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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
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

Because of a projected surge of several billion urban inhabitants by mid-century, a rising urgency exists to advance local and strategically deployed measures intended to ameliorate negative consequences on urban climate (e.g., heat stress, poor air quality, energy/water availability). Here we highlight the importance of incorporating scale-dependent built environment induced

Because of a projected surge of several billion urban inhabitants by mid-century, a rising urgency exists to advance local and strategically deployed measures intended to ameliorate negative consequences on urban climate (e.g., heat stress, poor air quality, energy/water availability). Here we highlight the importance of incorporating scale-dependent built environment induced solutions within the broader umbrella of urban sustainability outcomes, thereby accounting for fundamental physical principles. Contemporary and future design of settlements demands cooperative participation between planners, architects, and relevant stakeholders, with the urban and global climate community, which recognizes the complexity of the physical systems involved and is ideally fit to quantitatively examine the viability of proposed solutions. Such participatory efforts can aid the development of locally sensible approaches by integrating across the socioeconomic and climatic continuum, therefore providing opportunities facilitating comprehensive solutions that maximize benefits and limit unintended consequences.

ContributorsGeorgescu, Matei (Author) / Chow, Winston, 1951- (Author) / Brazel, Anthony J. (Author) / Trapido-Lurie, B (Author) / Roth, M (Author) / Benson-Lira, V (Author)
Created2015-06-09
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Description

We conducted microclimate simulations in ENVI-Met 3.1 to evaluate the impact of vegetation in lowering temperatures during an extreme heat event in an urban core neighborhood park in Phoenix, Arizona. We predicted air and surface temperatures under two different vegetation regimes: existing conditions representative of Phoenix urban core neighborhoods, and

We conducted microclimate simulations in ENVI-Met 3.1 to evaluate the impact of vegetation in lowering temperatures during an extreme heat event in an urban core neighborhood park in Phoenix, Arizona. We predicted air and surface temperatures under two different vegetation regimes: existing conditions representative of Phoenix urban core neighborhoods, and a proposed scenario informed by principles of landscape design and architecture and Urban Heat Island mitigation strategies. We found significant potential air and surface temperature reductions between representative and proposed vegetation scenarios:

1. A Park Cool Island effect that extended to non-vegetated surfaces.
2. A net cooling of air underneath or around canopied vegetation ranging from 0.9 °C to 1.9 °C during the warmest time of the day.
3. Potential reductions in surface temperatures from 0.8 °C to 8.4 °C in areas underneath or around vegetation.

ContributorsDeclet-Barreto, Juan (Author) / Brazel, Anthony J. (Author) / Martin, Chris A. (Author) / Chow, Winston, 1951- (Author) / Harlan, Sharon L. (Author)
Created2012-12-21
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Description

We examined the horizontal and vertical nocturnal cooling influence of a small park with irrigated lawn and xeric surfaces (∼3 ha) within a university campus of a hot arid city. Temperature data from 0.01- to 3-m heights observed during a bicycle traverse of the campus were combined with modeled spatial

We examined the horizontal and vertical nocturnal cooling influence of a small park with irrigated lawn and xeric surfaces (∼3 ha) within a university campus of a hot arid city. Temperature data from 0.01- to 3-m heights observed during a bicycle traverse of the campus were combined with modeled spatial temperature data simulated from a three-dimensional microclimate model (ENVI-met 3.1). A distinct park cool island, with mean observed magnitudes of 0.7–3.6°C, was documented for both traverse and model data with larger cooling intensities measured closer to surface level. Modeled results possessed varying but generally reasonable accuracy in simulating both spatial and temporal temperature data, although some systematic errors exist. A combination of several factors, such as variations in surface thermal properties, urban geometry, building orientation, and soil moisture, was likely responsible for influencing differential urban and non-urban near-surface temperatures. A strong inversion layer up to 1 m over non-urban surfaces was detected, contrasting with near-neutral lapse rates over urban surfaces. A key factor in the spatial expansion of the park cool island was the advection of cooler park air to adjacent urban surfaces, although this effect was mostly concentrated from 0- to 1-m heights over urban surfaces that were more exposed to the atmosphere.

