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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
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
Geology and its tangential studies, collectively known and referred to in this thesis as geosciences, have been paramount to the transformation and advancement of society, fundamentally changing the way we view, interact and live with the surrounding natural and built environment. It is important to recognize the value and importance of this interdisciplinary scientific field while reconciling its ties to imperial and colonizing extractive systems which have led to harmful and invasive endeavors. This intersection among geosciences, (environmental) justice studies, and decolonization is intended to promote inclusive pedagogical models through just and equitable methodologies and frameworks as to prevent further injustices and promote recognition and healing of old wounds. By utilizing decolonial frameworks and highlighting the voices of peoples from colonized and exploited landscapes, this annotated syllabus tackles the issues previously described while proposing solutions involving place-based education and the recentering of land within geoscience pedagogical models. (abstract)
ContributorsReed, Cameron E (Author) / Richter, Jennifer (Thesis director) / Semken, Steven (Committee member) / School of Earth and Space Exploration (Contributor, Contributor) / School of Sustainability (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The ASU COVID-19 testing lab process was developed to operate as the primary testing site for all ASU staff, students, and specified external individuals. Tests are collected at various collection sites, including a walk-in site at the SDFC and various drive-up sites on campus; analysis is conducted on ASU campus and results are distributed virtually to all patients via the Health Services patient portal. The following is a literature review on past implementations of various process improvement techniques and how they can be applied to the ABCTL testing process to achieve laboratory goals. (abstract)
ContributorsKrell, Abby Elizabeth (Co-author) / Bruner, Ashley (Co-author) / Ramesh, Frankincense (Co-author) / Lewis, Gabriel (Co-author) / Barwey, Ishna (Co-author) / Myers, Jack (Co-author) / Hymer, William (Co-author) / Reagan, Sage (Co-author) / Compton, Carolyn (Thesis director) / McCarville, Daniel R. (Committee member) / Industrial, Systems & Operations Engineering Prgm (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
For as long as humans have been working, they have been looking for ways to get that work done better, faster, and more efficient. Over the course of human history, mankind has created innumerable spectacular inventions, all with the goal of making the economy and daily life more efficient. Today, innovations and technological advancements are happening at a pace like never seen before, and technology like automation and artificial intelligence are poised to once again fundamentally alter the way people live and work in society. Whether society is prepared or not, robots are coming to replace human labor, and they are coming fast. In many areas artificial intelligence has disrupted entire industries of the economy. As people continue to make advancements in artificial intelligence, more industries will be disturbed, more jobs will be lost, and entirely new industries and professions will be created in their wake. The future of the economy and society will be determined by how humans adapt to the rapid innovations that are taking place every single day. In this paper I will examine the extent to which automation will take the place of human labor in the future, project the potential effect of automation to future unemployment, and what individuals and society will need to do to adapt to keep pace with rapidly advancing technology. I will also look at the history of automation in the economy. For centuries humans have been advancing technology to make their everyday work more productive and efficient, and for centuries this has forced humans to adapt to the modern technology through things like training and education. The thesis will additionally examine the ways in which the U.S. education system will have to adapt to meet the demands of the advancing economy, and how job retraining programs must be modernized to prepare workers for the changing economy.
ContributorsCunningham, Reed P. (Author) / DeSerpa, Allan (Thesis director) / Haglin, Brett (Committee member) / School of International Letters and Cultures (Contributor) / Department of Finance (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Businesses stand to face many uncertainties from the moment they start up to every moment in between. A business can try to recognize them and plan ahead, react to them as they occur, or be rocked by a black swan they never saw coming. How a business deals with unforeseen events can increase its potential for success or failure. With this in mind, there is no better bridge between the here and now and the future than planning for change in order to move a company toward preparing for change, adapting to change and achieving optimal results. Interested in taking a step toward the digital age, Alpha Homes Management, Inc. (Alpha Homes) sought our help to explore ideas and options to take their company to a new level. This Barrett Creative Project was centered on designing a system for Alpha Homes that will replace their outdated paper-based system with a more digital one. This aligns with the project also featured as a capstone project as required by the information technology degree expectations. In supplement to the capstone, and for the Barrett Creative Project, the final product was presented to the owners of Alpha Homes Management, Inc. to be utilized by the business. The end goal is to provide a platform which provides a paperless environment for documentation and bring the company a step closer to having a robust internet presence. Now that the web-based application product has been created and presented, the testing phase can now begin to evaluate its efficacy.
