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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

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
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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

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

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
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Description

Background: Extreme heat is a public health challenge. The scarcity of directly comparable studies on the association of heat with morbidity and mortality and the inconsistent identification of threshold temperatures for severe impacts hampers the development of comprehensive strategies aimed at reducing adverse heat-health events.

Objectives: This quantitative study was designed

Background: Extreme heat is a public health challenge. The scarcity of directly comparable studies on the association of heat with morbidity and mortality and the inconsistent identification of threshold temperatures for severe impacts hampers the development of comprehensive strategies aimed at reducing adverse heat-health events.

Objectives: This quantitative study was designed to link temperature with mortality and morbidity events in Maricopa County, Arizona, USA, with a focus on the summer season.

Methods: Using Poisson regression models that controlled for temporal confounders, we assessed daily temperature–health associations for a suite of mortality and morbidity events, diagnoses, and temperature metrics. Minimum risk temperatures, increasing risk temperatures, and excess risk temperatures were statistically identified to represent different “trigger points” at which heat-health intervention measures might be activated.

Results: We found significant and consistent associations of high environmental temperature with all-cause mortality, cardiovascular mortality, heat-related mortality, and mortality resulting from conditions that are consequences of heat and dehydration. Hospitalizations and emergency department visits due to heat-related conditions and conditions associated with consequences of heat and dehydration were also strongly associated with high temperatures, and there were several times more of those events than there were deaths. For each temperature metric, we observed large contrasts in trigger points (up to 22°C) across multiple health events and diagnoses.

Conclusion: Consideration of multiple health events and diagnoses together with a comprehensive approach to identifying threshold temperatures revealed large differences in trigger points for possible interventions related to heat. Providing an array of heat trigger points applicable for different end-users may improve the public health response to a problem that is projected to worsen in the coming decades.

ContributorsPettiti, Diana B. (Author) / Hondula, David M. (Author) / Yang, Shuo (Author) / Harlan, Sharon L. (Author) / Chowell, Gerardo (Author)
Created2016-02-01
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Description

Maricopa County, Arizona, anchor to the fastest growing megapolitan area in the United States, is located in a hot desert climate where extreme temperatures are associated with elevated risk of mortality. Continued urbanization in the region will impact atmospheric temperatures and, as a result, potentially affect human health. We aimed

Maricopa County, Arizona, anchor to the fastest growing megapolitan area in the United States, is located in a hot desert climate where extreme temperatures are associated with elevated risk of mortality. Continued urbanization in the region will impact atmospheric temperatures and, as a result, potentially affect human health. We aimed to quantify the number of excess deaths attributable to heat in Maricopa County based on three future urbanization and adaptation scenarios and multiple exposure variables.

Two scenarios (low and high growth projections) represent the maximum possible uncertainty range associated with urbanization in central Arizona, and a third represents the adaptation of high-albedo cool roof technology. Using a Poisson regression model, we related temperature to mortality using data spanning 1983–2007. Regional climate model simulations based on 2050-projected urbanization scenarios for Maricopa County generated distributions of temperature change, and from these predicted changes future excess heat-related mortality was estimated. Subject to urbanization scenario and exposure variable utilized, projections of heat-related mortality ranged from a decrease of 46 deaths per year (− 95%) to an increase of 339 deaths per year (+ 359%).

Projections based on minimum temperature showed the greatest increase for all expansion and adaptation scenarios and were substantially higher than those for daily mean temperature. Projections based on maximum temperature were largely associated with declining mortality. Low-growth and adaptation scenarios led to the smallest increase in predicted heat-related mortality based on mean temperature projections. Use of only one exposure variable to project future heat-related deaths may therefore be misrepresentative in terms of direction of change and magnitude of effects. Because urbanization-induced impacts can vary across the diurnal cycle, projections of heat-related health outcomes that do not consider place-based, time-varying urban heat island effects are neglecting essential elements for policy relevant decision-making.

ContributorsHondula, David M. (Author) / Georgescu, Matei (Author) / Balling, Jr., Robert C. (Author)
Created2014-04-28
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Description

Preventing heat-associated morbidity and mortality is a public health priority in Maricopa County, Arizona (United States). The objective of this project was to evaluate Maricopa County cooling centers and gain insight into their capacity to provide relief for the public during extreme heat events. During the summer of 2014, 53

Preventing heat-associated morbidity and mortality is a public health priority in Maricopa County, Arizona (United States). The objective of this project was to evaluate Maricopa County cooling centers and gain insight into their capacity to provide relief for the public during extreme heat events. During the summer of 2014, 53 cooling centers were evaluated to assess facility and visitor characteristics. Maricopa County staff collected data by directly observing daily operations and by surveying managers and visitors. The cooling centers in Maricopa County were often housed within community, senior, or religious centers, which offered various services for at least 1500 individuals daily. Many visitors were unemployed and/or homeless. Many learned about a cooling center by word of mouth or by having seen the cooling center’s location. The cooling centers provide a valuable service and reach some of the region’s most vulnerable populations. This project is among the first to systematically evaluate cooling centers from a public health perspective and provides helpful insight to community leaders who are implementing or improving their own network of cooling centers.

