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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
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 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
A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters.
ContributorsJones, Jeremiah (Author) / Gardner, Carl (Committee member) / Baer, Steven (Committee member) / Crook, Sharon (Committee member) / Kostelich, Eric (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2013
Description
Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess mortality. Age-specific mortality curves show elevated mortality for all age groups, especially the young, and senior sparing effects. The low value for reproduction number indicates that transmissibility was moderately low.
ContributorsJenner, Melinda Eva (Author) / Chowell-Puente, Gerardo (Thesis director) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
This paper explores two areas of study: Colony Collapse Disorder and urban apiculture--the practice of keeping bees in urban areas. Additionally, this paper discusses the ways in which Colony Collapse Disorder has encouraged an increase in urban beekeeping, and the possible role of urban apiculture as a means of combatting the negative effects of Colony Collapse Disorder. The symptoms, history, and possible causes of Colony Collapse Disorder are presented, as well as the important role that honey bees play in human agriculture. Following the discussion of Colony Collapse Disorder is a description of my urban beekeeping apprenticeship at Desert Marigold School where I kept bees, researched various hives, attended a beekeeping workshop in Tucson, and eventually built a hive and established a colony with my mentor. This paper includes a guide to beekeeping basics, as well as a guide to starting a hive based upon the lessons learned during my apprenticeship.
ContributorsRomero, Madelyn Rattan (Author) / Schoon, Michael (Thesis director) / Silcox, Holly (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / School of Geographical Sciences and Urban Planning (Contributor)
Created2015-05
Description
South Mountain is the largest municipal park in the nation. It is a bundled amenity, providing a series of linked services to the surrounding communities. A dataset of 19,209 homes in 155 neighborhoods within three miles of the park was utilized in order to complete a hedonic estimation for two nearby urban villages, Ahwatukee Foothills and South Mountain Village. Measures of access include proximity to the park, trailhead access, and adjacency to the park. Two regressions were estimated, the first including lot characteristics and subdivision fixed effects and the second using the coefficients for each subdivision as the dependent variable. These estimates describe how the location of a house in a subdivision contributes to its conditional mean price. As a result they offer a direct basis for capturing amenities measured at the neighborhood scale on home values. Park proximity, trailhead access and adjacency were found to significantly influence the price of homes at the 5% confidence level in Ahwatukee, but not in South Mountain Village. The results of this study can be applied to issues of environmental justice and park access in determining which areas and attributes of the park are associated with a high premium. Though South Mountain was preserved some time ago, development and future preservation in the City of Phoenix can be informed by such studies.
ContributorsRamakrishna, Saritha Kambhampati (Author) / Abbott, Joshua (Thesis director) / Smith, V. Kerry (Committee member) / Schoon, Michael (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / Economics Program in CLAS (Contributor) / Department of English (Contributor)
Created2015-05
Hiking and Hegemony: Destabilizing the nature/culture and gender binaries through outdoor recreation
Description
This paper explores the contested relationships between nature, culture, and gender. In order to analyze these relationships, we look specifically at outdoor recreation. Furthermore, we employ poststructuralist feminist theory in order to produce three frameworks; the first of which is titled Mother Nature’s Promiscuous Past. Rooted in Old World and colonial values, this framework illustrates the flawed feminization of nature by masculinity, and its subsequent extortion of anything related to femininity — including women and nature itself. This belief barred women from nature, resulting in a lack of access for women to outdoor recreation.
Our second framework, titled The Pleasurable Potential of Outdoor Recreation, cites second-wave feminism as a catalyst for women’s participation in wilderness exploration and outdoor recreation. The work of radical feminists and the women’s liberation movement in 1960s and 1970s empowered women at home, in the workplace, and eventually, in the outdoors; women reclaimed their wilderness, yet they continued to employ Framework One’s feminization of nature. Ecofeminsim brought together nature and women, seeking to bring justice to two groups wronged by the same entity: masculinity. In this context, outdoor recreation is empowering for women.
Despite the potential of Framework Two to reinscribe and better the experiences of women in outdoor recreation, we argue that both Frameworks One and Two perpetuate the gender binary and the nature/culture binary, because they are based upon the notion that women are in fact fundamentally different and separate from men, the notion that nature is an entity separate from culture, or human society, as well as the notion that nature is in fact a feminine entity.
Our third framework, Deer Pay No Mind to Your Genitals, engages poststructuralism, asserting that outdoor recreation and activities that occur in nature can serve to destabilize and deconstruct notions of the gender binary. However, we argue that care must be exercised during this process as not to perpetuate the problematic nature/culture binary, a phenomenon that is unproductive in terms of both sustainability and gender liberation. Outdoor recreation has been used by many as a tool to deconstruct numerous societal constraints, including the gender binary; this, however, continues to attribute escapist and isolationist qualities toward nature, and therefore perpetuating the nature/culture divide. Ultimately, we argue outdoor recreation can and should be used as a tool deconstruct the gender binary, however needs to account for the fact that if nature is helping to construct elements of culture, then the two cannot be separate.
Our second framework, titled The Pleasurable Potential of Outdoor Recreation, cites second-wave feminism as a catalyst for women’s participation in wilderness exploration and outdoor recreation. The work of radical feminists and the women’s liberation movement in 1960s and 1970s empowered women at home, in the workplace, and eventually, in the outdoors; women reclaimed their wilderness, yet they continued to employ Framework One’s feminization of nature. Ecofeminsim brought together nature and women, seeking to bring justice to two groups wronged by the same entity: masculinity. In this context, outdoor recreation is empowering for women.
Despite the potential of Framework Two to reinscribe and better the experiences of women in outdoor recreation, we argue that both Frameworks One and Two perpetuate the gender binary and the nature/culture binary, because they are based upon the notion that women are in fact fundamentally different and separate from men, the notion that nature is an entity separate from culture, or human society, as well as the notion that nature is in fact a feminine entity.
Our third framework, Deer Pay No Mind to Your Genitals, engages poststructuralism, asserting that outdoor recreation and activities that occur in nature can serve to destabilize and deconstruct notions of the gender binary. However, we argue that care must be exercised during this process as not to perpetuate the problematic nature/culture binary, a phenomenon that is unproductive in terms of both sustainability and gender liberation. Outdoor recreation has been used by many as a tool to deconstruct numerous societal constraints, including the gender binary; this, however, continues to attribute escapist and isolationist qualities toward nature, and therefore perpetuating the nature/culture divide. Ultimately, we argue outdoor recreation can and should be used as a tool deconstruct the gender binary, however needs to account for the fact that if nature is helping to construct elements of culture, then the two cannot be separate.
ContributorsPolick-Kirkpatrick, Kaelyn (Co-author) / Downing, Haley Marie (Co-author) / Dove-Viebahn, Aviva (Thesis director) / Schoon, Michael (Committee member) / School of Sustainability (Contributor) / School of Social Transformation (Contributor) / Economics Program in CLAS (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.
ContributorsSnyder, Lena Haley (Author) / Kostelich, Eric (Thesis director) / Frakes, David (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05