Matching Items (66)
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
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
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
Single cell heterogeneity plays an important role in the onset and progression of a variety of disease pathologies. One of the most notable examples of the impact of heterogeneity in the complexity of a disease is cancer. Traditionally, molecular analyses on cancer-related samples have been performed on bulk populations of cells, with the resultant data only representative of an average of the population, thereby concealing potentially relevant information about individual cells. Performing these studies at the single cell level is proposed to address this issue. However, current methods for the isolation and analysis of single cells often require specialized and expensive equipment that may be prohibitive to labs wishing to perform such analyses. Herein, a method for the isolation and gene expression analysis of single cells is described that (1) relies only on readily available, inexpensive materials, (2) is compatible with phase and fluorescent microscopy, and (3) allows for the ability to track specific cells throughout all measurements. This method utilizes random seeding of single cells on 72-well Terasaki plates (also called microtest plates) that have 20 µl, optically clear flat-bottomed wells in order to circumvent the need for specific hardware for cell isolation. Suspensions of the Barrett’s esophagus epithelial cell line CP-D stably expressing turboGFP and a related, GFP-negative BE cell line, CP-A, were prepared, seeded at a concentration of approximately 1-2 cells/well and incubated overnight. Wells containing single cells were visually identified using phase-contrast and fluorescent microscopy. Single cells were then lysed directly in the well, total RNA was isolated, and RT-qPCR was performed. RT-qPCR results reflected the ability to distinguish between turboGFP-expressing and non-expressing cells that matched previous identification by microscopy. These results indicate that this is a convenient and cost-effective method for studying gene expression in single cells.
ContributorsZiegler, Colleen Patricia (Author) / Chao, Joseph (Thesis director) / Tran, Thai (Committee member) / Yaron, Jordan (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2013-05
Description
Background
Grading schemes for breast cancer diagnosis are predominantly based on pathologists' qualitative assessment of altered nuclear structure from 2D brightfield microscopy images. However, cells are three-dimensional (3D) objects with features that are inherently 3D and thus poorly characterized in 2D. Our goal is to quantitatively characterize nuclear structure in 3D, assess its variation with malignancy, and investigate whether such variation correlates with standard nuclear grading criteria.
Methodology
We applied micro-optical computed tomographic imaging and automated 3D nuclear morphometry to quantify and compare morphological variations between human cell lines derived from normal, benign fibrocystic or malignant breast epithelium. To reproduce the appearance and contrast in clinical cytopathology images, we stained cells with hematoxylin and eosin and obtained 3D images of 150 individual stained cells of each cell type at sub-micron, isotropic resolution. Applying volumetric image analyses, we computed 42 3D morphological and textural descriptors of cellular and nuclear structure.
Principal Findings
We observed four distinct nuclear shape categories, the predominant being a mushroom cap shape. Cell and nuclear volumes increased from normal to fibrocystic to metastatic type, but there was little difference in the volume ratio of nucleus to cytoplasm (N/C ratio) between the lines. Abnormal cell nuclei had more nucleoli, markedly higher density and clumpier chromatin organization compared to normal. Nuclei of non-tumorigenic, fibrocystic cells exhibited larger textural variations than metastatic cell nuclei. At p<0.0025 by ANOVA and Kruskal-Wallis tests, 90% of our computed descriptors statistically differentiated control from abnormal cell populations, but only 69% of these features statistically differentiated the fibrocystic from the metastatic cell populations.
Conclusions
Our results provide a new perspective on nuclear structure variations associated with malignancy and point to the value of automated quantitative 3D nuclear morphometry as an objective tool to enable development of sensitive and specific nuclear grade classification in breast cancer diagnosis.
Grading schemes for breast cancer diagnosis are predominantly based on pathologists' qualitative assessment of altered nuclear structure from 2D brightfield microscopy images. However, cells are three-dimensional (3D) objects with features that are inherently 3D and thus poorly characterized in 2D. Our goal is to quantitatively characterize nuclear structure in 3D, assess its variation with malignancy, and investigate whether such variation correlates with standard nuclear grading criteria.
Methodology
We applied micro-optical computed tomographic imaging and automated 3D nuclear morphometry to quantify and compare morphological variations between human cell lines derived from normal, benign fibrocystic or malignant breast epithelium. To reproduce the appearance and contrast in clinical cytopathology images, we stained cells with hematoxylin and eosin and obtained 3D images of 150 individual stained cells of each cell type at sub-micron, isotropic resolution. Applying volumetric image analyses, we computed 42 3D morphological and textural descriptors of cellular and nuclear structure.
Principal Findings
We observed four distinct nuclear shape categories, the predominant being a mushroom cap shape. Cell and nuclear volumes increased from normal to fibrocystic to metastatic type, but there was little difference in the volume ratio of nucleus to cytoplasm (N/C ratio) between the lines. Abnormal cell nuclei had more nucleoli, markedly higher density and clumpier chromatin organization compared to normal. Nuclei of non-tumorigenic, fibrocystic cells exhibited larger textural variations than metastatic cell nuclei. At p<0.0025 by ANOVA and Kruskal-Wallis tests, 90% of our computed descriptors statistically differentiated control from abnormal cell populations, but only 69% of these features statistically differentiated the fibrocystic from the metastatic cell populations.
Conclusions
Our results provide a new perspective on nuclear structure variations associated with malignancy and point to the value of automated quantitative 3D nuclear morphometry as an objective tool to enable development of sensitive and specific nuclear grade classification in breast cancer diagnosis.
ContributorsNandakumar, Vivek (Author) / Kelbauskas, Laimonas (Author) / Hernandez, Kathryn (Author) / Lintecum, Kelly (Author) / Senechal, Patti (Author) / Bussey, Kimberly (Author) / Davies, Paul (Author) / Johnson, Roger (Author) / Meldrum, Deirdre (Author) / Ira A. Fulton Schools of Engineering (Contributor) / School of Electrical, Computer and Energy Engineering (Contributor) / Biodesign Institute (Contributor) / Center for Biosignatures Discovery Automation (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / Department of Physics (Contributor)
Created2012-01-05
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 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