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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
In an effort to address the lack of literature in on-campus active travel, this study aims to investigate the following primary questions:<br/>• What are the modes that students use to travel on campus?<br/>• What are the motivations that underlie the mode choice of students on campus?<br/>My first stage of research involved a series of qualitative investigations. I held one-on-one virtual interviews with students in which I asked them questions about the mode they use and why they feel that their chosen mode works best for them. These interviews served two functions. First, they provided me with insight into the various motivations underlying student mode choice. Second, they provided me with an indication of what explanatory variables should be included in a model of mode choice on campus.<br/>The first half of the research project informed a quantitative survey that was released via the Honors Digest to attract student respondents. Data was gathered on travel behavior as well as relevant explanatory variables.<br/>My analysis involved developing a logit model to predict student mode choice on campus and presenting the model estimation in conjunction with a discussion of student travel motivations based on the qualitative interviews. I use this information to make a recommendation on how campus infrastructure could be modified to better support the needs of the student population.
ContributorsMirtich, Laura Christine (Author) / Salon, Deborah (Thesis director) / Fang, Kevin (Committee member) / School of Public Affairs (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
This thesis focuses on the theoretical work done to determine thermodynamic properties of a chalcopyrite thin-film material for use as a photovoltaic material in a tandem device. The material of main focus here is ZnGeAs2, which was chosen for the relative abundance of constituents, favorable photovoltaic properties, and good lattice matching with ZnSnP2, the other component in this tandem device. This work is divided into two main chapters, which will cover: calculations and method to determine the formation energy and abundance of native point defects, and a model to calculate the vapor pressure over a ternary material from first-principles. The purpose of this work is to guide experimental work being done in tandem to synthesize ZnGeAs2 in thin-film form with high enough quality such that it can be used as a photovoltaic. Since properties of photovoltaic depend greatly on defect concentrations and film quality, a theoretical understanding of how laboratory conditions affect these properties is very valuable. The work done here is from first-principles and utilizes density functional theory using the local density approximation. Results from the native point defect study show that the zinc vacancy (VZn) and the germanium antisite (GeZn) are the more prominent defects; which most likely produce non-stoichiometric films. The vapor pressure model for a ternary system is validated using known vapor pressure for monatomic and binary test systems. With a valid ternary system vapor pressure model, results show there is a kinetic barrier to decomposition for ZnGeAs2.
ContributorsTucker, Jon R (Author) / Van Schilfgaarde, Mark (Thesis advisor) / Newman, Nathan (Committee member) / Adams, James (Committee member) / Arizona State University (Publisher)
Created2011
Description
Defines the concept of the arcology as conceived by architect Paolo Soleri. Arcology combines "architecture" and "ecology" and explores a visionary notion of a self-contained urban community that has agricultural, commercial, and residential facilities under one roof. Two real-world examples of these projects are explored: Arcosanti, AZ and Masdar City, Abu Dhabi, UAE. Key aspects of the arcology that could be applied to an existing urban fabric are identified, such as urban design fostering social interaction, reduction of automobile dependency, and a development pattern that combats sprawl. Through interviews with local representatives, a holistic approach to applying arcology concepts to the Phoenix Metro Area is devised.
