Matching Items (44)
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
Woody plant encroachment is a worldwide phenomenon linked to water availability in semiarid systems. Nevertheless, the implications of woody plant encroachment on the hydrologic cycle are poorly understood, especially at the catchment scale. This study takes place in a pair of small semiarid rangeland undergoing the encroachment of Prosopis velutina Woot., or velvet mesquite tree. The similarly-sized basins are in close proximity, leading to equivalent meteorological and soil conditions. One basin was treated for mesquite in 1974, while the other represents the encroachment process. A sensor network was installed to measure ecohydrological states and fluxes, including precipitation, runoff, soil moisture and evapotranspiration. Observations from June 1, 2011 through September 30, 2012 are presented to describe the seasonality and spatial variability of ecohydrological conditions during the North American Monsoon (NAM). Runoff observations are linked to historical changes in runoff production in each watershed. Observations indicate that the mesquite-treated basin generates more runoff pulses and greater runoff volume for small rainfall events, while the mesquite-encroached basin generates more runoff volume for large rainfall events. A distributed hydrologic model is applied to both basins to investigate the runoff threshold processes experienced during the NAM. Vegetation in the two basins is classified into grass, mesquite, or bare soil using high-resolution imagery. Model predictions are used to investigate the vegetation controls on soil moisture, evapotranspiration, and runoff generation. The distributed model shows that grass and mesquite sites retain the highest levels of soil moisture. The model also captures the runoff generation differences between the two watersheds that have been observed over the past decade. Generally, grass sites in the mesquite-treated basin have less plant interception and evapotranspiration, leading to higher soil moisture that supports greater runoff for small rainfall events. For large rainfall events, the mesquite-encroached basin produces greater runoff due to its higher fraction of bare soil. The results of this study show that a distributed hydrologic model can be used to explain runoff threshold processes linked to woody plant encroachment at the catchment-scale and provides useful interpretations for rangeland management in semiarid areas.
ContributorsPierini, Nicole A (Author) / Vivoni, Enrique R (Thesis advisor) / Wang, Zhi-Hua (Committee member) / Mays, Larry W. (Committee member) / Arizona State University (Publisher)
Created2013
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
Engineered pavements cover a large fraction of cities and offer significant potential for urban heat island mitigation. Though rapidly increasing research efforts have been devoted to the study of pavement materials, thermal interactions between buildings and the ambient environment are mostly neglected. In this study, numerical models featuring a realistic representation of building-environment thermal interactions, were applied to quantify the effect of pavements on the urban thermal environment at multiple scales. It was found that performance of pavements inside the canyon was largely determined by the canyon geometry. In a high-density residential area, modifying pavements had insignificant effect on the wall temperature and building energy consumption. At a regional scale, various pavement types were also found to have a limited cooling effect on land surface temperature and 2-m air temperature for metropolitan Phoenix. In the context of global climate change, the effect of pavement was evaluated in terms of the equivalent CO2 emission. Equivalent CO2 emission offset by reflective pavements in urban canyons was only about 13.9e46.6% of that without building canopies, depending on the canyon geometry. This study revealed the importance of building-environment thermal interactions in determining thermal conditions inside the urban canopy.
ContributorsYang, Jiachuan (Author) / Wang, Zhi-Hua (Author) / Kaloush, Kamil (Author) / Dylla, Heather (Author)
Created2016-08-22
Description
Biomarkers are the cornerstone of modern-day medicine. They are defined as any biological substance in or outside the body that gives insight to the body's condition. Doctors and researchers can measure specific biomarkers to diagnose and treat patients, such as the concentration of hemoglobin Alc and its connection to diabetes. There are a variety of methods, or assays, to detect biomarkers, but the most common assay is enzyme-linked immunosorbent assay (ELISA). A new-generation assay termed mass spectrometric immunoassay (MSIA) can measure proteoforms, the different chemical variations of proteins, and their relative abundance. ELISA on the other hand measures the overall concentration of protein in the sample. Measuring each of the proteoforms of a protein is important because only one or two variations could be biologically significant and/or cause diseases. However, running MSIA is expensive. For this reason, an alternative plate-based MSIA technique was tested for its ability to detect the proteoforms of a protein called apolipoprotein C-III (ApoC-III). This technique combines the protein capturing procedure of ELISA to isolate the protein with detection in a mass spectrometer. A larger amount of ApoC-III present in the body indicates a considerable risk for coronary heart disease. The precision of the assay is determined on the coefficient of variation (CV). A CV value is the ratio of standard deviation in relation to the mean, represented as a percentage. The smaller the percentage, the less variation the assay has, and therefore the more ability it has to detect subtle changes in the biomarker. An accepted CV would be less than 10% for single-day tests (intra-day) and less than 15% for multi-day tests (inter-day). The plate-based MSIA was started by first coating a 96-well round bottom plate with 2.5 micrograms of ApoC-III antibody. Next, a series of steps were conducted: a buffer wash, then the sample incubation, followed by another buffer wash and two consecutive water washes. After the final wash, the wells were filled with a MALDI matrix, then spotted onto a gold plate to dry. The dry gold target was then placed into a MALDI-TOF mass spectrometer to produce mass spectra for each spot. The mass spectra were calibrated and the area underneath each of the four peaks representing the ApoC-III proteoforms was exported as an Excel file. The intra-day CV values were found by dividing the standard deviation by the average relative abundance of each peak. After repeating the same procedure for three more days, the inter-day CVs were found using the same method. After completing the experiment, the CV values were all within the acceptable guidelines. Therefore, the plate-based MSIA is a viable alternative for finding proteoforms than the more expensive MSIA tips. To further validate this, additional tests will need to be conducted with different proteins and number of samples to determine assay flexibility.
