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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
Motor learning is the process of improving task execution according to some measure of performance. This can be divided into skill learning, a model-free process, and adaptation, a model-based process. Prior studies have indicated that adaptation results from two complementary learning systems with parallel organization. This report attempted to answer the question of whether a similar interaction leads to savings, a model-free process that is described as faster relearning when experiencing something familiar. This was tested in a two-week reaching task conducted on a robotic arm capable of perturbing movements. The task was designed so that the two sessions differed in their history of errors. By measuring the change in the learning rate, the savings was determined at various points. The results showed that the history of errors successfully modulated savings. Thus, this supports the notion that the two complementary systems interact to develop savings. Additionally, this report was part of a larger study that will explore the organizational structure of the complementary systems as well as the neural basis of this motor learning.
ContributorsRuta, Michael (Author) / Santello, Marco (Thesis director) / Blais, Chris (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / School of Human Evolution & Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Neurostimulation methods currently include deep brain stimulation (DBS), optogenetic, transcranial direct-current stimulation (tDCS), and transcranial magnetic stimulation (TMS). TMS and tDCS are noninvasive techniques whereas DBS and optogenetic require surgical implantation of electrodes or light emitting devices. All approaches, except for optogenetic, have been implemented in clinical settings because they have demonstrated therapeutic utility and clinical efficacy for neurological and psychiatric disorders. When applied for therapeutic applications, these techniques suffer from limitations that hinder the progression of its intended use to treat compromised brain function. DBS requires an invasive surgical procedure that surfaces complications from infection, longevity of electrical components, and immune responses to foreign materials. Both TMS and tDCS circumvent the problems seen with DBS as they are noninvasive procedures, but they fail to produce the spatial resolution required to target specific brain structures. Realizing these restrictions, we sought out to use ultrasound as a neurostimulation modality. Ultrasound is capable of achieving greater resolution than TMS and tDCS, as we have demonstrated a ~2mm lateral resolution, which can be delivered noninvasively. These characteristics place ultrasound superior to current neurostimulation methods. For these reasons, this dissertation provides a developed protocol to use transcranial pulsed ultrasound (TPU) as a neurostimulation technique. These investigations implement electrophysiological, optophysiological, immunohistological, and behavioral methods to elucidate the effects of ultrasound on the central nervous system and raise questions about the functional consequences. Intriguingly, we showed that TPU was also capable of stimulating intact sub-cortical circuits in the anesthetized mouse. These data reveal that TPU can evoke synchronous oscillations in the hippocampus in addition to increasing expression of brain-derived neurotrophic factor (BDNF). Considering these observations, and the ability to noninvasively stimulate neuronal activity on a mesoscale resolution, reveals a potential avenue to be effective in clinical settings where current brain stimulation techniques have shown to be beneficial. Thus, the results explained by this dissertation help to pronounce the significance for these protocols to gain translational recognition.
ContributorsTufail, Yusuf Zahid (Author) / Tyler, William J (Thesis advisor) / Duch, Carsten (Committee member) / Muthuswamy, Jitendran (Committee member) / Santello, Marco (Committee member) / Tillery, Stephen H (Committee member) / Arizona State University (Publisher)
Created2011
Description
An accurate sense of upper limb position is crucial to reaching movements where sensory information about upper limb position and target location is combined to specify critical features of the movement plan. This dissertation was dedicated to studying the mechanisms of how the brain estimates the limb position in space and the consequences of misestimation of limb position on movements. Two independent but related studies were performed. The first involved characterizing the neural mechanisms of limb position estimation in the non-human primate brain. Single unit recordings were obtained in area 5 of the posterior parietal cortex in order to examine the role of this area in estimating limb position based on visual and somatic signals (proprioceptive, efference copy). When examined individually, many area 5 neurons were tuned to the position of the limb in the workspace but very few neurons were modulated by visual feedback. At the population level however decoding of limb position was somewhat more accurate when visual feedback was provided. These findings support a role for area 5 in limb position estimation but also suggest that visual signals regarding limb position are only weakly represented in this area, and only at the population level. The second part of this dissertation focused on the consequences of misestimation of limb position for movement production. It is well known that limb movements are inherently variable. This variability could be the result of noise arising at one or more stages of movement production. Here we used biomechanical modeling and simulation techniques to characterize movement variability resulting from noise in estimating limb position ('sensing noise') and in planning required movement vectors ('planning noise'), and compared that to the variability expected due to noise in movement execution. We found that the effects of sensing and planning related noise on movement variability were dependent upon both the planned movement direction and the initial configuration of the arm and were different in many respects from the effects of execution noise.
