated wastewater for environmental flows, there are numerous unresolved ecohydrological issues regarding the efficacy of effluent to sustain groundwater-dependent riparian ecosystems. This research examined how nutrient-rich effluent, released into waterways with varying depths to groundwater, influences riparian plant community development. Statewide analysis of spatial and temporal patterns of effluent generation and release revealed that hydrogeomorphic setting significantly influences downstream riparian response. Approximately 70% of effluent released is into deep groundwater systems, which produced the lowest riparian development. A greenhouse study assessed how varying concentrations of nitrogen and phosphorus, emulating levels in effluent, influenced plant community response. With increasing nitrogen concentrations, vegetation emerging from riparian seed banks had greater biomass, reduced species richness, and greater abundance of nitrophilic species. The effluent-dominated Santa Cruz River in southern Arizona, with a shallow groundwater upper reach and deep groundwater lower reach, served as a study river while the San Pedro River provided a control. Analysis revealed that woody species richness and composition were similar between the two systems. Hydric pioneers (Populus fremontii, Salix gooddingii) were dominant at perennial sites on both rivers. Nitrophilic species (Conium maculatum, Polygonum lapathifolium) dominated herbaceous plant communities and plant heights were greatest in effluent-dominated reaches. Riparian vegetation declined with increasing downstream distance in the upper Santa Cruz, while patterns in the lower Santa Cruz were confounded by additional downstream agricultural input and a channelized floodplain. There were distinct longitudinal and lateral shifts toward more xeric species with increasing downstream distance and increasing lateral distance from the low-flow channel. Patterns in the upper and lower Santa Cruz reaches indicate that water availability drives riparian vegetation outcomes below treatment facilities. Ultimately, this research informs decision processes and increases adaptive capacity for water resources policy and management through the integration of ecological data in decision frameworks regarding the release of effluent for environmental flows.
ContributorsWhite, Margaret Susan (Author) / Stromberg, Juliet C. (Thesis advisor) / Fisher, Stuart G. (Committee member) / White, Dave (Committee member) / Holway, James (Committee member) / Wu, Jianguo (Committee member) / Arizona State University (Publisher)
Created2011
Description
Driven by concern over environmental, economic and social problems, small, place based communities are engaging in processes of transition to become more sustainable. These communities may be viewed as innovative front runners of a transition to a more sustainable society in general, each one, an experiment in social transformation. These experiments present learning opportunities to build robust theories of community transition and to create specific, actionable knowledge to improve, replicate, and accelerate transitions in real communities. Yet to date, there is very little empirical research into the community transition phenomenon. This thesis empirically develops an analytical framework and method for the purpose of researching community transition processes, the ultimate goal of which is to arrive at a practice of evidence based transitions. A multiple case study approach was used to investigate three community transitions while simultaneously developing the framework and method in an iterative fashion. The case studies selected were Ashton Hayes, a small English village, BedZED, an urban housing complex in London, and Forres, a small Scottish town. Each community was visited and data collected by interview and document analysis. The research design brings together elements of process tracing, transformative planning and governance, sustainability assessment, transition path analysis and transition management within a multiple case study envelope. While some preliminary insights are gained into community transitions based on the three cases the main contribution of this thesis is in the creation of the research framework and method. The general framework and method developed has potential for standardizing and synthesizing research of community transition processes leading to both theoretical and practical knowledge that allows sustainability transition to be approached with confidence and not just hope.
ContributorsForrest, Nigel (Author) / Wiek, Arnim (Thesis advisor) / Golub, Aaron (Thesis advisor) / Redman, Charles (Committee member) / White, Dave (Committee member) / Arizona State University (Publisher)
Created2011
Description
The sacred San Francisco Peaks in northern Arizona have been at the center of a series of land development controversies since the 1800s. Most recently, a controversy arose over a proposal by the ski area on the Peaks to use 100% reclaimed water to make artificial snow. The current state of the San Francisco Peaks controversy would benefit from a decision-making process that holds sustainability policy at its core. The first step towards a new sustainability-focused deliberative process regarding a complex issue like the San Francisco Peaks controversy requires understanding the issue's origins and the perspectives of the people involved in the issue. My thesis provides an historical analysis of the controversy and examines some of the laws and participatory mechanisms that have shaped the decision-making procedures and power structures from the 19th century to the early 21st century.