ContributorsTieu, Luc (Author) / Borges, Chad (Thesis director) / Nedelkov, Dobrin (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12
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
Description
Climate is a critical determinant of agricultural productivity, and the ability to accurately predict this productivity is necessary to provide guidance regarding food security and agricultural management. Previous predictions vary in approach due to the myriad of factors influencing agricultural productivity but generally suggest long-term declines in productivity and agricultural land suitability under climate change. In this paper, I relate predicted climate changes to yield for three major United States crops, namely corn, soybeans, and wheat, using a moderate emissions scenario. By adopting data-driven machine learning approaches, I used the following machine learning methods: random forest (RF), extreme gradient boosting (XGB), and artificial neural networks (ANN) to perform comparative analysis and ensemble methodology. I omitted the western US due to the region's susceptibility to water stress and the prevalence of artificial irrigation as a means to compensate for dry conditions. By considering only climate, the model's results suggest an ensemble mean decline in crop yield of 23.4\% for corn, 19.1\% for soybeans, and 7.8\% for wheat between the years of 2017 and 2100. These results emphasize potential negative impacts of climate change on the current agricultural industry as a result of shifting bio-climactic conditions.
ContributorsSwarup, Shray (Author) / Eikenberry, Steffen (Thesis director) / Mahalov, Alex (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor)
Created2023-05
Description
This thesis project explores the extent to which elected education officials, specifically school board members, with a background in education make policy decisions differently than those who do not have a background in education. This line of questioning began with a project completed in a class I took in the fall semester of 2023 - Innovations in School Democracy, where students chose a critical issue in the education sphere and situated it within the context of civic education. The critical issue I addressed at the time was the significant number of individuals in “high-ranking” positions in the education field who do not appear to have a background in anything education-related, outside of their own schooling. The issue lies with the fact that these individuals are making large scale policy decisions that impact all students, teachers, parents, and school faculty members within their district without having any research or practice-based educational foundation or experience to draw upon for their decision making.
For the purpose of this thesis, I expanded this phenomenon beyond the realm of civic education by performing a comparative analysis of elected education official decision-making between school boards that have members with educational backgrounds and those who don’t, in addition to analyzing the stances and policies of the Superintendent of Public Instruction. The goal of this analysis is to see how, or if, decisions differ and to what extent those decisions appear to be driven by current political ideologies versus educational research and best practices. I hypothesize that elected education officials who have a background in education will make decisions that are more student- and educator-focused and have fewer indicators of a specific partisan political ideology. Conversely, I hypothesize the opposite for decision-making by officials without an education background, where I expect to find more evidence of influential partisan political ideology.
In order to determine if a decision-making gap exists, I examined school board websites and pulled district-related news articles in order to cross-analyze the verbiage on specific political buzzwords or phrases that could be clearly linked to a political party’s ideology or stance on public schooling matters and policies. I performed a similar search through the campaign platform and current Arizona Education System biographical page for Superintendent Tom Horne. To begin this investigation, thirty school districts in the state of Arizona were selected for preliminary research - ten small districts, ten medium-size districts, and ten large districts. Through the use of school district websites and the biographies of school board members, I determined which school boards had individuals with a background in education and which did not. From there, two school boards from each district size category were selected for examination - one board categorized as having a strong educational background presence and one board that either had very minimal presence, or none at all. From this research, I intended to present preliminary findings about the extent to which differences in policy-making decisions relate to school board member education background and experience, as well as the degree to which explicit partisan politicization appears to influence such decisions. Upon completion of this limited research, my findings ended up deriving more directly from the mission and vision statements of school districts and school boards, though policy decisions were still loosely analyzed through district media articles. However, my research on Superintendent Horne lent itself well to answer all three of my proposed research questions.
ContributorsGraves, Olivia (Author) / Hermanns, Carl (Thesis director) / Schugurensky, Daniel (Committee member) / Bartlett, Tara (Committee member) / Barrett, The Honors College (Contributor) / School of Social Transformation (Contributor) / Department of Psychology (Contributor)
Created2024-05