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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
Since the Convention on Biological Diversity was established in 1992, more importance has been given to the conservation of genetic resources in the international community. In 2001, the International Treaty on Plant Genetic Resources for Food and Agriculture (PGRFA) focused on conserving plant genetic resources, including crop wild relatives (CWR). Some of these genetic resources hold desirable traits--such as transfer of plant disease resistance, improvement of nutritional content, or increased resistance to climate change--that can improve commercial crops. For many years, ex situex situ conservation was the prevalent form of protecting plant genetic resources. However, after PGRFA was published in 1998, in situ techniques have increasingly been applied to conserve wild relatives and enhance domesticated crops.In situ techniques are preferred when possible, since they allow for continued evolution of traits through natural selection, and viability of seed stock through continuous germination and regeneration. In my research, I identified regions in Bolivia and rated them according to their potential for successful programs of iin situ conservation of wild crop relatives. In particular, I analyzed areas according to the following criteria: a) The prevalence of CWRs. b) The impacts of climate change, land use change, population growth, and economic development on the continued viability of CWRs in an area. c) The socio-political and economic conditions that might impede or facilitate successful conservation programs and outcomes. This work focuses on three genera of particular importance in Bolivia: Peanut (Arachis spp.), Potato (Solanum spp.) and Quinoa (Chenopodium spp.). I analyzed the above factors for each municipality in Bolivia (the smallest scale for which appropriate data were available). The results indicate which municipalities are most likely to successfully engage in CWR conservation projects. Finally, I present guidelines for the creation of conservation projects that pinpoint some of the potential risks and difficulties with in situ conservation programs in Bolivia and more generally.
ContributorsGonzalez-Paredes, Cecilia (Author) / Kinzig, Ann (Thesis advisor) / Aggarwal, Rimjhim (Committee member) / Chhetri, Netra (Committee member) / Arizona State University (Publisher)
Created2011
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 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
Description
More than 90 million Americans suffer from low health literacy levels that can lead to detrimental health practices. One of the greatest issues stemming from low health literacy is the misuse of medication, which results in 125,000 deaths per year and close to $200 billion dollars in health care funds (Ngoh 2009). With their implementation into neighborhood settings and consequently the everyday lives of individuals, pharmacies show potential in being great assets towards increasing health literacy on an individual and societal level. However, pharmacists must first be made aware of the opportunities and challenges that exist concerning this effort. Through a three step literature review and corresponding comparative analysis, the results of this study show that pharmacists should focus on four main areas: overall assessment of health literacy in a pharmacy setting, individualization and tailoring of health/ medication plans, development of verbal and written communication tools, and the pharmacist-patient relationship. Each area presents a set of opportunities and challenges that must be accounted for in order to design more effective initiatives and tools in the pharmacists' aim to increase health literacy.
ContributorsMergens, Rianna Lynn (Author) / Robert, Jason Scott (Thesis director) / Maienschein, Jane (Committee member) / Kinzig, Ann (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2013-05
Description
Sustainable urbanism offers a set of best practice planning and design prescriptions intended to reverse the negative environmental consequences of urban sprawl, which dominates new urban development in the United States. Master planned developments implementing sustainable urbanism are proliferating globally, garnering accolades within the planning community and skepticism among social scientists. Despite attention from supporters and critics alike, little is known about the actual environmental performance of sustainable urbanism. This dissertation addresses the reasons for this paucity of evidence and the capacity of sustainable urbanism to deliver the espoused environmental outcomes through alternative urban design and the conventional master planning framework for development through three manuscripts. The first manuscript considers the reasons why geography, which would appear to be a natural empirical home for research on sustainable urbanism, has yet to accumulate evidence that links design alternatives to environmental outcomes or to explain the social processes that mediate those outcomes. It argues that geography has failed to develop a coherent subfield based on nature-city interactions and suggests interdisciplinary bridging concepts to invigorate greater interaction between the urban and nature-society geographic subfields. The subsequent chapters deploy these bridging concepts to empirically examine case-studies in sustainable urbanism. The second manuscript utilizes fine scale spatial data to quantify differences in ecosystem services delivery across three urban designs in two phases of Civano, a sustainable urbanism planned development in Tucson, Arizona, and an adjacent, typical suburban development comparison community. The third manuscript considers the extent to which conventional master planning processes are fundamentally at odds with urban environmental sustainability through interviews with stakeholders involved in three planned developments: Civano (Tucson, Arizona), Mueller (Austin, Texas), and Prairie Crossing (Grayslake, Illinois). Findings from the three manuscripts reveal deep challenges in conceptualizing an empirical area of inquiry on sustainable urbanism, measuring the outcomes of urban design alternatives, and innovating planning practice within the constraints of existing institutions that facilitate conventional development. Despite these challenges, synthesizing the insights of geography and cognate fields holds promise in building an empirical body of knowledge that complements pioneering efforts of planners to innovate urban planning practice through the sustainable urbanism alternative.
