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- Creators: Department of Information Systems
- Resource Type: Text
- Status: Published
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
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
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
The advertising agency, in its variety of forms, is one of the most powerful forces in the modern world. Its products are seen globally through various multimedia outlets and they strongly impact culture and economy. Since its conception in 1843 by Volney Palmer, the advertising agency has evolved into the recognizable—and unrecognizable—firms scattered around the world today. In the United States alone, there are roughly 13.4 thousand agencies, many of which also have branches in other countries. The evolution of the modern advertising agency coincided with, and even preceded, some of the major inflection points in history. Understanding how and why changes in advertising agencies affected these inflection points provides a glimpse of understanding into the relationship between advertising, business, and societal values.
In the pages ahead we will explore the future of the advertising industry. We will analyze our research to uncover the underlying trends pointing towards what is to come and work to apply those explanations to our understanding of advertising in the future.
In the pages ahead we will explore the future of the advertising industry. We will analyze our research to uncover the underlying trends pointing towards what is to come and work to apply those explanations to our understanding of advertising in the future.
ContributorsHarris, Chase (Co-author) / Potthoff, Zachary (Co-author) / Gray, Nancy (Thesis director) / Samper, Adriana (Committee member) / Department of Information Systems (Contributor) / Department of Marketing (Contributor) / Herberger Institute for Design and the Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The town of Guadalupe, Arizona has a long history of divided residents and high poverty rates. The high levels of poverty in the town can be attributed to numerous factors, most notably high rates of drug abuse, low high school graduation rates, and teen pregnancy. The town has named one of its most pressing issues of today to be youth disengagement. There are currently a handful of residents and community members passionate about finding a solution to this issue. After working with Guadalupe's Ending Hunger Task Force and resident youth, I set out to create a program design for a Guadalupe Youth Council. This council will contribute to combating youth disengagement. The program design will assist the task force in creating a standing youth council and deciding on the structure and role the council has in the town. I will offer learning outcomes and suggestions to the Task Force, youth council staff, and the youth of the youth council. This study contains an analysis of relevant literature, youth focus group results and data, and how the information gathered has contributed to the design of the youth council. The results of this study contain recommendations about four themes within the program design of a youth council: size, recruitment, activities and engagement, and adult support. The results also explore how the youth council will impact the power, policy, and behavior of Guadalupe youth.
ContributorsBalderas, Erica Theresa (Author) / Wang, Lili (Thesis director) / Avalos, Francisco (Committee member) / School of Community Resources and Development (Contributor) / Department of Information Systems (Contributor) / W.P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This thesis project was conducted to create a practical tool to help micro and small local food enterprises identify potential strategies and sources of finance. Currently, many of these enterprises are unable to obtain the financial capital needed to start-up or maintain operations.
Sources and strategies of finance studied and ultimately included in the tool were Loans, Equity, Membership, Crowdfunding, and Grants. The tool designed was a matrix that takes into account various criteria of the business (e.g. business lifecycle, organizational structure, business performance) and generates a financial plan based on these criteria and how they align with the selected business strategies. After strategies are found, stakeholders can search through an institutional database created in conjunction with the matrix tool to find possible institutional providers of financing that relate to the strategy or strategies found.
The tool has shown promise in identifying sources of finance for micro and small local food enterprises in practical use with hypothetical business cases, however further practical use is necessary to provide further input and revise the tool as needed. Ultimately, the tool will likely become fully user-friendly and stakeholders will not need the assistance of another expert helping them to use it. Finally, despite the promise of the tool itself, the fundamental and underlying problem that many of these businesses face (lack of infrastructure and knowledge) still exists, and while this tool can also help capacity-building efforts towards both those seeking and those providing finance, an institutional attitude adjustment towards social and alternative enterprises is necessary in order to further simplify the process of obtaining finance.
Sources and strategies of finance studied and ultimately included in the tool were Loans, Equity, Membership, Crowdfunding, and Grants. The tool designed was a matrix that takes into account various criteria of the business (e.g. business lifecycle, organizational structure, business performance) and generates a financial plan based on these criteria and how they align with the selected business strategies. After strategies are found, stakeholders can search through an institutional database created in conjunction with the matrix tool to find possible institutional providers of financing that relate to the strategy or strategies found.
The tool has shown promise in identifying sources of finance for micro and small local food enterprises in practical use with hypothetical business cases, however further practical use is necessary to provide further input and revise the tool as needed. Ultimately, the tool will likely become fully user-friendly and stakeholders will not need the assistance of another expert helping them to use it. Finally, despite the promise of the tool itself, the fundamental and underlying problem that many of these businesses face (lack of infrastructure and knowledge) still exists, and while this tool can also help capacity-building efforts towards both those seeking and those providing finance, an institutional attitude adjustment towards social and alternative enterprises is necessary in order to further simplify the process of obtaining finance.
