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Global behavior of finite energy solutions to the focusing nonlinear Schrödinger Equation in d dimension

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

A low-energy, low-cost field deployable sampler for microbial DNA profiling

Description

Filtration for microfluidic sample-collection devices is desirable for sample selection, concentration, preprocessing, and downstream manipulation, but microfabricating the required sub-micrometer filtration structure is an elaborate process. This thesis presents a simple method to fabricate polydimethylsiloxane (PDMS) devices with an integrated membrane filter that will sample, lyse, and extract the DNA…

Filtration for microfluidic sample-collection devices is desirable for sample selection, concentration, preprocessing, and downstream manipulation, but microfabricating the required sub-micrometer filtration structure is an elaborate process. This thesis presents a simple method to fabricate polydimethylsiloxane (PDMS) devices with an integrated membrane filter that will sample, lyse, and extract the DNA from microorganisms in aqueous environments. An off-the-shelf membrane filter disc was embedded in a PDMS layer and sequentially bound with other PDMS channel layers. No leakage was observed during filtration. This device was validated by concentrating a large amount of cyanobacterium Synechocystis in simulated sample water with consistent performance across devices. After accumulating sufficient biomass on the filter, a sequential electrochemical lysing process was performed by applying 5VDC across the filter. This device was further evaluated by delivering several samples of differing concentrations of cyanobacterium Synechocystis then quantifying the DNA using real-time PCR. Lastly, an environmental sample was run through the device and the amount of photosynthetic microorganisms present in the water was determined. The major breakthroughs in this design are low energy demand, cheap materials, simple design, straightforward fabrication, and robust performance, together enabling wide-utility of similar chip-based devices for field-deployable operations in environmental micro-biotechnology.

ContributorsLecluse, Aurelie (Author) / Meldrum, Deirdre (Thesis advisor) / Chao, Joseph (Thesis advisor) / Westerhoff, Paul (Committee member) / Arizona State University (Publisher)

Created2011

Optimizing micro-vortex chamber for living single cell rotation

Description

Single cell phenotypic heterogeneity studies reveal more information about the pathogenesis process than conventional bulk methods. Furthermore, investigation of the individual cellular response mechanism during rapid environmental changes can only be achieved at single cell level. By enabling the study of cellular morphology, a single cell three-dimensional (3D) imaging system…

Single cell phenotypic heterogeneity studies reveal more information about the pathogenesis process than conventional bulk methods. Furthermore, investigation of the individual cellular response mechanism during rapid environmental changes can only be achieved at single cell level. By enabling the study of cellular morphology, a single cell three-dimensional (3D) imaging system can be used to diagnose fatal diseases, such as cancer, at an early stage. One proven method, CellCT, accomplishes 3D imaging by rotating a single cell around a fixed axis. However, some existing cell rotating mechanisms require either intricate microfabrication, and some fail to provide a suitable environment for living cells. This thesis develops a microvorterx chamber that allows living cells to be rotated by hydrodynamic alone while facilitating imaging access. In this thesis work, 1) the new chamber design was developed through numerical simulation. Simulations revealed that in order to form a microvortex in the side chamber, the ratio of the chamber opening to the channel width must be smaller than one. After comparing different chamber designs, the trapezoidal side chamber was selected because it demonstrated controllable circulation and met the imaging requirements. Microvortex properties were not sensitive to the chambers with interface angles ranging from 0.32 to 0.64. A similar trend was observed when chamber heights were larger than chamber opening. 2) Micro-particle image velocimetry was used to characterize microvortices and validate simulation results. Agreement between experimentation and simulation confirmed that numerical simulation was an effective method for chamber design. 3) Finally, cell rotation experiments were performed in the trapezoidal side chamber. The experimental results demonstrated cell rotational rates ranging from 12 to 29 rpm for regular cells. With a volumetric flow rate of 0.5 µL/s, an irregular cell rotated at a mean rate of 97 ± 3 rpm. Rotational rates can be changed by altering inlet flow rates.

ContributorsZhang, Wenjie (Author) / Frakes, David (Thesis advisor) / Meldrum, Deirdre (Thesis advisor) / Chao, Shih-hui (Committee member) / Wang, Xiao (Committee member) / Arizona State University (Publisher)

Created2011

Coherent Doppler LIDAR for boundary layer studies and wind energy

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

A distributed component-based software framework for laboratory automation systems

Description

Laboratory automation systems have seen a lot of technological advances in recent times. As a result, the software that is written for them are becoming increasingly sophisticated. Existing software architectures and standards are targeted to a wider domain of software development and need to be customized in order to use…