ContributorsBerisha, Vjollca (Author) / Hondula, David M. (Author) / Roach, Matthew (Author) / White, Jessica R. (Author) / McKinney, Benita (Author) / Bentz, Darcie (Author) / Mohamed, Ahmed (Author) / Uebelherr, Joshua (Author) / Goodin, Kate (Author)
Created2016-09-23
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Description

This study aims to examine the relationship between urban densification and pedestrian thermal comfort at different times of the year, and to understand how this can impact patterns of activity in downtown areas. The focus of the research is on plazas in the urban core of downtown Tempe, given their

This study aims to examine the relationship between urban densification and pedestrian thermal comfort at different times of the year, and to understand how this can impact patterns of activity in downtown areas. The focus of the research is on plazas in the urban core of downtown Tempe, given their importance to the pedestrian landscape. With that in mind, the research question for the study is: how does the microclimate of a densifying urban core affect thermal comfort in plazas at different times of the year? Based on the data, I argue that plazas in downtown Tempe are not maximally predisposed to pedestrian thermal comfort in the summer or the fall. Thus, the proposed intervention to improve thermal comfort in downtown Tempe’s plazas is the implementation of decision support tools focused on education, community engagement, and thoughtful building designs for heat safety.

ContributorsCox, Nicole (Author) / Redman, Charles (Thesis director) / Hondula, David M. (Committee member) / School of Social Transformation (Contributor) / School of Sustainability (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
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Description

Arizona is a unique state in that rain is not a normal occurrence throughout most of the year (NWS). Arizona averages from less than three months to half a month of measurable precipitation days per year (WRCC). With that, it is important to know the public’s understanding as well as

Arizona is a unique state in that rain is not a normal occurrence throughout most of the year (NWS). Arizona averages from less than three months to half a month of measurable precipitation days per year (WRCC). With that, it is important to know the public’s understanding as well as their general trend of likeness towards the weather forecasts they receive. A questionnaire was distributed to 426 people in the state of Arizona to review what they understand from the forecasts and what they would like to see on social media and television.

ContributorsHermansen, Alexis Nicole (Author) / Alvarez, Melanie (Thesis director) / Cerveny, Randall (Committee member) / Hondula, David M. (Committee member) / Walter Cronkite School of Journalism & Mass Comm (Contributor) / School of Geographical Sciences and Urban Planning (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description

Many people use public transportation in their daily lives, which is often praised at as a healthy and sustainable choice to make. However, in extreme temperatures this also puts people at a greater risk for negative consequences resulting from such exposure to heat. In Phoenix, public transportation riders are faced

Many people use public transportation in their daily lives, which is often praised at as a healthy and sustainable choice to make. However, in extreme temperatures this also puts people at a greater risk for negative consequences resulting from such exposure to heat. In Phoenix, public transportation riders are faced with extreme heat in the summer along with the increased internal heat production caused by the physical activity required to use public transportation. In this study, I estimated total exposure and average exposure per rider for six stops in Phoenix. To do this I used City of Phoenix ridership data, weather data, and survey responses from an ASU City of Phoenix Bus Stop Survey conducted in summer 2016. These data sets were combined by multiplying different metrics to produce various exposure values. During analysis two sets of calculations were made. One keeping weather constant and another keeping ridership constant. I found that there was a large range of exposure between the selected stops and that the thermal environment influences the amount of exposure depending on the time of day the exposure is occurring. During the morning a greener location leads to less exposure, while in the afternoon an urban location leads to less exposure. Know detailed information about exposure at these stops I was also able to evaluate survey participants' thermal comfort at each stop and how it may relate to exposure. These findings are useful in making educated transportation planning decisions and improving the quality of life for people living in places with extreme summer temperatures.

ContributorsGerster, Katrina Ashley (Author) / Hondula, David M. (Thesis director) / Watkins, Lance (Committee member) / School of Geographical Sciences and Urban Planning (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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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

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.
Created2017-05