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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 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
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
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
DescriptionA small-scale aquaponic system was created to demonstrate the sustainable properties of the system as well as the effectiveness of raising fish and plants symbiotically.
ContributorsSerna, Desiree Marie (Author) / Schoon, Michael (Thesis director) / Peterson, Greg (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2014-05
Description
The following Student Sustainability Consultant's Portfolio was created with the intention of being duplicated and utilized by Arizona State University (ASU) students to build their own Portfolio and to help prepare them for success after graduation. Student Consultants in GreenLight Solutions (GLS) are in a unique position to prepare themselves to create value for organizations while in school, and then continue to after graduation. When I enrolled in the School of Sustainability as an undergraduate transfer student I heard some constructive criticism from graduates of the school. Those students shared that while they had attained a great theoretical understanding of the science of sustainability, they lacked the ability to apply their knowledge in a practical way. They were struggling with finding work in their field because they could not communicate to employers how their knowledge was useful. They did not know how to apply their sustainability knowledge to create value for an organization. I did not want to have that same problem when I graduated. Enter GreenLight Solutions.
ContributorsKeleher, Kevin Robert (Author) / Schoon, Michael (Thesis director) / Basile, George (Committee member) / Buch, Rajesh (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / Department of Supply Chain Management (Contributor)
Created2013-12
Description
My project is an examination of the process ASU Tempe campus took to institute an organics collection program. Working from a sustainability science perspective I demonstrate the structural and logistical barriers faced during program creation and expansion. My examination lead to the creation of a manual designed as a tool for other organizations in which I document ASU's process and provide information on key steps and procedures necessary to implement a unique organics collection program.
ContributorsSchumacher, Katherine Marie (Author) / Schoon, Michael (Thesis director) / Brundiers, Katja (Committee member) / Levine, Alana (Committee member) / Barrett, The Honors College (Contributor) / T. Denny Sanford School of Social and Family Dynamics (Contributor) / School of Sustainability (Contributor)
Created2013-05
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 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
Description
The purpose of this thesis is to compare ecolabeling to conservation easements for facilitating multi-use land between food production and conservation. Biodiversity has been on the decline as human agriculture uses more land. According to Encyclopedia Britannica “Half of the world’s habitable land (some 51 million square km [19.7 million square miles]) has been converted to agriculture, and some 77 percent of agricultural land (some 40 million square km [15.4 million square miles]) is used for grazing by cattle, sheep, goats, and other livestock. This massive conversion of forests, wetlands, grasslands, and other terrestrial ecosystems has produced a 60 percent decline (on average) in the number of vertebrates worldwide since 1970”(Rafferty 2010). The purpose of this paper is to explore ways individual landowners and private businesses can continue to operate profitably on their land while reversing the harmful loss to biodiversity observed in the past 50 years. Two of the most popular methods of achieving conservation on workable land are ecolabeling and conservation easements.
ContributorsWilcox, Christopher James (Author) / Leonard, Brian (Thesis director) / Schoon, Michael (Committee member) / Dean, W.P. Carey School of Business (Contributor) / Department of Supply Chain Management (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12