ContributorsBrice-Nash, Tristan (Co-author) / Alfawzan, Mohammad (Co-author) / Doheny, Damien (Thesis director) / Rodriguez, Carlos (Committee member) / Information Technology (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
An ethical dilemma is not a matter of “right” versus “wrong,” but rather it is a situation of conflicting values. A common ethical dilemma is that of honesty versus loyalty—is it better to tell the truth, or remain loyal to the company? In the Japanese culture, truth is circumstantial and can vary with different situations. In a way, the Japanese idea of honesty reflects how highly they value loyalty. This overlap of values results in the lack of an ethical dilemma for the Japanese, which creates a new risk for fraud. Without this struggle, a Japanese employee does not have strong justification against committing fraud if it aligns with his values of honesty and loyalty.
This paper looks at the Japanese values relating to honesty and loyalty to show how much these ideas overlap. The lack of a conflict of values creates a risk for fraud, which will be shown through an analysis of the scandals of two Japanese companies, Toshiba and Olympus. These scandals shine light on the complexity of the ethical dilemma for the Japanese employees; since their sense of circumstantial honesty encourages them to lie if it maintains the harmony of the group, there is little stopping them from committing the fraud that their superiors asked them to commit.
In a global economy, understanding the ways that values impact business and decisions is important for both interacting with others and anticipating potential conflicts, including those that may result in or indicate potential red flags for fraud.
This paper looks at the Japanese values relating to honesty and loyalty to show how much these ideas overlap. The lack of a conflict of values creates a risk for fraud, which will be shown through an analysis of the scandals of two Japanese companies, Toshiba and Olympus. These scandals shine light on the complexity of the ethical dilemma for the Japanese employees; since their sense of circumstantial honesty encourages them to lie if it maintains the harmony of the group, there is little stopping them from committing the fraud that their superiors asked them to commit.
In a global economy, understanding the ways that values impact business and decisions is important for both interacting with others and anticipating potential conflicts, including those that may result in or indicate potential red flags for fraud.
ContributorsTabar, Kelly Ann (Author) / Samuelson, Melissa (Thesis director) / Goldman, Alan (Committee member) / WPC Graduate Programs (Contributor) / W.P. Carey School of Business (Contributor) / School of Accountancy (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This paper will be exploring a marketing plan for a Kpop Fan artist, Jennifer Lee. Kpop is a genre of music originating from South Korea that provides a whole-package entertainment. Fan artists are producers who create produce for the consumption and purchase of other Kpop fans. The paper will consider segmentation and the products and platforms that best target them in order to maximize revenue. A survey was performed with a sample size of 314 participants to find out consumer behavior and preference as well as producer situation. Consumers come from both the United States and abroad. Customers come directly and almost exclusively from followers. Therefore, increasing the number of followers on Instagram is essential to increasing revenue. Jennifer has time, resource, and ability constraints, while the market has limited potential. The conclusion is that Jennifer should become more organized as a business. To grow her following, she should cater more towards the most popular fandoms (BTS), make art tutorials, consider collaborations, and better inform followers of her products/services available for purchase. The social media platforms key to marketing Jennifer's products are Instagram and Twitter. Other platforms to be used to increase exposure are Tumblr, Amino Apps, DeviantArt, Reddit, and YouTube. She must also declutter all of these virtual storefronts of unnecessary content to varying degrees in order to build ease of access and a trustworthy brand image. The best platforms for transaction is a personal store, RedBubble (a website that allows users to sell a variety of products with their uploaded images printed onto them), Patreon, and in-person at conventions.
ContributorsXu, Everest Christine (Author) / Eaton, Kathryn (Thesis director) / Ingram-Waters, Mary (Committee member) / Department of Marketing (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
In recent years, sex trafficking awareness and intervention have skyrocketed in the United States. The 2016 Polaris Hotline Statistics Sheet reports a drastic increase of reported sex trafficking cases over the span of four years, with only 3,409 cases of human trafficking in 2012 and 8,042 in 2016, 73% of which were specifically sex trafficking cases (Polaris Project, 2016). The incidence of sex trafficking has not increased, but rather, attention to sex trafficking and implementation of legislation has increased awareness and reporting (Farrell et al., 2012). While this rise in public awareness of sex trafficking has positively impacted victim identification, there has not been an increase in convicting sex traffickers (Polaris Project, 2016). According to the 2016 Trafficking in Persons Report, 3,000 federal investigations that involved human trafficking, the majority of which specifically involved sex trafficking, were opened in 2015. Of these federal investigations, only 10% led to case prosecutions. Analyzing the relationship of law enforcement, specifically vice units, and victims of sex trafficking is just one of the many ways to address this complex issue. This study consisted of a qualitative analysis of the makeup, training, and policing methods of vice units nationwide. It further aimed to determine the vice officer perceptions regarding the elements that make sex trafficking cases convictable.
ContributorsPradhan, Krishnaa (Author) / Maienschein, Jane (Thesis director) / Kinzig, Ann (Committee member) / Kim, Grace (Committee member) / Barrett, The Honors College (Contributor)
Created2018-05