Matching Items (72)
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
Salmonella enterica is a gastrointestinal (GI) pathogen that can cause systemic diseases. It invades the host through the GI tract and can induce powerful immune responses in addition to disease. Thus, it is considered as a promising candidate to use as oral live vaccine vectors. Scientists have been making great efforts to get a properly attenuated Salmonella vaccine strain for a long time, but could not achieve a balance between attenuation and immunogenicity. So the regulated delayed attenuation/lysis Salmonella vaccine vectors were proposed as a design to seek this balance. The research work is progressing steadily, but more improvements need to be made. As one of the possible improvements, the cyclic adenosine monophosphate (cAMP) -independent cAMP receptor protein (Crp*) is expected to protect the Crp-dependent crucial regulator, araC PBAD, in these vaccine designs from interference by glucose, which decreases synthesis of cAMP, and enhance the colonizing ability by and immunogenicity of the vaccine strains. In this study, the cAMP-independent crp gene mutation, crp-70, with or without araC PBAD promoter cassette, was introduced into existing Salmonella vaccine strains. Then the plasmid stability, growth rate, resistance to catabolite repression, colonizing ability, immunogenicity and protection to challenge of these new strains were compared with wild-type crp or araC PBAD crp strains using western blots, enzyme-linked immunosorbent assays (ELISA) and animal studies, so as to evaluate the effects of the crp-70 mutation on the vaccine strains. The performances of the crp-70 strains in some aspects were closed to or even exceeded the crp+ strains, but generally they did not exhibit the expected advantages compared to their wild-type parents. Crp-70 rescued the expression of araC PBAD fur from catabolite repression. The strain harboring araC PBAD crp-70 was severely affected by its slow growth, and its colonizing ability and immunogenicity was much weaker than the other strains. The Pcrp crp-70 strain showed relatively good ability in colonization and immune stimulation. Both the araC PBAD crp-70 and the Pcrp crp-70 strains could provide certain levels of protection against the challenge with virulent pneumococci, which were a little lower than for the crp+ strains.
ContributorsShao, Shihuan (Author) / Curtiss, Roy (Thesis advisor) / Arizona State University (Publisher)
Created2012
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
It is important to consider factors that contribute to successful fertilization and the development of viable offspring. Better understanding the factors that contribute to infertility can be used to assist in the development of viable offspring, especially for human beings looking to successfully reproduce. Identifying paternal effect genes, genes that come from the father, introduces more targets that can be manipulated to produce specific reproductive effects. Use of Drosophila melanogaster as a model to study reproduction has increased, in part, due to the use of the GAL4 system. In this system, the GAL4 gene encodes an 881 amino acid protein that binds to the 4-site Upstream Activating Sequence (UAS) to induce transcription of the gene of interest. These sequences constitute the two components of the system: the driver (GAL4) and the responder (gene of interest) \u2014 each of which is maintained as a separate parental line. Effects of the GAL4 driver line "driving" transcription of the responder can be assessed by examining the offspring. One of the more common uses of the GAL4 system involves analyzing phenotypic effects of reducing or eliminating expression of a target gene through the induction of RNAi transcription, which often results in toxicity, lethality, or reduced viability. Utilizing these principles, we strove to demonstrate the effect of knocking down the expression of testis-specific sperm-leucyl-aminopeptidases gene CG13340 on progeny by inducing expression of RNAi with two distinct GAL4 driver lines - one with a nonspecific actin-binding activation sequence and the other with a testis-specific activation sequence. Comparison of both GAL4 driver lines to crosses using N01 wild type ("wt") flies verify that inducing RNAi transcription using the GAL4 system results in reduction of proper offspring development. Further studies using D. melanogaster and the GAL4 system can improve knowledge of factors contributing to male fertility and also be applied to better understand mammalian, specifically human, fertility.
ContributorsEvans, Donna Marie (Author) / Karr, Timothy L. (Thesis director) / Roland, Kenneth (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor) / Department of English (Contributor)
Created2014-05
DescriptionA novel and unconventional approach for delivering a eukaryotic apoptosis factor, TNF-related apoptosis-inducing ligand (TRAIL), to cancer cells within and around necrotizing tumors by utilizing a S. Typhimurium purine requiring auxotroph as a biological vector to develop two anticancer therapies with multiple modality and broad economic feasibility.
ContributorsKoons, Andrew (Author) / Curtiss, Roy (Thesis director) / Lake, Douglas (Committee member) / Janthakahalli, Nagaraj Vinay (Committee member) / Barrett, The Honors College (Contributor)
Created2013-12
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
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