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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
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
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 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
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
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
Description
Droughts are a common phenomenon of the arid South-west USA climate. Despite water limitations, the region has been substantially transformed by agriculture and urbanization. The water requirements to support these human activities along with the projected increase in droughts intensity and frequency challenge long term sustainability and water security, thus the need to spatially and temporally characterize land use/land cover response to drought and quantify water consumption is crucial. This dissertation evaluates changes in `undisturbed' desert vegetation in response to water availability to characterize climate-driven variability. A new model coupling phenology and spectral unmixing was applied to Landsat time series (1987-2010) in order to derive fractional cover (FC) maps of annuals, perennials, and evergreen vegetation. Results show that annuals FC is controlled by short term water availability and antecedent soil moisture. Perennials FC follow wet-dry multi-year regime shifts, while evergreen is completely decoupled from short term changes in water availability. Trend analysis suggests that different processes operate at the local scale. Regionally, evergreen cover increased while perennials and annuals cover decreased. Subsequently, urban land cover was compared with its surrounding desert. A distinct signal of rain use efficiency and aridity index was documented from remote sensing and a soil-water-balance model. It was estimated that a total of 295 mm of water input is needed to sustain current greenness. Finally, an energy balance model was developed to spatio-temporally estimate evapotranspiration (ET) as a proxy for water consumption, and evaluate land use/land cover types in response to drought. Agricultural fields show an average ET of 9.3 mm/day with no significant difference between drought and wet conditions, implying similar level of water usage regardless of climatic conditions. Xeric neighborhoods show significant variability between dry and wet conditions, while mesic neighborhoods retain high ET of 400-500 mm during drought due to irrigation. Considering the potentially limited water availability, land use/land cover changes due to population increases, and the threat of a warming and drying climate, maintaining large water-consuming, irrigated landscapes challenges sustainable practices of water conservation and the need to provide amenities of this desert area for enhancing quality of life.
ContributorsKaplan, Shai (Author) / Myint, Soe Win (Thesis advisor) / Brazel, Anthony J. (Committee member) / Georgescu, Matei (Committee member) / Arizona State University (Publisher)
Created2014
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 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
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
Urban areas produce an urban heat island (UHI), which is manifest as warmer temperatures compared to the surrounding and less developed areas. While it is understood that UHI's are warmer than their surrounding areas, attributing the amount of heat added by the urban area is not easily determined. Current generation modeling systems require diurnal anthropogenic heating profiles. Development of diurnal cycle profiles of anthropogenic heating will help the modeling community as there is currently no database for anthropogenic heating profiles for cities across the United States. With more accurate anthropogenic heating profiles, climate models will be better able to show how humans directly impact the urban climate. This research attempts to create anthropogenic heating profiles for 61 cities in the United States. The method used climate, electricity, natural gas, and transportation data to develop anthropogenic heating profiles for each state. To develop anthropogenic heating profiles, profiles are developed for buildings, transportation, and human metabolism using the most recently available data. Since utilities are reluctant to release data, the building energy profile is developed using statewide electricity by creating a linear regression between the climate and electricity usage. A similar method is used to determine the contribution of natural gas consumption. These profiles are developed for each month of the year, so annual changes in anthropogenic heating can be seen. These profiles can then be put into climate models to enable more accurate urban climate modeling.
ContributorsMilne, Jeffrey (Author) / Georgescu, Matei (Thesis director) / Sailor, David (Committee member) / Brazel, Anthony (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Geographical Sciences and Urban Planning (Contributor)
Created2014-05
Description
Modeling results incorporating several distinct urban expansion futures for the United States in 2100 show that, in the absence of any adaptive urban design, megapolitan expansion, alone and separate from greenhouse gas-induced forcing, can be expected to raise near-surface temperatures 1–2 °C not just at the scale of individual cities but over large regional swaths of the country. This warming is a significant fraction of the 21st century greenhouse gas-induced climate change simulated by global climate models. Using a suite of regional climate simulations, we assessed the efficacy of commonly proposed urban adaptation strategies, such as green, cool roof, and hybrid approaches, to ameliorate the warming. Our results quantify how judicious choices in urban planning and design cannot only counteract the climatological impacts of the urban expansion itself but also, can, in fact, even offset a significant percentage of future greenhouse warming over large scales. Our results also reveal tradeoffs among different adaptation options for some regions, showing the need for geographically appropriate strategies rather than one size fits all solutions.
ContributorsGeorgescu, Matei (Author) / Morefield, Philip E. (Author) / Bierwagen, Britta G. (Author) / Weaver, Christopher P. (Author)
Created2014-02-25