Matching Items (80)
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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
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

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
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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

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

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
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Description

Critical flicker fusion thresholds (CFFTs) describe when quick amplitude modulations of a light source become undetectable as the frequency of the modulation increases and are thought to underlie a number of visual processing skills, including reading. Here, we compare the impact of two vision-training approaches, one involving contrast sensitivity training

Critical flicker fusion thresholds (CFFTs) describe when quick amplitude modulations of a light source become undetectable as the frequency of the modulation increases and are thought to underlie a number of visual processing skills, including reading. Here, we compare the impact of two vision-training approaches, one involving contrast sensitivity training and the other directional dot-motion training, compared to an active control group trained on Sudoku. The three training paradigms were compared on their effectiveness for altering CFFT. Directional dot-motion and contrast sensitivity training resulted in significant improvement in CFFT, while the Sudoku group did not yield significant improvement. This finding indicates that dot-motion and contrast sensitivity training similarly transfer to effect changes in CFFT. The results, combined with prior research linking CFFT to high-order cognitive processes such as reading ability, and studies showing positive impact of both dot-motion and contrast sensitivity training in reading, provide a possible mechanistic link of how these different training approaches impact reading abilities.

ContributorsZhou, Tianyou (Author) / Nanez, Jose (Author) / Zimmerman, Daniel (Author) / Holloway, Steven (Author) / Seitz, Aaron (Author) / New College of Interdisciplinary Arts and Sciences (Contributor)
Created2016-10-26
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Although autism spectrum disorder (ASD) is a serious lifelong condition, its underlying neural mechanism remains unclear. Recently, neuroimaging-based classifiers for ASD and typically developed (TD) individuals were developed to identify the abnormality of functional connections (FCs). Due to over-fitting and interferential effects of varying measurement conditions and demographic distributions, no

Although autism spectrum disorder (ASD) is a serious lifelong condition, its underlying neural mechanism remains unclear. Recently, neuroimaging-based classifiers for ASD and typically developed (TD) individuals were developed to identify the abnormality of functional connections (FCs). Due to over-fitting and interferential effects of varying measurement conditions and demographic distributions, no classifiers have been strictly validated for independent cohorts. Here we overcome these difficulties by developing a novel machine-learning algorithm that identifies a small number of FCs that separates ASD versus TD. The classifier achieves high accuracy for a Japanese discovery cohort and demonstrates a remarkable degree of generalization for two independent validation cohorts in the USA and Japan. The developed ASD classifier does not distinguish individuals with major depressive disorder and attention-deficit hyperactivity disorder from their controls but moderately distinguishes patients with schizophrenia from their controls. The results leave open the viable possibility of exploring neuroimaging-based dimensions quantifying the multiple-disorder spectrum.

ContributorsYahata, Noriaki (Author) / Morimoto, Jun (Author) / Hashimoto, Ryuichiro (Author) / Lisi, Giuseppe (Author) / Shibata, Kazuhisa (Author) / Kawakubo, Yuki (Author) / Kuwabara, Hitoshi (Author) / Kuroda, Miho (Author) / Yamada, Takashi (Author) / Megumi, Fukuda (Author) / Imamizu, Hiroshi (Author) / Nanez, Jose (Author) / Takahashi, Hidehiko (Author) / Okamoto, Yasumasa (Author) / Kasai, Kiyoto (Author) / Kato, Nobumasa (Author) / Sasaki, Yuka (Author) / Watanabe, Takeo (Author) / Kawato, Mitsuo (Author) / New College of Interdisciplinary Arts and Sciences (Contributor)
Created2016-04-14
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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
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Description
Historically, Supreme Court interpretations of the Constitution of the United States have been significantly important, impacting the lives of every American. This honors thesis seeks to understand the ways in which the Constitution has been interpreted through the lens of political ideology. Using constitutional theory, I explain how the political

Historically, Supreme Court interpretations of the Constitution of the United States have been significantly important, impacting the lives of every American. This honors thesis seeks to understand the ways in which the Constitution has been interpreted through the lens of political ideology. Using constitutional theory, I explain how the political ideologies of classical liberalism, conservatism, libertarianism, and progressive liberalism have played a role in the interpretations of the First, Second, and Fourth Amendments. I also examine how these ideological interpretations have changed from 1776 to 2017, dividing the history of the United States into four eras: the Founding Era, the Civil War Era, the New Deal Era, and the Modern Era. First, the First Amendment's clauses on religion are examined, where I focus on the separation between church and state as well as the concepts of "establishment" and "free exercise." The First Amendment transitions from classically liberal, to conservative, to progressively liberal and classically liberal, to progressively liberal and libertarian. Next, we look at the Second Amendment's notions of a "militia" and the "right to keep and bear arms." The Second Amendment's interpretations begin classically liberal, then change to classically liberal and progressively liberal, to progressively liberal, to conservative. Finally, the analysis on the Fourth Amendment's "unreasonable searches and seizures" as well as "warrants" lends evidence to ideological interpretations. The Fourth Amendment, like the other two, starts classically liberal for two eras, then becomes libertarian, and finally ends libertarian and conservative. The implications of each of these conclusions are then discussed, with emphasis on public opinion in society during the era in question, the ways in which the ideologies in each era seem to build upon one another, the ideologies of the justices who wrote the opinions, and the ideology of the court.
Created2017-12
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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

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