ContributorsSpencer, Sarah Anne (Author) / Manuel-Navarrete, David (Thesis director) / Salon, Deborah (Committee member) / Barrett, The Honors College (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Sustainability (Contributor)
Created2015-05
Description
Electromigration in metal interconnects is the most pernicious failure mechanism in semiconductor integrated circuits (ICs). Early electromigration investigations were primarily focused on aluminum interconnects for silicon-based ICs. An alternative metallization compatible with gallium arsenide (GaAs) was required in the development of high-powered radio frequency (RF) compound semiconductor devices operating at higher current densities and elevated temperatures. Gold-based metallization was implemented on GaAs devices because it uniquely forms a very low resistance ohmic contact and gold interconnects have superior electrical and thermal conductivity properties. Gold (Au) was also believed to have improved resistance to electromigration due to its higher melting temperature, yet electromigration reliability data on passivated Au interconnects is scarce and inadequate in the literature. Therefore, the objective of this research was to characterize the electromigration lifetimes of passivated Au interconnects under precisely controlled stress conditions with statistically relevant quantities to obtain accurate model parameters essential for extrapolation to normal operational conditions. This research objective was accomplished through measurement of electromigration lifetimes of large quantities of passivated electroplated Au interconnects utilizing high-resolution in-situ resistance monitoring equipment. Application of moderate accelerated stress conditions with a current density limited to 2 MA/cm2 and oven temperatures in the range of 300°C to 375°C avoided electrical overstress and severe Joule-heated temperature gradients. Temperature coefficients of resistance (TCRs) were measured to determine accurate Joule-heated Au interconnect film temperatures. A failure criterion of 50% resistance degradation was selected to prevent thermal runaway and catastrophic metal ruptures that are problematic of open circuit failure tests. Test structure design was optimized to reduce resistance variation and facilitate failure analysis. Characterization of the Au microstructure yielded a median grain size of 0.91 ìm. All Au lifetime distributions followed log-normal distributions and Black's model was found to be applicable. An activation energy of 0.80 ± 0.05 eV was measured from constant current electromigration tests at multiple temperatures. A current density exponent of 1.91 was extracted from multiple current densities at a constant temperature. Electromigration-induced void morphology along with these model parameters indicated grain boundary diffusion is dominant and the void nucleation mechanism controlled the failure time.
ContributorsKilgore, Stephen (Author) / Adams, James (Thesis advisor) / Schroder, Dieter (Thesis advisor) / Krause, Stephen (Committee member) / Gaw, Craig (Committee member) / Arizona State University (Publisher)
Created2013
Description
The contemporary architectural pedagogy is far removed from its ancestry: the classical Beaux-Arts and polytechnic schools of the 19th century and the Bauhaus and Vkhutemas models of the modern period. Today, the "digital" has invaded the academy and shapes pedagogical practices, epistemologies, and ontologies within it, and this invasion is reflected in teaching practices, principles, and tools. Much of this digital integration goes unremarked and may not even be explicitly taught. In this qualitative research project, interviews with 18 leading architecture lecturers, professors, and deans from programs across the United States were conducted. These interviews focused on advanced practices of digital architecture, such as the use of digital tools, and how these practices are viewed. These interviews yielded a wealth of information about the uses (and abuses) of advanced digital technologies within the architectural academy, and the results were analyzed using the methods of phenomenology and grounded theory. Most schools use digital technologies to some extent, although this extent varies greatly. While some schools have abandoned hand-drawing and other hand-based craft almost entirely, others have retained traditional techniques and use digital technologies sparingly. Reasons for using digital design processes include industry pressure as well as the increased ability to solve problems and the speed with which they could be solved. Despite the prevalence of digital design, most programs did not teach related design software explicitly, if at all, instead requiring students (especially graduate students) to learn to use them outside the design studio. Some of the problems with digital design identified in the interviews include social problems such as alienation as well as issues like understanding scale and embodiment of skill.
ContributorsAlqabandy, Hamad (Author) / Brandt, Beverly (Thesis advisor) / Mesch, Claudia (Committee member) / Newton, David (Committee member) / Arizona State University (Publisher)
Created2012
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 thesis is a qualitative research study that focuses on siblings of children with Autistic Spectrum Disorder (ASD). Even though it is expected that having a child with ASD in the family will influence the whole family including siblings of the child with ASD, the sibling population is rarely included in research related to children with ASD, and there is only limited services available for them. This exploratory study (n=6) is aimed at better understanding the siblings' lives in their family settings in order to identify the siblings' unmet needs and determine how they have been influenced by the child with ASD. This study is also aimed at identifying the most appropriate support for the siblings to help them cope better. The study followed the Resiliency Model of Family Stress, Adjustment, and Adaptation and a narrative theory approach. An in-depth interview with the parents was conducted for the study, so the findings reflect the parents' perception of the siblings. All the themes emerged into two categories: life in the family setting and supports. The findings indicate that the families are striving for balance between the siblings and the children with ASD, but still tend to focus more on the children with ASD. Also, the families tend to have autonomous personal support systems. The parents tend to perceive that these personal support systems are good enough for the siblings; therefore, the parents do not feel that formal support for the siblings was necessary. As a result of the findings, recommendations are made for the organizations that work with individuals with ASD to provide more appropriate services for the families of children with ASD, including siblings. Also, recommendations are made for future studies to clarify more factors related to the siblings due to the limitation of this study; the siblings' lives were reflected vicariously via the parents.
