Matching Items (37)
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
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
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
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
One of the identified health risk areas for human spaceflight is infectious disease, particularly involving environmental microorganisms already found on the International Space Station (ISS). In particular, bacteria belonging to the Burkholderia cepacia complex (Bcc) which can cause human disease in those who are immunocompromised, have been identified in the ISS water supply. This present study characterized the effect of spaceflight analog culture conditions on Bcc to certain physiological stresses (acid and thermal as well as intracellular survival in U927 human macrophage cells). The NASA-designed Rotating Wall Vessel (RWV) bioreactor was used as the spaceflight analogue culture system in these studies to grow Bcc bacterial cells under Low Shear Modeled Microgravity (LSMMG) conditions. Results show that LSMMG culture increased the resistance of Bcc to both acid and thermal stressors, but did not alter phagocytic uptake in 2-D monolayers of human monocytes.
ContributorsVu, Christian-Alexander (Author) / Nickerson, Cheryl (Thesis director) / Barrila, Jennifer (Committee member) / Ott, Mark (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor)
Created2023-05