Laboratory automation systems have seen a lot of technological advances in recent times. As a result, the software that is written for them are becoming increasingly sophisticated. Existing software architectures and standards are targeted to a wider domain of software development and need to be customized in order to use them for developing software for laboratory automation systems. This thesis proposes an architecture that is based on existing software architectural paradigms and is specifically tailored to developing software for a laboratory automation system. The architecture is based on fairly autonomous software components that can be distributed across multiple computers. The components in the architecture make use of asynchronous communication methodologies that are facilitated by passing messages between one another. The architecture can be used to develop software that is distributed, responsive and thread-safe. The thesis also proposes a framework that has been developed to implement the ideas proposed by the architecture. The framework is used to develop software that is scalable, distributed, responsive and thread-safe. The framework currently has components to control very commonly used laboratory automation devices such as mechanical stages, cameras, and also to do common laboratory automation functionalities such as imaging.

ContributorsKuppuswamy, Venkataramanan (Author) / Meldrum, Deirdre (Thesis advisor) / Collofello, James (Thesis advisor) / Sarjoughian, Hessam S. (Committee member) / Johnson, Roger (Committee member) / Arizona State University (Publisher)

Created2012

A chip for hydrodynamic microvortical rotation of live single cells

Description

Single cell analysis has become increasingly important in understanding disease onset, progression, treatment and prognosis, especially when applied to cancer where cellular responses are highly heterogeneous. Through the advent of single cell computerized tomography (Cell-CT), researchers and clinicians now have the ability to obtain high resolution three-dimensional (3D) reconstructions of…

Single cell analysis has become increasingly important in understanding disease onset, progression, treatment and prognosis, especially when applied to cancer where cellular responses are highly heterogeneous. Through the advent of single cell computerized tomography (Cell-CT), researchers and clinicians now have the ability to obtain high resolution three-dimensional (3D) reconstructions of single cells. Yet to date, no live-cell compatible version of the technology exists. In this thesis, a microfluidic chip with the ability to rotate live single cells in hydrodynamic microvortices about an axis parallel to the optical focal plane has been demonstrated. The chip utilizes a novel 3D microchamber design arranged beneath a main channel creating flow detachment into the chamber, producing recirculating flow conditions. Single cells are flowed through the main channel, held in the center of the microvortex by an optical trap, and rotated by the forces induced by the recirculating fluid flow. Computational fluid dynamics (CFD) was employed to optimize the geometry of the microchamber. Two methods for the fabrication of the 3D microchamber were devised: anisotropic etching of silicon and backside diffuser photolithography (BDPL). First, the optimization of the silicon etching conditions was demonstrated through design of experiment (DOE). In addition, a non-conventional method of soft-lithography was demonstrated which incorporates the use of two positive molds, one of the main channel and the other of the microchambers, compressed together during replication to produce a single ultra-thin (<200 µm) negative used for device assembly. Second, methods for using thick negative photoresists such as SU-8 with BDPL have been developed which include a new simple and effective method for promoting the adhesion of SU-8 to glass. An assembly method that bonds two individual ultra-thin (<100 µm) replications of the channel and the microfeatures has also been demonstrated. Finally, a pressure driven pumping system with nanoliter per minute flow rate regulation, sub-second response times, and < 3% flow variability has been designed and characterized. The fabrication and assembly of this device is inexpensive and utilizes simple variants of conventional microfluidic fabrication techniques, making it easily accessible to the single cell analysis community.

ContributorsMyers, Jakrey R (Author) / Meldrum, Deirdre (Thesis advisor) / Johnson, Roger (Committee member) / Frakes, David (Committee member) / Arizona State University (Publisher)

Created2012

Model agnostic extreme sub-pixel visual measurement and optimal characterization

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

Multiple Trigger Points for Quantifying Heat-Health Impacts: New Evidence from a Hot Climate

Description

Background: Extreme heat is a public health challenge. The scarcity of directly comparable studies on the association of heat with morbidity and mortality and the inconsistent identification of threshold temperatures for severe impacts hampers the development of comprehensive strategies aimed at reducing adverse heat-health events.

Objectives: This quantitative study was designed…

Background: Extreme heat is a public health challenge. The scarcity of directly comparable studies on the association of heat with morbidity and mortality and the inconsistent identification of threshold temperatures for severe impacts hampers the development of comprehensive strategies aimed at reducing adverse heat-health events.

Objectives: This quantitative study was designed to link temperature with mortality and morbidity events in Maricopa County, Arizona, USA, with a focus on the summer season.

Methods: Using Poisson regression models that controlled for temporal confounders, we assessed daily temperature–health associations for a suite of mortality and morbidity events, diagnoses, and temperature metrics. Minimum risk temperatures, increasing risk temperatures, and excess risk temperatures were statistically identified to represent different “trigger points” at which heat-health intervention measures might be activated.