ContributorsJeong, Seong Hae (Author) / Marsiglia, Flavio F (Thesis advisor) / Ayers, Stephanie (Committee member) / Adams, James (Committee member) / Arizona State University (Publisher)
Created2013
Description
In the middle of the 20th century, juried annuals of Native American painting in art museums were unique opportunities because of their select focus on two-dimensional art as opposed to "craft" objects and their inclusion of artists from across the United States. Their first fifteen years were critical for patronage and widespread acceptance of modern easel painting. Held at the Philbrook Art Center in Tulsa (1946-1979), the Denver Art Museum (1951-1954), and the Museum of New Mexico Art Gallery in Santa Fe (1956-1965), they were significant not only for the accolades and prestige they garnered for award winners, but also for setting standards of quality and style at the time. During the early years of the annuals, the art was changing, some moving away from conventional forms derived from the early art training of the 1920s and 30s in the Southwest and Oklahoma, and incorporating modern themes and styles acquired through expanded opportunities for travel and education. The competitions reinforced and reflected a variety of attitudes about contemporary art which ranged from preserving the authenticity of the traditional style to encouraging experimentation. Ultimately becoming sites of conflict, the museums that hosted annuals contested the directions in which artists were working. Exhibition catalogs, archived documents, and newspaper and magazine articles about the annuals provide details on the exhibits and the changes that occurred over time. The museums' guidelines and motivations, and the statistics on the award winners reveal attitudes toward the art. The institutions' reactions in the face of controversy and their adjustments to the annuals' guidelines impart the compromises each made as they adapted to new trends that occurred in Native American painting over a fifteen year period. This thesis compares the approaches of three museums to their juried annuals and establishes the existence of a variety of attitudes on contemporary Native American painting from 1946-1960. Through this collection of institutional views, the competitions maintained a patronage base for traditional style painting while providing opportunities for experimentation, paving the way for the great variety and artistic progress of Native American painting today.
ContributorsPeters, Stephanie (Author) / Duncan, Kate (Thesis advisor) / Fahlman, Betsy (Thesis advisor) / Mesch, Claudia (Committee member) / Arizona State University (Publisher)
Created2012
Description
This report will review the mechanical and microstructural properties of the refractory element rhenium (Re) deposited using Laser Additive Manufacturing (LAM). With useable structural strength over 2200 °C, existing applications up to 2760 °C, very high strength, ductility and chemical resistance, interest in Re is understandable. This study includes data about tensile properties including tensile data up to 1925 °C, fracture modes, fatigue and microstructure including deformation systems and potential applications of that information. The bulk mechanical test data will be correlated with nanoindentation and crystallographic examination. LAM properties are compared to the existing properties found in the literature for other manufacturing processes. The literature indicates that Re has three significant slip systems but also twins as part of its deformation mechanisms. While it follows the hcp metal characteristics for deformation, it has interesting and valuable extremes such as high work hardening, potentially high strength, excellent wear resistance and superior elevated temperature strength. These characteristics are discussed in detail.
ContributorsAdams, Robbie (Author) / Chawla, Nikhilesh (Thesis advisor) / Adams, James (Committee member) / Krause, Stephen (Committee member) / Arizona State University (Publisher)
Created2012