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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
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
Along with the number of technologies that have been introduced over a few years ago, gesture-based human-computer interactions are becoming the new phase in encompassing the creativity and abilities for users to communicate and interact with devices. Because of how the nature of defining free-space gestures influence user's preference and the length of usability of gesture-driven devices, defined low-stress and intuitive gestures for users to interact with gesture recognition systems are necessary to consider. To measure stress, a Galvanic Skin Response instrument was used as a primary indicator, which provided evidence of the relationship between stress and intuitive gestures, as well as user preferences towards certain tasks and gestures during performance. Fifteen participants engaged in creating and performing their own gestures for specified tasks that would be required during the use of free-space gesture-driven devices. The tasks include "activation of the display," scroll, page, selection, undo, and "return to main menu." They were also asked to repeat their gestures for around ten seconds each, which would give them time and further insight of how their gestures would be appropriate or not for them and any given task. Surveys were given at different time to the users: one after they had defined their gestures and another after they had repeated their gestures. In the surveys, they ranked their gestures based on comfort, intuition, and the ease of communication. Out of those user-ranked gestures, health-efficient gestures, given that the participants' rankings were based on comfort and intuition, were chosen in regards to the highest ranked gestures.
ContributorsLam, Christine (Author) / Walker, Erin (Thesis director) / Danielescu, Andreea (Committee member) / Barrett, The Honors College (Contributor) / Ira A. Fulton School of Engineering (Contributor) / School of Arts, Media and Engineering (Contributor) / Department of English (Contributor) / Computing and Informatics Program (Contributor)
Created2015-05
Description
G3Box's 2013 Marketing Plan outlines a strategic plan and short term operational strategies for the company. The document includes a discussion of the company's decision to enter the market for healthcare facilities in developing counties, and a situation assessment of the market conditions. G3Box is targeting small and large NGOs that currently provide healthcare facilities in developing countries. The market size for healthcare aid in developing countries is estimated to be $1.7 billion. The plan also analyses the customer's value chain and buying cycle by using voice of the customer data. The strategic position analysis profiles G3Box's competition and discusses the company's differential advantage versus other options for healthcare facilities in developing countries. Next the document discusses G3Box's market strategy and implementation, along with outlining a value proposition for the company. G3Box has two objectives for 2013: 1) Increase sales revenue to $1.3 million and 2) increase market presence to 25%. In order to reach these objectives, G3Box has developed a primary and secondary strategic focus for each objective. The primary strategies are relationship selling and online marketing. The secondary strategies are developing additional value-added activities and public relations.
ContributorsWalters, John (Author) / Denning, Michael (Thesis director) / Ostrom, Lonnie (Committee member) / Carroll, James (Committee member) / Barrett, The Honors College (Contributor) / Ira A. Fulton School of Engineering (Contributor)
Created2012-12
Description
The majority of the 52 photovoltaic installations at ASU are governed by power purchase agreements (PPA) that set a fixed per kilowatt-hour rate at which ASU buys power from the system owner over the period of 15-20 years. PPAs require accurate predictions of the system output to determine the financial viability of the system installations as well as the purchase price. The research was conducted using PPAs and historical solar power production data from the ASU's Energy Information System (EIS). The results indicate that most PPAs slightly underestimate the annual energy yield. However, the modeled power output from PVsyst indicates that higher energy outputs are possible with better system monitoring.
ContributorsVulic, Natasa (Author) / Bowden, Stuart (Thesis director) / Bryan, Harvey (Committee member) / Sharma, Vivek (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / Ira A. Fulton School of Engineering (Contributor)
Created2012-12
Description
The 21st century engineer will face a diverse set of challenges spread out along a broad spectrum of disciplines. Among others, the fields of energy, healthcare, cyberspace, virtual reality, and neuroscience require monumental efforts by the new generation of engineers to meet the demands of a growing society. However the most important, and likely the most under recognized, challenge lies in developing advanced personalized learning. It is the core foundation from which the rest of the challenges can be accomplished. Without an effective method of teaching engineering students how to realize these grand challenges, the knowledge pool from which to draw new innovations and discoveries will be greatly diminished. This paper introduces the Inventors Workshop (IW), a hands-on, passion-based approach to personalized learning. It is intended to serve as a manual that will inform the next generation of student leaders and inventioneers about the core concepts the Inventors Workshop was built upon, and how to continue improvement into the future. Due to the inherent complexities in the grand challenge of personalized learning, the IW has developed a multifaceted solution that is difficult to explain in a single phrase. To enable comprehension of the IW's full vision, the process undergone to date of establishing and expanding the IW is described. In addition, research has been conducted to determine a variety of paths the Inventors Workshop may utilize in future expansion. Each of these options is explored and related to the core foundations of the IW to assist future leaders and partners in effectively improving personalized learning at ASU and beyond.
