Matching Items (157)
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
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
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
Mathematical epidemiology, one of the oldest and richest areas in mathematical biology, has significantly enhanced our understanding of how pathogens emerge, evolve, and spread. Classical epidemiological models, the standard for predicting and managing the spread of infectious disease, assume that contacts between susceptible and infectious individuals depend on their relative frequency in the population. The behavioral factors that underpin contact rates are not generally addressed. There is, however, an emerging a class of models that addresses the feedbacks between infectious disease dynamics and the behavioral decisions driving host contact. Referred to as “economic epidemiology” or “epidemiological economics,” the approach explores the determinants of decisions about the number and type of contacts made by individuals, using insights and methods from economics. We show how the approach has the potential both to improve predictions of the course of infectious disease, and to support development of novel approaches to infectious disease management.
ContributorsPerrings, Charles (Author) / Castillo-Chavez, Carlos (Author) / Chowell-Puente, Gerardo (Author) / Daszak, Peter (Author) / Fenichel, Eli P. (Author) / Finnoff, David (Author) / Horan, Richard D. (Author) / Kilpatrick, A. Marm (Author) / Kinzig, Ann (Author) / Kuminoff, Nicolai (Author) / Levin, Simon (Author) / Morin, Benjamin (Author) / Smith, Katherine F. (Author) / Springborn, Michael (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / W.P. Carey School of Business (Contributor) / Economics (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-12-01
Description
While non-invasive breast cancer treatments may be considered less costly in the short-term, over the course of a lifetime, a more aggressive treatment can be overall less costly, especially with recurrence cases; however, these more aggressive treatments are not necessarily covered by insurance and are difficult to discuss in the short amount of time in physician consultations. This analysis studied data from 982 women diagnosed with breast cancer over a five-year period to evaluate monetary costs associated with treatment options and incorporated five in-depth interviews to understand experiences and non-monetary costs. Data showed the most expensive option was a unilateral mastectomy with radiation therapy and the least costly option was breast conserving surgery. Interviews determined each woman evaluated the monetary costs with each treatment but most heavily focused on personal values, biases and recommended opinions when deciding on a treatment. The use of prompt sheets before physician appointments and consultations, along with the addition of financial counselor meeting with each patient can improve patient satisfaction and alleviate stress by simplifying a woman's choice in deciding a treatment. In addition, increased insurance coverage to include every treatment chosen by women (rather than on a case-by-case basis), specifically contralateral prophylactic mastectomy and additional screening options, could decrease long term costs \u2014 both monetarily and in quality of life for patients.
ContributorsOsumi, Alana (Author) / LaRosa, Julia (Thesis director) / Sivanantham, Jai (Committee member) / Barrett, The Honors College (Contributor) / W.P. Carey School of Business (Contributor)
Created2018-12
Description
In 2016, in the United States alone, the cosmetics industry made an estimated 62.46 billion dollars in revenue (Revenue of the Cosmetic Industry in the U.S. 2002-2016 | Forecast). With a consistent increase in sales in the last several years, the industry has reached continued success even during times of hardship, such as the Great Recession of 2008. The use of Corporate Social Responsibility (CSR), external campaigns, and thoughtful packaging and ingredients resonates with targeted consumers. This has served as an effective strategy to maintain growth in the industry. Cosmetic companies promote their brand image using these sustainability tactics, but there seems to be a lack of transparency in this unregulated industry. The purpose of this thesis is to determine if the cosmetics industry is a good steward of the sustainability movement. Important terms and concepts relating to the industry will be discussed, then an analysis of sustainability focused cosmetic brands will be provided, which highlights the extent to which these brands engage in activities that promote sustainability. This is followed by an application of findings to a company that could benefit from using such practices. Overall, the analysis of the different brands proved to be shocking and disappointing. This is due to the sheer amount that scored very poorly based on the sustainability criteria developed. The cosmetics industry is too inconsistent and too unregulated to truly act as a good steward for sustainability. Though some companies in the industry succeed, these accomplishments are not consistent across all cosmetic companies. Hence, the cosmetics industry as a good steward for sustainability can only be as strong as its weakest link.