ContributorsMahoney, Maren (Author) / Hirt, Paul W. (Thesis advisor) / Tsosie, Rebecca (Committee member) / White, Dave (Committee member) / Arizona State University (Publisher)
Created2011
Description
Despite similar climate, ecosystem, and population size, the cities of Hermosillo, Mexico and Mesa, USA manage their water very differently. Mesa has a stable and resilient system organized around state and federal regulations. Hermosillo, after rapidly industrializing, has not been able to cope with climate change and long-term drought conditions. Water distribution statistics, stakeholders, policy structure, and government organization were combined in an organizational framework to compare the practices of the two cities. These inputs were weighed against the outcomes and the sustainability of each system. While Mesa is part of a massive metropolitan area, Hermosillo is still developing into a metropolitan center and does not have access to the same infrastructure and resources. In Hermosillo local needs are frequently discounted in favor of broad political goals.
ContributorsMoe, Rud Lamb (Author) / Chhetri, Netra (Thesis director) / White, Dave (Committee member) / Robles-Morua, Agustin (Committee member) / Barrett, The Honors College (Contributor) / School of Earth and Space Exploration (Contributor) / School of Sustainability (Contributor) / School of Geographical Sciences and Urban Planning (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
Of all the signals and cues that orchestrate the activities of a social insect colony, the reproductives' fertility pheromones are perhaps the most fundamental. These pheromones regulate reproductive division of labor, a defining characteristic of eusociality. Despite their critical role, reproductive fertility pheromones are not evenly expressed across the development of a social insect colony and may even be absent in the earliest colony stages. In the ant Camponotus floridanus, queens of incipient colonies do not produce the cuticular hydrocarbons that serve as fertility and egg-marking signals in this species. My dissertation investigates the consequences of the dramatic change in the quantity of these pheromones that occurs as the colony grows. C. floridanus workers from large, established colonies use egg surface hydrocarbons to discriminate among eggs. Eggs with surface hydrocarbons typical of eggs laid by established queens are nurtured, whereas eggs lacking these signals (i.e., eggs laid by workers and incipient queens) are destroyed. I characterized how workers from incipient colonies responded to eggs lacking queen fertility hydrocarbons. I found that established-queen-laid eggs, incipient-queen-laid eggs, and worker-laid eggs were not destroyed by workers at this colony stage. Destruction of worker-laid eggs is a form of policing, and theoretical models predict that policing should be strongest in incipient colonies. Since there was no evidence of policing by egg-eating in incipient C. floridanus colonies, I searched for evidence of another policing mechanism at this colony stage. Finding none, I discuss reasons why policing behavior may not be expressed in incipient colonies. I then considered the mechanism that accounts for the change in workers' response to eggs. By manipulating ants' egg experience and testing their egg-policing decisions, I found that ants use a combination of learned and innate criteria to discriminate between targets of care and destruction. Finally, I investigated how the increasing strength of queen-fertility hydrocarbons affects nestmate recognition, which also relies on cuticular hydrocarbons. I found that queens with strong fertility hydrocarbons can be transferred between established colonies without aggression, but they cannot be introduced into incipient colonies. Queens from incipient colonies cannot be transferred into incipient or established colonies.
ContributorsMoore, Dani (Author) / Liebig, Juergen (Thesis advisor) / Gadau, Juergen (Committee member) / Pratt, Stephen (Committee member) / Smith, Brian (Committee member) / Rutowski, Ronald (Committee member) / Arizona State University (Publisher)
Created2012