ContributorsEngelhoven, V. Logan (Author) / Burleson, Winslow (Thesis director) / Peck, Sidnee (Committee member) / Fortun, A. L. Cecil (Committee member) / Barrett, The Honors College (Contributor) / Ira A. Fulton School of Engineering (Contributor)
Created2012-12
ContributorsShah, Beejal (Author) / Nakamura, Mutsumi (Thesis director) / Balasooriya, Janaka (Committee member) / Wilkerson, Kelly (Committee member) / Ira A. Fulton School of Engineering (Contributor) / Barrett, The Honors College (Contributor)
Created2012-12
Description
Electrospun nanofibers can be prepared from various kinds of inorganic substances by electro-spinning techniques. They have great potential in many applications including super capacitors, lithium ion batteries, filtration, catalyst and enzyme carriers, and sensors [1]. The traditional way to produce electrospun nanofibers is needle based electro-spinning [1]. However, electrospun nanofibers have not been widely used in practice because of low nanofiber production rates. One way to largely increase the electro-spinning productivity is needleless electro-spinning. In 2005, Jirsak et al. patented a rotating roller fiber generator for the mass production of nanofibers [2]. Elmarco Corporation commercialized this technique to manufacture nanofiber equipment for the production of all sorts of organic and inorganic nanofibers, and named it "NanospiderTM". For this project, my goal is to build a needleless electro-spinner to produce nanofibers as the separator of lithium ion batteries. The model of this project is based on the design of rotating roller fiber generator, and is adapted from a project at North Dakota State University in 2011 [3].
ContributorsQiao, Guanhao (Author) / Yu, Hongyu (Thesis director) / Jiang, Hanqing (Committee member) / Goryll, Michael (Committee member) / Barrett, The Honors College (Contributor) / Ira A. Fulton School of Engineering (Contributor)
Created2012-12
Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
ContributorsCole, Alexandra Shea (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / School of International Letters and Cultures (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
This work presents a thorough analysis of reconstruction of global wave fields (governed by the inhomogeneous wave equation and the Maxwell vector wave equation) from sensor time series data of the wave field. Three major problems are considered. First, an analysis of circumstances under which wave fields can be fully reconstructed from a network of fixed-location sensors is presented. It is proven that, in many cases, wave fields can be fully reconstructed from a single sensor, but that such reconstructions can be sensitive to small perturbations in sensor placement. Generally, multiple sensors are necessary. The next problem considered is how to obtain a global approximation of an electromagnetic wave field in the presence of an amplifying noisy current density from sensor time series data. This type of noise, described in terms of a cylindrical Wiener process, creates a nonequilibrium system, derived from Maxwell’s equations, where variance increases with time. In this noisy system, longer observation times do not generally provide more accurate estimates of the field coefficients. The mean squared error of the estimates can be decomposed into a sum of the squared bias and the variance. As the observation time $\tau$ increases, the bias decreases as $\mathcal{O}(1/\tau)$ but the variance increases as $\mathcal{O}(\tau)$. The contrasting time scales imply the existence of an ``optimal'' observing time (the bias-variance tradeoff). An iterative algorithm is developed to construct global approximations of the electric field using the optimal observing times. Lastly, the effect of sensor acceleration is considered. When the sensor location is fixed, measurements of wave fields composed of plane waves are almost periodic and so can be written in terms of a standard Fourier basis. When the sensor is accelerating, the resulting time series is no longer almost periodic. This phenomenon is related to the Doppler effect, where a time transformation must be performed to obtain the frequency and amplitude information from the time series data. To obtain frequency and amplitude information from accelerating sensor time series data in a general inhomogeneous medium, a randomized algorithm is presented. The algorithm is analyzed and example wave fields are reconstructed.
ContributorsBarclay, Bryce Matthew (Author) / Mahalov, Alex (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Moustaoui, Mohamed (Committee member) / Motsch, Sebastien (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2023