ContributorsMamus, Sydney Wasescha (Author) / Ostrom, Amy (Thesis director) / Kristofferson, Kirk (Committee member) / Department of Marketing (Contributor) / W.P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This report was commissioned to provide an analysis and evaluation of consumer perceptions and branding as it relates to the political and social climate in America. To be able to do this, the paper analyzes shifts in the external environment as well as researching case studies and online consumer perception surveys. Overall, this paper aims to examine the distributed survey and attempt to correlate and identify how branding, consumer perceptions, and social and political issues all can work and affect one another. Through the administration of this survey, we were able to formulate a conclusion that points towards the importance of brands actively adhering to changing consumer preferences, ideals, and expectations.
ContributorsClark, Sydney (Co-author) / Loera, Carolina (Co-author) / Montoya, Detra (Thesis director) / Samper, Adriana (Committee member) / W.P. Carey School of Business (Contributor) / Department of Marketing (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The use of generalized linear models in loss reserving is not new; many statistical models have been developed to fit the loss data gathered by various insurance companies. The most popular models belong to what Glen Barnett and Ben Zehnwirth in "Best Estimates for Reserves" call the "extended link ratio family (ELRF)," as they are developed from the chain ladder algorithm used by actuaries to estimate unpaid claims. Although these models are intuitive and easy to implement, they are nevertheless flawed because many of the assumptions behind the models do not hold true when fitted with real-world data. Even more problematically, the ELRF cannot account for environmental changes like inflation which are often observed in the status quo. Barnett and Zehnwirth conclude that a new set of models that contain parameters for not only accident year and development period trends but also payment year trends would be a more accurate predictor of loss development. This research applies the paper's ideas to data gathered by Company XYZ. The data was fitted with an adapted version of Barnett and Zehnwirth's new model in R, and a trend selection algorithm was developed to accompany the regression code. The final forecasts were compared to Company XYZ's booked reserves to evaluate the predictive power of the model.
ContributorsZhang, Zhihan Jennifer (Author) / Milovanovic, Jelena (Thesis director) / Tomita, Melissa (Committee member) / Zicarelli, John (Committee member) / W.P. Carey School of Business (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This research aims to look at the lower level collegiate athletics, Intramural sports and club sports, in comparison to Division 1 varsity athletics to see how their sport lives differ and why they are still competing when the reward does not seem as grand as the Varsity athletics. The findings show that the socially ingrained aspect of sports is the reason that most lower level athletes keep competing.
ContributorsHarvey, Abigail (Author) / Jonsson, Hjorleifur (Thesis director) / Jackson, Victoria (Committee member) / School of Human Evolution and Social Change (Contributor) / W.P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This report will provide an analysis of frontier market equity-based investment funds with respect to bivariate correlation analysis, global integration analysis, and US optimized portfolio statistics. My analysis has indicated strong diversification benefits of including frontier market equities in a US portfolio, given its low correlation to US equity concentrated portfolios especially portfolios that would consist of midcap and smallcap stocks. With the drawbacks of the bivariate correlation test, an additional global integration analysis has been included to reaffirm the value frontier markets offer in the form of integration. Integration is a second layer of the diversification analysis. I find that when analyzing frontier markets (FM) against developed markets (DM) there exhibits significantly less integration as compared to emerging markets against developed markets. This analysis goes one step further and quantifies integration of specific frontier market funds against the broader emerging and developed markets. This study finds that iShares MSCI frontier 100 ETF (Ticker: FM) exhibits the least integration amongst Guggenheim Frontier Markets ETF (Ticker: FRN), Templeton Frontier Markets A (Ticker: TFMAX), and Morgan Stanley Frontier Emg (Ticker: MFMIX). Lastly, this analysis covers the inadequacy with using Sharpe ratios and minimum volatility parameters to achieve portfolio optimization under a Monte-Carlo style 1000 portfolio simulation with frontier market funds in a broader US equity portfolio but finds better results when using a US equity and US bond combination portfolio. Overall, this analysis of frontier markets and frontier market funds has shown there still exists significant diversification benefits to US Investors when they engage in FM investments, specifically through diversified FM investment funds.
ContributorsHardy, Gunner Laine (Author) / Pruitt, Seth (Thesis director) / Brada, Josef (Committee member) / W.P. Carey School of Business (Contributor) / Economics Program in CLAS (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05