ContributorsTurner, Victoria (Author) / Gober, Patricia (Thesis advisor) / Eakin, Hallie (Committee member) / Kinzig, Ann (Committee member) / Talen, Emily (Committee member) / Arizona State University (Publisher)
Created2013
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 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
Description
Waste generation in the U.S. has reached new heights, but the exploitation of Native American lands for waste disposal is nothing new. Many of the negative effects of massive waste production and toxic pollution, such as poor health outcomes and decreased property values, disproportionately burden impoverished, minority communities inside and outside the United States (Brulle and Pellow, 2006). Native American communities have long been exploited for their natural resources and land-use, but in recent decades Indian country has also become a common place to store nuclear, hazardous and municipal wastes. This project is a case study of a local Indian reservation, the Salt River Pima-Maricopa Indian Community, and examined the socio-historical context of the landfill operations in terms of five principles of environmental justice. Each principle was defined and key moments from the SRPMIC's landfill history were discussed to demonstrate ways that the situation has improved, stayed the same or worsened with regard to the rights outlined in each principle. It was concluded that there needs to be an acknowledgement by involved municipalities and industries of the historical context that make the SRPMIC and other nearby Native American communities "ideal" contractors for waste management. Additionally, while the SRPMIC could currently benefit from looking into the principles of environmental justice as a guide to manage past and operating landfills, the Community will have a specific opportunity to revisit these issues under closer scrutiny during the closure of the Salt River Landfill in 2032 in order to ensure more environmentally just outcomes. Finally, it was concluded that scholarship at the intersection of environmental justice and Native American communities should continue because looking closer at the ways that local Native American communities are facing and resisting environmental injustice can serve to develop future models for other communities facing similar challenges to achieving environmental justice.
ContributorsScott, Nicole Danielle (Author) / Kinzig, Ann (Thesis director) / Harlan, Sharon (Committee member) / Maienschein, Jane (Committee member) / Barrett, The Honors College (Contributor) / School of Community Resources and Development (Contributor) / School of Social Transformation (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2015-05
Description
Clean water for drinking, food preparation, and bathing is essential for astronaut health and safety during long duration habitation of the International Space Station (ISS), including future missions to Mars. Despite stringent water treatment and recycling efforts on the ISS, it is impossible to completely prevent microbial contamination of onboard water supplies. In this work, we used a spaceflight analogue culture system to better understand how the microgravity environment can influence the pathogenesis-related characteristics of Burkholderia cepacia complex (Bcc), an opportunistic pathogen previously recovered from the ISS water system. The results of the present study suggest that there may be important differences in how this pathogen can respond and adapt to spaceflight and other low fluid shear environments encountered during their natural life cycles. Future studies are aimed at understanding the underlying mechanisms responsible for these phenotypes.
ContributorsKang, Bianca Younseon (Author) / Nickerson, Cheryl (Thesis director) / Barrila, Jennifer (Committee member) / Ott, Mark (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
This project examines a complex issue in urban ecology: the impact of biodiversity on ecosystem services, and considers how this varies across cities. Data were gathered on multiple economic and ecological parameters for a selection of seven cities around the world and analyzed via multiple linear regression in order to assess any relationships that may be at play. Significance values were then calculated to further define the relationships between the data. Analysis found that both biophysical and socioeconomic factors affected ecosystem services, although not all hypotheses regarding these relationships were met. Conclusions indicate that this model was fairly effective in describing physical drivers of ecosystem services, but were not as clear regarding social drivers. Further study regarding social parameters' effect on ecosystem services is recommended.
ContributorsMcDannald, Lindsay JoAnne (Author) / Perrings, Charles (Thesis director) / Kinzig, Ann (Committee member) / Grimm, Nancy (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor) / School of Sustainability (Contributor)
Created2014-05
Description
Smoke exposure in preterm infants can cause adverse health outcomes in these children. Preterm infants exposed to tobacco smoke have an increased risk for sudden infant death syndrome (SIDS), and metabolic syndrome, asthma, respiratory infections, ear infections and decreased cognitive function compared to healthy infants (Wilson 2011, Blizzard 2003, Bock 2008, Hutchison 1998). A smoking cessation program for parents of pre-term infants at Aultman Hospital in Canton, Ohio was designed to help parents of pre-term infants cease smoking behavior. The outcomes of this program were intended to be the topic of my honors thesis; however, lack of participation in the program shifted my research focus to designing a program, based on a review of "best practices" in the literature, that might increase participation. Among those parents who were asked to participate (N=56), being of low socioeconomic status correlated highest with smoking behavior . Through a literature review, I determined that the best practices to enhance participation for this group would be to include motivational interviewing, the phone number to a toll free quit line, and alternate smoking resources (pamphlets, alternative DVD's) for these Neonatal Intensive Care Unit (NICU) parents at Aultman. By the parent's participation in the Aultman smoking cessation program, long-term health outcomes of their newborns may improve by reducing their exposure to tobacco smoke. These children may grow up in an environment with less smoke exposure, which may decrease their risk of disease (Bock 2008).
ContributorsLach, Laura Elizabeth (Author) / Kinzig, Ann (Thesis director) / Oswalt, Krista (Committee member) / Mossman, Kenneth (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2013-05