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- Member of: ASU Electronic Theses and Dissertations
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
Infrastructure systems are facing non-stationary challenges that stem from climate change and the increasingly complex interactions between the social, ecological, and technological systems (SETSs). It is crucial for transportation infrastructures—which enable residents to access opportunities and foster prosperity, quality of life, and social connections—to be resilient under these non-stationary challenges. Vulnerability assessment (VA) examines the potential consequences a system is likely to experience due to exposure to perturbation or stressors and lack of the capacity to adapt. Post-fire debris flow and heat represent particularly challenging problems for infrastructure and users in the arid U.S. West. Post-fire debris flow, which is manifested with heat and drought, produces powerful runoff threatening physical transportation infrastructures. And heat waves have devastating health effects on transportation infrastructure users, including increased mortality rates. VA anticipates the potential consequences of these perturbations and enables infrastructure stakeholders to improve the system's resilience. The current transportation climate VA—which only considers a single direct climate stressor on the infrastructure—falls short of addressing the wildfire and heat challenges. This work proposes advanced transportation climate VA methods to address the complex and multiple climate stressors and the vulnerability of infrastructure users. Two specific regions were chosen to carry out the progressive transportation climate VA: 1) the California transportation networks’ vulnerability to post-fire debris flows, and 2) the transportation infrastructure user’s vulnerability to heat exposure in Phoenix.
ContributorsLi, Rui (Author) / Chester, Mikhail V. (Thesis advisor) / Middel, Ariane (Committee member) / Hondula, David M. (Committee member) / Pendyala, Ram (Committee member) / Arizona State University (Publisher)
Created2022
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
Machine learning (ML) and deep learning (DL) has become an intrinsic part of multiple fields. The ability to solve complex problems makes machine learning a panacea. In the last few years, there has been an explosion of data generation, which has greatly improvised machine learning models. But this comes with a cost of high computation, which invariably increases power usage and cost of the hardware. In this thesis we explore applications of ML techniques, applied to two completely different fields - arts, media and theater and urban climate research using low-cost and low-powered edge devices. The multi-modal chatbot uses different machine learning techniques: natural language processing (NLP) and computer vision (CV) to understand inputs of the user and accordingly perform in the play and interact with the audience. This system is also equipped with other interactive hardware setups like movable LED systems, together they provide an experiential theatrical play tailored to each user. I will discuss how I used edge devices to achieve this AI system which has created a new genre in theatrical play. I will then discuss MaRTiny, which is an AI-based bio-meteorological system that calculates mean radiant temperature (MRT), which is an important parameter for urban climate research. It is also equipped with a vision system that performs different machine learning tasks like pedestrian and shade detection. The entire system costs around $200 which can potentially replace the existing setup worth $20,000. I will further discuss how I overcame the inaccuracies in MRT value caused by the system, using machine learning methods. These projects although belonging to two very different fields, are implemented using edge devices and use similar ML techniques. In this thesis I will detail out different techniques that are shared between these two projects and how they can be used in several other applications using edge devices.
ContributorsKulkarni, Karthik Kashinath (Author) / Jayasuriya, Suren (Thesis advisor) / Middel, Ariane (Thesis advisor) / Yu, Hongbin (Committee member) / Arizona State University (Publisher)
Created2021
Description
Cities globally are experiencing substantial warming due to ongoing urbanization and climate change. However, existing efforts to mitigate urban heat focus mainly on new technologies, exacerbate social injustices, and ignore the need for a sustainability lens that considers environmental, social, and economic perspectives. Heat in urban areas is amplified and urgently needs to be considered as a critical sustainability issue that crosses disciplinary and sectoral (traditional) boundaries. The missing urgency is concerning because urban overheating is a multi-faceted threat to the well-being and performance of individuals as well as the energy efficiency and economy of cities. Urban heat consequences require transformation in ways of thinking by involving the best available knowledge engaging scientists, policymakers, and communities. To do so, effective heat mitigation planning requires a considerable amount of diverse knowledge sources, yet urban planners face multiple barriers to effective heat mitigation, including a lack of usable, policy-relevant science and governance structures. To address these issues, transdisciplinary approaches, such as co-production via partnerships and the creation of usable, policy-relevant science, are necessary to allow for sustainable and equitable heat mitigation that allow cities to work toward multiple Sustainable Development Goals (SDGs) using a systems approach. This dissertation presents three studies that contribute to a sustainability lens on urban heat, improve the holistic and multi-perspective understanding of heat mitigation strategies, provide contextual guidance for reflective pavement as a heat mitigation strategy, and evaluate a multilateral, sustainability-oriented, co-production partnership to foster heat resilience equitably in cities. Results show that science and city practice communicate differently about heat mitigation strategies while both avoid to communicate disservices and trade-offs. Additionally, performance evaluation of heat mitigation strategies for decision-making needs to consider multiple heat metrics, people, and background climate. Lastly, the partnership between science, city practice, and community needs to be evaluated to be accountable and provide a pathway of growth for all partners. The outcomes of this dissertation advance research and awareness of urban heat for science, practice, and community, and provide guidance to improve holistic and sustainable decision-making in cities and partnerships to address SDGs around urban heat.
