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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

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
Does School Participatory Budgeting Increase Students’ Political Efficacy? Bandura’s “Sources,” Civic Pedagogy, and Education for Democracy
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

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
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Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
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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

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
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Description
Consideration of both biological and human-use dynamics in coupled social-ecological systems is essential for the success of interventions such as marine reserves. As purely human institutions, marine reserves have no direct effects on ecological systems. Consequently, the success of a marine reserve depends on managers` ability to alter human behavior

Consideration of both biological and human-use dynamics in coupled social-ecological systems is essential for the success of interventions such as marine reserves. As purely human institutions, marine reserves have no direct effects on ecological systems. Consequently, the success of a marine reserve depends on managers` ability to alter human behavior in the direction and magnitude that supports reserve objectives. Further, a marine reserve is just one component in a larger coupled social-ecological system. The social, economic, political, and biological landscape all determine the social acceptability of a reserve, conflicts that arise, how the reserve interacts with existing fisheries management, accuracy of reserve monitoring, and whether the reserve is ultimately able to meet conservation and fishery enhancement goals. Just as the social-ecological landscape is critical at all stages for marine reserve, from initial establishment to maintenance, the reserve in turn interacts with biological and human use dynamics beyond its borders. Those interactions can lead to the failure of a reserve to meet management goals, or compromise management goals outside the reserve. I use a bio-economic model of a fishery in a spatially patchy environment to demonstrate how the pre-reserve fisheries management strategy determines the pattern of fishing effort displacement once the reserve is established, and discuss the social, political, and biological consequences of different patterns for the reserve and the fishery. Using a stochastic bio-economic model, I demonstrate how biological and human use connectivity can confound the accurate detection of reserve effects by violating assumptions in the quasi-experimental framework. Finally, I examine data on recreational fishing site selection to investigate changes in response to the announcement of enforcement of a marine reserve in the Gulf of California, Mexico. I generate a scale of fines that would fully or partially protect the reserve, providing a data-driven way for managers to balance biological and socio-economic goals. I suggest that natural resource managers consider human use dynamics with the same frequency, rigor, and tools as they do biological stocks.
ContributorsFujitani, Marie (Author) / Abbott, Joshua (Thesis advisor) / Fenichel, Eli (Thesis advisor) / Gerber, Leah (Committee member) / Anderies, John (Committee member) / Arizona State University (Publisher)
Created2014
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Description
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity

This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2012
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DescriptionThis paper provides an analysis of the differences in impacts made by companies that promote their sustainability efforts. A comparison of companies reveals that the ones with greater supply chain influence and larger consumer bases can make more concrete progress in terms of accomplishment for the sustainability realm.
ContributorsBeaubien, Courtney Lynn (Author) / Anderies, John (Thesis director) / Allenby, Brad (Committee member) / Janssen, Marco (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2013-05
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Description

Engineered pavements cover a large fraction of cities and offer significant potential for urban heat island mitigation. Though rapidly increasing research efforts have been devoted to the study of pavement materials, thermal interactions between buildings and the ambient environment are mostly neglected. In this study, numerical models featuring a realistic

Engineered pavements cover a large fraction of cities and offer significant potential for urban heat island mitigation. Though rapidly increasing research efforts have been devoted to the study of pavement materials, thermal interactions between buildings and the ambient environment are mostly neglected. In this study, numerical models featuring a realistic representation of building-environment thermal interactions, were applied to quantify the effect of pavements on the urban thermal environment at multiple scales. It was found that performance of pavements inside the canyon was largely determined by the canyon geometry. In a high-density residential area, modifying pavements had insignificant effect on the wall temperature and building energy consumption. At a regional scale, various pavement types were also found to have a limited cooling effect on land surface temperature and 2-m air temperature for metropolitan Phoenix. In the context of global climate change, the effect of pavement was evaluated in terms of the equivalent CO2 emission. Equivalent CO2 emission offset by reflective pavements in urban canyons was only about 13.9e46.6% of that without building canopies, depending on the canyon geometry. This study revealed the importance of building-environment thermal interactions in determining thermal conditions inside the urban canopy.

ContributorsYang, Jiachuan (Author) / Wang, Zhi-Hua (Author) / Kaloush, Kamil (Author) / Dylla, Heather (Author)
Created2016-08-22
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Description

In this synthesis, we hope to accomplish two things: 1) reflect on how the analysis of the new archaeological cases presented in this special feature adds to previous case studies by revisiting a set of propositions reported in a 2006 special feature, and 2) reflect on four main ideas that

In this synthesis, we hope to accomplish two things: 1) reflect on how the analysis of the new archaeological cases presented in this special feature adds to previous case studies by revisiting a set of propositions reported in a 2006 special feature, and 2) reflect on four main ideas that are more specific to the archaeological cases: i) societal choices are influenced by robustness–vulnerability trade-offs, ii) there is interplay between robustness–vulnerability trade-offs and robustness–performance trade-offs, iii) societies often get locked in to particular strategies, and iv) multiple positive feedbacks escalate the perceived cost of societal change. We then discuss whether these lock-in traps can be prevented or whether the risks associated with them can be mitigated. We conclude by highlighting how these long-term historical studies can help us to understand current society, societal practices, and the nexus between ecology and society.

ContributorsSchoon, Michael (Author) / Fabricius, Christo (Author) / Anderies, John (Author) / Nelson, Margaret (Author) / College of Liberal Arts and Sciences (Contributor)
Created2011
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Description

What relationships can be understood between resilience and vulnerability in social-ecological systems? In particular, what vulnerabilities are exacerbated or ameliorated by different sets of social practices associated with water management? These questions have been examined primarily through the study of contemporary or recent historic cases. Archaeology extends scientific observation beyond

What relationships can be understood between resilience and vulnerability in social-ecological systems? In particular, what vulnerabilities are exacerbated or ameliorated by different sets of social practices associated with water management? These questions have been examined primarily through the study of contemporary or recent historic cases. Archaeology extends scientific observation beyond all social memory and can thus illuminate interactions occurring over centuries or millennia. We examined trade-offs of resilience and vulnerability in the changing social, technological, and environmental contexts of three long-term, pre-Hispanic sequences in the U.S. Southwest: the Mimbres area in southwestern New Mexico (AD 650–1450), the Zuni area in northern New Mexico (AD 850–1540), and the Hohokam area in central Arizona (AD 700–1450). In all three arid landscapes, people relied on agricultural systems that depended on physical and social infrastructure that diverted adequate water to agricultural soils. However, investments in infrastructure varied across the cases, as did local environmental conditions. Zuni farming employed a variety of small-scale water control strategies, including centuries of reliance on small runoff agricultural systems; Mimbres fields were primarily watered by small-scale canals feeding floodplain fields; and the Hohokam area had the largest canal system in pre-Hispanic North America. The cases also vary in their historical trajectories: at Zuni, population and resource use remained comparatively stable over centuries, extending into the historic period; in the Mimbres and Hohokam areas, there were major demographic and environmental transformations. Comparisons across these cases thus allow an understanding of factors that promote vulnerability and influence resilience in specific contexts.

ContributorsNelson, Margaret (Author) / Kintigh, Keith (Author) / Abbott, David (Author) / Anderies, John (Author) / College of Liberal Arts and Sciences (Contributor)
Created2010