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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

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 paper analyzes the impact of the December 2022 winter storm on Southwest Airlines (SWA). The storm caused delays and cancellations for all airlines, but SWA was the only major airline that was unable to recover fully. The disruption was unique due to the higher volume of people traveling during

This paper analyzes the impact of the December 2022 winter storm on Southwest Airlines (SWA). The storm caused delays and cancellations for all airlines, but SWA was the only major airline that was unable to recover fully. The disruption was unique due to the higher volume of people traveling during the holiday season and the lack of good alternative transportation for stranded passengers. The paper explains SWA's point-to-point (PTP) model, which allows them to offer competitive ticket prices, and organizational factors that have helped them hold a significant market share. The paper also discusses previous failures of SWA's IT and aircraft maintenance management systems and the outdated crewing system, which were not addressed until after the storm. The paper uses AnyLogic agent based modeling to investigate why SWA was so affected and why it took them so long to recover.

ContributorsBray, Mariana (Author) / McCarville, Daniel (Thesis director) / Kucukozyigit, Ali (Committee member) / Barrett, The Honors College (Contributor) / Industrial, Systems & Operations Engineering Prgm (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2023-05
Description
Within recent years, the drive for increased sustainability within large corporations has drastically increased. One critical measure within sustainability is the diversion rate, or the amount of waste diverted from landfills to recycling, repurposing, or reselling. There are a variety of different ways in which a company can improve their

Within recent years, the drive for increased sustainability within large corporations has drastically increased. One critical measure within sustainability is the diversion rate, or the amount of waste diverted from landfills to recycling, repurposing, or reselling. There are a variety of different ways in which a company can improve their diversion rate, such as repurposing paper. A conventional method would be to simply have a recycling bin for collecting all paper, but the concern for large companies then becomes a security issue as confidential papers may not be safe in a traditional recycling bin. Salt River Project (SRP) has tackled this issue by hiring a third-party vendor (TPV) and having all paper placed into designated, secure shredding bins whose content is shredded upon collection and ultimately recycled into new material. However, while this effort is improving their diversion, the question has arisen of how to make the program viable in the long term based on the costs required to sustain it. To tackle this issue, this thesis will focus on creating a methodology and sampling plan to determine the appropriate level of a third-party recycling service required and to guide efficient bin-sizing solutions. This will in turn allow for SRP to understand how much paper waste is being produced and how accurately they are being charged for TPV services.
ContributorsHolladay, Amy E. (Author) / Escobedo, Adolfo (Thesis director) / Kucukozyigit, Ali (Committee member) / Industrial, Systems & Operations Engineering Prgm (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05