ContributorsSchneider, Florian Arwed (Author) / Middel, Ariane (Thesis advisor) / Vanos, Jennifer K (Committee member) / Withycombe Keeler, Lauren (Committee member) / Arizona State University (Publisher)
Created2023
Description
Extreme heat and its human impacts are significant public health challenges that disproportionately affect certain populations. Often, people with the least resources to cope with the heat also live in the hottest regions of cities. Previous heat vulnerability research has predominantly been conducted at a coarse geographic scale, yet translating relationships measured at aggregated scales to the individual level can result in ecological fallacy. Prior work has also primarily studied the most severe health outcomes: hospitalization/emergency care and mortality. It is likely that magnitudes more people are experiencing negative health impacts from heat that do not necessarily result in medical care. Such less severe impacts are under-researched in the literature.This dissertation addresses these knowledge gaps by identifying how social characteristics and physical measurements of heat at the individual and household level act independently and in concert to influence human heat-related outcomes, especially less severe outcomes. In the first paper, meta-analysis was used to quantify the summary effects of vulnerability indicators on incidence of heat-related illness. More proximal vulnerability indicators (e.g., residential air conditioning use, indoor heat exposure, etc.) tended to have the strongest impact on odds of experiencing heat-related illness than more distal indicators. In the next paper, indoor air temperature observations were related to the social characteristics of the residents. The strongest predictor of indoor air temperature was the residents’ ideal thermally comfortable temperature, despite affordability. In the final paper, fine scale biometeorological observations of the outdoor thermal environment near residents’ homes were linked to their experience with heat-related illness. The outdoor thermal environment appeared to have a stronger, more consistent impact on heat-related illness among households in a lower income neighborhood compared to a higher income one. These findings affirm the value of employing residential heat mitigation solutions at the individual and household scale, indoors and outdoors. Across all chapters, the indoor thermal environment, and the ability to modify it, had a clear impact on residents’ comfort and health. Solutions that target the most proximal causal factors of heat-related illness will likely have the greatest impact on reducing the burden of heat on human health and well-being.
ContributorsWright, Mary K (Author) / Hondula, David M (Thesis advisor) / Larson, Kelli L (Committee member) / Middel, Ariane (Committee member) / Arizona State University (Publisher)
Created2023
Description
The measurement of the radiation and convection that the human body experiences are important for ensuring safety in extreme heat conditions. The radiation from the surroundings on the human body is most often measured using globe or cylindrical radiometers. The large errors stemming from differences in internal and exterior temperatures and indirect estimation of convection can be resolved by simultaneously using three cylindrical radiometers (1 cm diameter, 9 cm height) with varying surface properties and internal heating. With three surface balances, the three unknowns (heat transfer coefficient, shortwave, and longwave radiation) can be solved for directly. As compared to integral radiation measurement technique, however, the bottom mounting using a wooden-dowel of the three-cylinder radiometers resulted in underestimated the total absorbed radiation. This first part of this thesis focuses on reducing the size of the three-cylinder radiometers and an alternative mounting that resolves the prior issues. In particular, the heat transfer coefficient in laminar wind tunnel with wind speed of 0.25 to 5 m/s is measured for six polished, heated cylinders with diameter of 1 cm and height of 1.5 to 9 cm mounted using a wooden dowel. For cylinders with height of 6 cm and above, the heat transfer coefficients are independent of the height and agree with the Hilpert correlation for infinitely long cylinder. Subsequently, a side-mounting for heated 6 cm tall cylinder with top and bottom metallic caps is developed and tested within the wind tunnel. The heat transfer coefficient is shown to be independent of the flow-side mounting and in agreement with the Hilpert correlation.
The second part of this thesis explores feasibility of employing the three-cylinder concept to measuring all air-flow parameters relevant to human convection including mean wind speed, turbulence intensity and length scale. Heated cylinders with same surface properties but varying diameters are fabricated. Uniformity of their exterior temperature, which is fundamental to the three-cylinder anemometer concept, is tested during operation using infrared camera. To provide a lab-based method to measure convection from the cylinders in turbulent flow, several designs of turbulence-generating fractal grids are laser-cut and introduced into the wind tunnel.
ContributorsGupta, Mahima (Author) / Rykaczewski, Konrad (Thesis advisor) / Pathikonda, Gokul (Thesis advisor) / Middel, Ariane (Committee member) / Arizona State University (Publisher)
Created2024
Description
The global increase in urbanization has raised questions about urban sustainability to which multiple research communities have entered. Those communities addressing interest in the urban heat island (UHI) effect and extreme temperatures include land system science, urban/landscape ecology, and urban climatology. General investigations of UHI have focused primarily on land surface and canopy layer air temperatures. The surface temperature is of prime importance to UHI studies because of its central rule in the surface energy balance, direct effects on air temperature, and outdoor thermal comfort. Focusing on the diurnal surface temperature variations in Phoenix, Arizona, especially on the cool (green space) island effect and the surface heat island effect, the dissertation develops three research papers that improve the integration among the abovementioned sub-fields. Specifically, these papers involve: (1) the quantification and modeling of the diurnal cooling benefits of green space; (2) the optimization of green space locations to reduce the surface heat island effect in daytime and nighttime; and, (3) an evaluation of the effects of vertical urban forms on land surface temperature using Google Street View. These works demonstrate that the pattern of new green spaces in central Phoenix could be optimized such that 96% of the maximum daytime and nighttime cooling benefits would be achieved, and that Google Street View data offers an alternative to other data, providing the vertical dimensions of land-cover for addressing surface temperature impacts, increasing the model accuracy over the use of horizontal land-cover data alone. Taken together, the dissertation points the way towards the integration of research directions to better understand the consequences of detailed land conditions on temperatures in urban areas, providing insights for urban designs to alleviate these extremes.
ContributorsZhang, Yujia (Author) / Turner, Billie (Thesis advisor) / Murray, Alan T. (Committee member) / Myint, Soe W (Committee member) / Middel, Ariane (Committee member) / Arizona State University (Publisher)
Created2018