ContributorsChow, Winston, 1951- (Author) / Pope, Ronald L. (Author) / Martin, Chris A. (Author) / Brazel, Anthony J. (Author)
Created2010-05-21
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Description

This review investigates the possible reasons and motivations underpinning the large body of work, as well as summarizing specific themes, approaches, and theoretical contributions arising from such study.

ContributorsChow, Winston, 1951- (Author) / Brennan, Dean (Author) / Brazel, Anthony J. (Author)
Created2011-08-18
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Description
This research project investigated known and novel differential genetic variants and their associated molecular pathways involved in Type II diabetes mellitus for the purpose of improving diagnosis and treatment methods. The goal of this investigation was to 1) identify the genetic variants and SNPs in Type II diabetes to develo

This research project investigated known and novel differential genetic variants and their associated molecular pathways involved in Type II diabetes mellitus for the purpose of improving diagnosis and treatment methods. The goal of this investigation was to 1) identify the genetic variants and SNPs in Type II diabetes to develop a gene regulatory pathway, and 2) utilize this pathway to determine suitable drug therapeutics for prevention and treatment. Using a Gene Set Enrichment Analysis (GSEA), a set of 1000 gene identifiers from a Mayo Clinic database was analyzed to determine the most significant genetic variants related to insulin signaling pathways involved in Type II Diabetes. The following genes were identified: NRAS, KRAS, PIK3CA, PDE3B, TSC1, AKT3, SOS1, NEU1, PRKAA2, AMPK, and ACC. In an extensive literature review and cross-analysis with Kegg and Reactome pathway databases, novel SNPs located on these gene variants were identified and used to determine suitable drug therapeutics for treatment. Overall, understanding how genetic mutations affect target gene function related to Type II Diabetes disease pathology is crucial to the development of effective diagnosis and treatment. This project provides new insight into the molecular basis of the Type II Diabetes, serving to help untangle the regulatory complexity of the disease and aid in the advancement of diagnosis and treatment. Keywords: Type II Diabetes mellitus, Gene Set Enrichment Analysis, genetic variants, KEGG Insulin Pathway, gene-regulatory pathway
ContributorsBucklin, Lindsay (Co-author) / Davis, Vanessa (Co-author) / Holechek, Susan (Thesis director) / Wang, Junwen (Committee member) / Nyarige, Verah (Committee member) / School of Human Evolution & Social Change (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
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Description
This research project investigated known and novel differential genetic variants and their associated molecular pathways involved in Type II diabetes mellitus for the purpose of improving diagnosis and treatment methods. The goal of this investigation was to 1) identify the genetic variants and SNPs in Type II diabetes to develo

This research project investigated known and novel differential genetic variants and their associated molecular pathways involved in Type II diabetes mellitus for the purpose of improving diagnosis and treatment methods. The goal of this investigation was to 1) identify the genetic variants and SNPs in Type II diabetes to develop a gene regulatory pathway, and 2) utilize this pathway to determine suitable drug therapeutics for prevention and treatment. Using a Gene Set Enrichment Analysis (GSEA), a set of 1000 gene identifiers from a Mayo Clinic database was analyzed to determine the most significant genetic variants related to insulin signaling pathways involved in Type II Diabetes. The following genes were identified: NRAS, KRAS, PIK3CA, PDE3B, TSC1, AKT3, SOS1, NEU1, PRKAA2, AMPK, and ACC. In an extensive literature review and cross-analysis with Kegg and Reactome pathway databases, novel SNPs located on these gene variants were identified and used to determine suitable drug therapeutics for treatment. Overall, understanding how genetic mutations affect target gene function related to Type II Diabetes disease pathology is crucial to the development of effective diagnosis and treatment. This project provides new insight into the molecular basis of the Type II Diabetes, serving to help untangle the regulatory complexity of the disease and aid in the advancement of diagnosis and treatment.
ContributorsDavis, Vanessa Brooke (Co-author) / Bucklin, Lindsay (Co-author) / Holechek, Susan (Thesis director) / Wang, Junwen (Committee member) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
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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