ContributorsDwyer, Robert Francis (Author) / Wiek, Arnim (Thesis director) / Forrest, Nigel (Committee member) / Department of Finance (Contributor) / Department of Information Systems (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
RecyclePlus is an iOS mobile application that allows users to be knowledgeable in the realms of sustainability. It gives encourages users to be environmental responsible by providing them access to recycling information. In particular, it allows users to search up certain materials and learn about its recyclability and how to properly dispose of the material. Some searches will show locations of facilities near users that collect certain materials and dispose of the materials properly. This is a full stack software project that explores open source software and APIs, UI/UX design, and iOS development.
ContributorsTran, Nikki (Author) / Ganesh, Tirupalavanam (Thesis director) / Meuth, Ryan (Committee member) / Watts College of Public Service & Community Solut (Contributor) / Department of Information Systems (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
In the past ten years, the United States’ sound recording industries have experienced significant decreases in employment opportunities for aspiring audio engineers from economic imbalances in the music industry’s digital streaming era and reductions in government funding for career and technical education (CTE). The Recording Industry Association of America reports promises of music industry sustainability based on increasing annual revenues in paid streaming services and artists’ high creative demand. The rate of new audio engineer entries in the sound recording subsection of the music industry is not viable to support streaming artists’ high demand to engineer new music recordings. Offering CTE programs in secondary education is rare for aspiring engineers with insufficient accessibility to pursue a post-secondary or vocational education because of financial and academic limitations. These aspiring engineers seek alternatives for receiving an informal education in audio engineering on the Internet using video sharing services like YouTube to search for tutorials and improve their engineering skills. The shortage of accessible educational materials on the Internet restricts engineers from advancing their own audio engineering education, reducing opportunities to enter a desperate job market in need of independent, home studio-based engineers. Content creators on YouTube take advantage of this situation and commercialize their own video tutorial series for free and selling paid subscriptions to exclusive content. This is misleading for newer engineers because these tutorials omit important understandings of fundamental engineering concepts. Instead, content creators teach inflexible engineering methodologies that are mostly beneficial to their own way of thinking. Content creators do not often assess the incompatibility of teaching their own methodologies to potential entrants in a profession that demands critical thinking skills requiring applied fundamental audio engineering concepts and techniques. This project analyzes potential solutions to resolve the deficiencies in online audio engineering education and experiments with structuring simple, deliverable, accessible educational content and materials to new entries in audio engineering. Designing clear, easy to follow material to these new entries in audio engineering is essential for developing a strong understanding for the application of fundamental concepts in future engineers’ careers. Approaches to creating and designing educational content requires translating complex engineering concepts through simplified mediums that reduce limitations in learning for future audio engineers.
ContributorsBurns, Triston Connor (Author) / Tobias, Evan (Thesis director) / Libman, Jeff (Committee member) / Department of Information Systems (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
This paper looks at the growth of influencer marketing in application and how it has shifted the relationship between brands and consumers. Barriers to enter the space and methods of practice are discussed and analyzed to project the accessibility of obtaining influencer status. Best practices for brands and influencers are outlined based on research, and key findings are analyzed from interviewed participants that play an active role in the field. Another component of the paper includes the discussion of the significance of platform dependence regarding influencers and brands using social media channels to reach consumers. The dynamic of the relationship that exists between consumers, brands and platforms is demonstrated through a model to demonstrate the interdependence of the relationship. The final component of the paper involves the exploration of the field as an active participant through an experiment that was conducted by the researcher on behalf of the question: can anyone be an influencer? The answer to this question is explored through personal accounts on the journey during an eight month process of testing content creation and promotion to build awareness and increase engagement. The barriers to enter the space as an influencer and to collaborate with brands is addressed through the process of testing tactics and strategies on social channels, along with travel expeditions across Arizona to contribute to content creation purposed into blog articles. The findings throughout the paper are conclusive that the value of influencer marketing is increasing as more brands validate and utilize this method in their marketing efforts.
ContributorsDavis, Natalie Marie (Author) / Giles, Bret (Thesis director) / Schlacter, John (Committee member) / Department of Information Systems (Contributor) / Department of Marketing (Contributor) / Walter Cronkite School of Journalism and Mass Communication (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Pandora is a play exploring our relationship with gendered technology through the lens of artificial intelligence. Can women be subjective under patriarchy? Do robots who look like women have subjectivity? Hoping to create a better version of ourselves, The Engineer must navigate the loss of her creation, and Pandora must navigate their new world. The original premiere run was March 27-28, 2018, original cast: Caitlin Andelora, Rikki Tremblay, and Michael Tristano Jr.
ContributorsToye, Abigail Elizabeth (Author) / Linde, Jennifer (Thesis director) / Abele, Kelsey (Committee member) / Department of Information Systems (Contributor) / Economics Program in CLAS (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05