Matching Items (60)
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
Clean water for drinking, food preparation, and bathing is essential for astronaut health and safety during long duration habitation of the International Space Station (ISS), including future missions to Mars. Despite stringent water treatment and recycling efforts on the ISS, it is impossible to completely prevent microbial contamination of onboard water supplies. In this work, we used a spaceflight analogue culture system to better understand how the microgravity environment can influence the pathogenesis-related characteristics of Burkholderia cepacia complex (Bcc), an opportunistic pathogen previously recovered from the ISS water system. The results of the present study suggest that there may be important differences in how this pathogen can respond and adapt to spaceflight and other low fluid shear environments encountered during their natural life cycles. Future studies are aimed at understanding the underlying mechanisms responsible for these phenotypes.
ContributorsKang, Bianca Younseon (Author) / Nickerson, Cheryl (Thesis director) / Barrila, Jennifer (Committee member) / Ott, Mark (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
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
Lonsdaleite, also called hexagonal diamond, has been widely used as a marker of asteroidal impacts. It is thought to play a central role during the graphite-to-diamond transformation, and calculations suggest that it possesses mechanical properties superior to diamond. However, despite extensive efforts, lonsdaleite has never been produced or described as a separate, pure material. Here we show that defects in cubic diamond provide an explanation for the characteristic d-spacings and reflections reported for lonsdaleite. Ultrahigh-resolution electron microscope images demonstrate that samples displaying features attributed to lonsdaleite consist of cubic diamond dominated by extensive {113} twins and {111} stacking faults. These defects give rise to nanometre-scale structural complexity. Our findings question the existence of lonsdaleite and point to the need for re-evaluating the interpretations of many lonsdaleite-related fundamental and applied studies.
ContributorsNemeth, Peter (Author) / Garvie, Laurence (Author) / Aoki, Toshihiro (Author) / Dubrovinskaia, Natalia (Author) / Dubrovinsky, Leonid (Author) / Buseck, Peter (Author) / Department of Chemistry and Biochemistry (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Earth and Space Exploration (Contributor) / Center for Meteorite Studies (Contributor) / Ira A. Fulton Schools of Engineering (Contributor) / LeRoy Eyring Center for Solid State Science (Contributor) / School of Molecular Sciences (Contributor)
Created2014-11-01
Description
Spaceflight and spaceflight analogue culture enhance the virulence and pathogenesis-related stress resistance of the foodborne pathogen Salmonella enterica serovar Typhimurium (S. Typhimurium). This is an alarming finding as it suggests that astronauts may have an increased risk of infection during spaceflight. This risk is further exacerbated as multiple studies indicate that spaceflight negatively impacts aspects of the immune system. In order to ensure astronaut safety during long term missions, it is important to study the phenotypic effects of the microgravity environment on a range of medically important microbial pathogens that might be encountered by the crew. This ground-based study uses the NASA-engineered Rotating Wall Vessel (RWV) bioreactor as a spaceflight analogue culture system to grow bacteria under low fluid shear forces relative to those encountered in microgravity, and interestingly, in the intestinal tract during infection. The culture environment in the RWV is commonly referred to as low shear modeled microgravity (LSMMG). In this study, we characterized the stationary phase stress response of the enteric pathogen, Salmonella enterica serovar Enteritidis (S. Enteritidis), to LSMMG culture. We showed that LSMMG enhanced the resistance of stationary phase cultures of S. Enteritidis to acid and thermal stressors, which differed from the LSSMG stationary phase response of the closely related pathovar, S. Typhimurium. Interestingly, LSMMG increased the ability of both S. Enteritidis and S. Typhimurium to adhere to, invade into, and survive within an in vitro 3-D intestinal co-culture model containing immune cells. Our results indicate that LSMMG regulates pathogenesis-related characteristics of S. Enteritidis in ways that may present an increased health risk to astronauts during spaceflight missions.
ContributorsKoroli, Sara (Author) / Nickerson, Cheryl (Thesis director) / Barrila, Jennifer (Committee member) / Ott, C. Mark (Committee member) / School of Life Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
The International Space Station (ISS) utilizes recycled water for consumption, cleaning and air humidity control. The Environmental Control and Life Support Systems (ECLSS) have been rigorously tested at the NASA Johnson Space Center. Despite the advanced engineering of the water recovery system, bacterial biofilms have been recovered from this potable water source. Microbial contamination of potable water poses a potential threat to crew members onboard the ISS. Because astronauts have been found to have compromised immune systems, bacterial strains that would not typically be considered a danger must be carefully studied to better understand the mechanisms enabling their survival, including polymicrobial interactions. The need for a more thorough understanding of the effect of spaceflight environment on polymicrobial interactions and potential impact on crew health and vehicle integrity is heightened since 1) several potential pathogens have been isolated from the ISS potable water system, 2) spaceflight has been shown to induce unexpected alterations in microbial responses, and 3) emergent phenotypes are often observed when multiple bacterial species are co- cultured together, as compared to pure cultures of single species. In order to address these concerns, suitable growth media are required that will not only support the isolation of these microbes but also the ability to distinguish between them when grown as mixed cultures. In this study, selective and/or differential media were developed for bacterial isolates collected from the ISS potable water supply. In addition to facilitating discrimination between bacteria, the ideal media for each strain was intended to have a 100% recovery rate compared to traditional R2A media. Antibiotic and reagent susceptibility and resistance tests were conducted for the purpose of developing each individual medium. To study a wide range of targets, 12 antibiotics were selected from seven major classes, including penicillin, cephalosporins, fluoroquinolones, aminoglycosides, glycopeptides/lipoglycopeptides, macrolides/lincosamides/streptogramins, tetracyclines, in addition to seven unclassified antibiotics and three reagents. Once developed, medium efficacy was determined by means of growth curve experiments. The development of these media is a critical step for further research into the mechanisms utilized by these strains to survive the harsh conditions of the ISS water system. Furthermore, with an understanding of the complex nature of these polymicrobial communities, specific contamination targeting and control can be conducted to reduce the risk to crew members. Understanding these microbial species and their susceptibilities has potential application for future NASA human explorations, including those to Mars.
ContributorsKing, Olivia Grace (Author) / Nickerson, Cheryl (Thesis director) / Barrila, Jennifer (Committee member) / Ott, Mark (Committee member) / School of Sustainability (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
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