Results: We found significant and consistent associations of high environmental temperature with all-cause mortality, cardiovascular mortality, heat-related mortality, and mortality resulting from conditions that are consequences of heat and dehydration. Hospitalizations and emergency department visits due to heat-related conditions and conditions associated with consequences of heat and dehydration were also strongly associated with high temperatures, and there were several times more of those events than there were deaths. For each temperature metric, we observed large contrasts in trigger points (up to 22°C) across multiple health events and diagnoses.

Conclusion: Consideration of multiple health events and diagnoses together with a comprehensive approach to identifying threshold temperatures revealed large differences in trigger points for possible interventions related to heat. Providing an array of heat trigger points applicable for different end-users may improve the public health response to a problem that is projected to worsen in the coming decades.

ContributorsPettiti, Diana B. (Author) / Hondula, David M. (Author) / Yang, Shuo (Author) / Harlan, Sharon L. (Author) / Chowell, Gerardo (Author)

Created2016-02-01

Challenges Associated with Projecting Urbanization-Induced Heat-Related Mortality

Description

Maricopa County, Arizona, anchor to the fastest growing megapolitan area in the United States, is located in a hot desert climate where extreme temperatures are associated with elevated risk of mortality. Continued urbanization in the region will impact atmospheric temperatures and, as a result, potentially affect human health. We aimed…

Maricopa County, Arizona, anchor to the fastest growing megapolitan area in the United States, is located in a hot desert climate where extreme temperatures are associated with elevated risk of mortality. Continued urbanization in the region will impact atmospheric temperatures and, as a result, potentially affect human health. We aimed to quantify the number of excess deaths attributable to heat in Maricopa County based on three future urbanization and adaptation scenarios and multiple exposure variables.

Two scenarios (low and high growth projections) represent the maximum possible uncertainty range associated with urbanization in central Arizona, and a third represents the adaptation of high-albedo cool roof technology. Using a Poisson regression model, we related temperature to mortality using data spanning 1983–2007. Regional climate model simulations based on 2050-projected urbanization scenarios for Maricopa County generated distributions of temperature change, and from these predicted changes future excess heat-related mortality was estimated. Subject to urbanization scenario and exposure variable utilized, projections of heat-related mortality ranged from a decrease of 46 deaths per year (− 95%) to an increase of 339 deaths per year (+ 359%).

Projections based on minimum temperature showed the greatest increase for all expansion and adaptation scenarios and were substantially higher than those for daily mean temperature. Projections based on maximum temperature were largely associated with declining mortality. Low-growth and adaptation scenarios led to the smallest increase in predicted heat-related mortality based on mean temperature projections. Use of only one exposure variable to project future heat-related deaths may therefore be misrepresentative in terms of direction of change and magnitude of effects. Because urbanization-induced impacts can vary across the diurnal cycle, projections of heat-related health outcomes that do not consider place-based, time-varying urban heat island effects are neglecting essential elements for policy relevant decision-making.

ContributorsHondula, David M. (Author) / Georgescu, Matei (Author) / Balling, Jr., Robert C. (Author)

Created2014-04-28

Assessing Adaptation Strategies for Extreme Heat: A Public Health Evaluation of Cooling Centers in Maricopa County, Arizona

Description

Preventing heat-associated morbidity and mortality is a public health priority in Maricopa County, Arizona (United States). The objective of this project was to evaluate Maricopa County cooling centers and gain insight into their capacity to provide relief for the public during extreme heat events. During the summer of 2014, 53…

Preventing heat-associated morbidity and mortality is a public health priority in Maricopa County, Arizona (United States). The objective of this project was to evaluate Maricopa County cooling centers and gain insight into their capacity to provide relief for the public during extreme heat events. During the summer of 2014, 53 cooling centers were evaluated to assess facility and visitor characteristics. Maricopa County staff collected data by directly observing daily operations and by surveying managers and visitors. The cooling centers in Maricopa County were often housed within community, senior, or religious centers, which offered various services for at least 1500 individuals daily. Many visitors were unemployed and/or homeless. Many learned about a cooling center by word of mouth or by having seen the cooling center’s location. The cooling centers provide a valuable service and reach some of the region’s most vulnerable populations. This project is among the first to systematically evaluate cooling centers from a public health perspective and provides helpful insight to community leaders who are implementing or improving their own network of cooling centers.

ContributorsBerisha, Vjollca (Author) / Hondula, David M. (Author) / Roach, Matthew (Author) / White, Jessica R. (Author) / McKinney, Benita (Author) / Bentz, Darcie (Author) / Mohamed, Ahmed (Author) / Uebelherr, Joshua (Author) / Goodin, Kate (Author)

Created2016-09-23