ContributorsShi, Ying (Author) / Buneo, Christopher A (Thesis advisor) / Helms Tillery, Stephen (Committee member) / Santello, Marco (Committee member) / He, Jiping (Committee member) / Santos, Veronica (Committee member) / Arizona State University (Publisher)
Created2011
Description
Anticipatory planning of digit positions and forces is critical for successful dexterous object manipulation. Anticipatory (feedforward) planning bypasses the inherent delays in reflex responses and sensorimotor integration associated with reactive (feedback) control. It has been suggested that feedforward and feedback strategies can be distinguished based on the profile of grip and load force rates during the period between initial contact with the object and object lift. However, this has not been validated in tasks that do not constrain digit placement. The purposes of this thesis were (1) to validate the hypothesis that force rate profiles are indicative of the control strategy used for object manipulation and (2) to test this hypothesis by comparing manipulation tasks performed with and without digit placement constraints. The first objective comprised two studies. In the first study an additional light or heavy mass was added to the base of the object. In the second study a mass was added, altering the object's center of mass (CM) location. In each experiment digit force rates were calculated between the times of initial digit contact and object lift. Digit force rates were fit to a Gaussian bell curve and the goodness of fit was compared across predictable and unpredictable mass and CM conditions. For both experiments, a predictable object mass and CM elicited bell shaped force rate profiles, indicative of feedforward control. For the second objective, a comparison of performance between subjects who performed the grasp task with either constrained or unconstrained digit contact locations was conducted. When digit location was unconstrained and CM was predictable, force rates were well fit to a bell shaped curve. However, the goodness of fit of the force rate profiles to the bell shaped curve was weaker for the constrained than the unconstrained digit placement condition. These findings seem to indicate that brain can generate an appropriate feedforward control strategy even when digit placement is unconstrained and an infinite combination of digit placement and force solutions exists to lift the object successfully. Future work is needed that investigates the role digit positioning and tactile feedback has on anticipatory control of object manipulation.
ContributorsCooperhouse, Michael A (Author) / Santello, Marco (Thesis advisor) / Helms Tillery, Stephen (Committee member) / Buneo, Christopher (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
Medical practice surrounding tuberculosis (TB) treatment in two nineteenth-century Scottish charitable hospitals reveals that in developing empirically-positioned constructs of this and related diseases, medical practitioners drew upon social assumptions about women and the working classes, thus reinforcing rather than shedding cultural notions of who becomes ill and why. TB is a social disease, its distribution determined by relationships among human groups; primary among these is the patient-practitioner relationship, owing to the social role of medical treatment in restoring the ill to both health and society. To clarify the influence of cultural context upon the evolution of medical constructs of TB, I examined Glasgow Royal Infirmary (GRI) and Royal Infirmary of Edinburgh (RIE) ward journals, admissions registers, and institution management records from 1794 through 1905. Medical practice at the turn of the nineteenth century was dominated by observation and questioning of the patient, concordant with conceptions of physicians' labor as mental rather than physical. This changed with the introduction of the stethoscope in the 1820s, which together with the dissection of the poor allowed by the 1832 Anatomy Act ushered in disease concepts emphasizing pathological anatomy. Relationships between patient and practitioner also altered at this time, exhibiting distrust and medical dominance. The mid-Victorian era was notable for clinicians' increasing interest in immorality's contributions to ill health, absent in earlier practice and linked to conceptions of women and the working classes as inherently pathological. In 1882, discovery of the tubercle bacillus challenged existing nutritional, hereditary, and environmental explanations for TB. Although practitioners utilized bacteriological methods, this discovery did not revolutionize diagnosis or treatment. Rather, these older models were incorporated with perceived behavioral, environmental, and biological degradation of the working classes, rendering marginalized groups "soil" prepared for the "seeds" of disease -- at risk, but also to blame. This framework, in which marginalized groups contribute to their increased risk for disease through refusal to accord with hegemonically-established "healthy" behavior, persists. As a result, meaningful change in TB rates will need to address these longstanding contributions of social inequality to Western medical treatment.
ContributorsFarnbach Pearson, Amy Walker (Author) / Buikstra, Jane E. (Thesis advisor) / Fuchs, Rachel G (Committee member) / Brewis Slade, Alexandra (Committee member) / Roberts, Charlotte A. (Committee member) / Arizona State University (Publisher)
Created2013