Matching Items (83)
Filtering by
- Status: Published
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
This thesis explores and analyzes the emergence of for-profit stem cell clinics in the United States, specifically in the Phoenix metropolitan area. Stem cell therapy is an emerging field that has great potential in preventing or treating a number of diseases. Certain companies are currently researching the application of stem cells as therapeutics. At present the FDA has only approved one stem cell-based product; however, there are a number of companies currently offering stem cell therapies. In the past five years, most news articles discussing these companies offering stem cell treatments talk of clinics in other countries. Recently, there seems to be a number of stem cell clinics appearing in the United States. Using a web search engine, fourteen stem cell clinics were identified and analyzed in the Phoenix metropolitan area. Each clinic was analyzed by their four key characteristics: business operations, stem cell types, stem cell isolation methods, and their position with the FDA. Based off my analysis, most of the identified clinics are located in Scottsdale or Phoenix. Some of these clinics even share the same location as another medical practice. Each of the fourteen clinics treat more than one type of health condition. The stem clinics make use of four stem cell types and three different isolation methods to obtain the stem cells. The doctors running these clinics almost always treat health conditions outside of their expertise. Some of these clinics even claim they are not subject to FDA regulation.
ContributorsAmrelia, Divya Vikas (Author) / Brafman, David (Thesis director) / Frow, Emma (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
This thesis shows analyses of mixing and transport patterns associated with Hurricane Katrina as it hit the United States in August of 2005. Specifically, by applying atmospheric velocity information from the Weather Research and Forecasting System, finite-time Lyapunov exponents have been computed and the Lagrangian Coherent Structures have been identified. The chaotic dynamics of material transport induced by the hurricane are results from these structures within the flow. Boundaries of the coherent structures are highlighted by the FTLE field. Individual particle transport within the hurricane is affected by the location of these boundaries. In addition to idealized fluid particles, we also studied inertial particles which have finite size and inertia. Basing on established Maxey-Riley equations of the dynamics of particles of finite size, we obtain a reduced equation governing the position process. Using methods derived from computer graphics, we identify maximizers of the FTLE field. Following and applying these ideas, we analyze the dynamics of inertial particle transport within Hurricane Katrina, through comparison of trajectories of dierent sized particles and by pinpointing the location of the Lagrangian Coherent Structures.
ContributorsWake, Christian (Author) / Tang, Wenbo (Thesis director) / Moustaoui, Mohamed (Committee member) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
The goal of this project was to examine the separatricies that define regions of distinct flow behaviors in realistic time-dependent dynamical systems. In particular, we adapted previously available methods for computing the Finite-Time Lyapunov Exponent (FTLE) to a set of measured wind velocity data in order to visualize the separatricies as ridges of the FTLE field in a section of the atmosphere. This visualization required a number of alterations to the original methods, including interpolation techniques and two different adaptive refinement schemes for producing more detailed results. Overall, there were two computations performed with the wind velocity data: once along a single spherical surface, on which the separatricies could be visualized as material lines, and then along a three-dimensional section of the atmosphere, for which the separatricies were material surfaces. The resulting figures provide an image of the Antarctic polar vortex from the wind velocity data, which is consistent with other data gathered on the same date.
ContributorsUpton, James Thomas (Author) / Tang, Wenbo (Thesis director) / Moustaoui, Mohamed (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2014-05
Description
Using weather data from the Weather Research and Forecasting model (WRF), we analyze the transport of inertial particles in Hurricane Katrina in order to identify coherent patterns of motion. For our analysis, we choose a Lagrangian approach instead of an Eulerian approach because the Lagrangian approach is objective and frame-independent, and gives results which are better defined. In particular, we locate Lagrangian Coherent Structures (LCS), which are smooth sets of fluid particles which are locally most hyperbolic (either attracting or repelling). We implement a variational method for locating LCS and compare the results to previous computation of LCS using Finite-Time Lyapunov Exponents (FTLE) to identify regions of high stretching in the fluid flow.
ContributorsDeibel, Angelica Rae (Author) / Tang, Wenbo (Thesis director) / Moustaoui, Mohamed (Committee member) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2013-05
Description
As life expectancy increases worldwide, age related diseases are becoming greater health concerns. One of the most prevalent age-related diseases in the United States is dementia, with Alzheimer’s disease (AD) being the most common form, accounting for 60-80% of cases. Genetics plays a large role in a person’s risk of developing AD. Familial AD, which makes up less than 1% of all AD cases, is caused by autosomal dominant gene mutations and has almost 100% penetrance. Genetic risk factors are believed to make up about 49%-79% of the risk in sporadic cases. Many different genetic risk factors for both familial and sporadic AD have been identified, but there is still much work to be done in the field of AD, especially in non-Caucasian populations. This review summarizes the three major genes responsible for familial AD, namely APP, PSEN1 and PSEN2. Also discussed are seven identified genetic risk factors for sporadic AD, single nucleotide polymorphisms in the APOE, ABCA7, NEDD9, CASS4, PTK2B, CLU, and PICALM genes. An overview of the main function of the proteins associated with the genes is given, along with the supposed connection to AD pathology.
ContributorsRichey, Alexandra Emmeline (Author) / Brafman, David (Thesis director) / Raman, Sreedevi (Committee member) / School of International Letters and Cultures (Contributor) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Cell viability is an important assessment in cell culture to characterize the health of the cell population and confirm if cells are alive. Morphology or end-line assays are used to determine cell viability of entire populations. Intracellular pO2 levels is indicative of cell health and metabolism that can be used as a factor to asses cell viability in an in-line assay. Siloxane based pO2 sensing nanoprobes present a modality to visualize intracellular pO2. Using fluorescent lifetime imaging microscopy (FLIM), pO2 levels can be mapped intracellular as a highly functional in-line assay for cell viability. FLIM is an imaging modality that reconstructs an image based of its fluorescent lifetime. Nanoprobes were synthesized in different manufacturing/storage conditions. The nanoprobes for both long- and short-term storage were characterized in a cell free environment testing for changes in fluorescent intensity, average and maximum nanoprobe diameter. The nanoprobes were validated in two different culture systems, 2D and microcarrier culture systems, for human derived neural progenitor cells (NPCs) and neurons. Long- and short-term storage nanoprobes were used to label different neuronal based culture systems to asses labeling efficiency through fluorescent microscopy and flow cytometry. NPCs and neurons in each culture system was tested to see if nanoprobe labeling effected cellular phenotype for traits such as: cell proliferation, gene expression, and calcium imaging. Long-term and short-term storage nanoprobes were successfully validated for both NPCs and neurons in all culture systems. Assessments of the pO2 sensing nanoprobes will be further developed to create a highly functional and efficient in-line test for cell viability.
ContributorsLeyasi, Salma (Author) / Brafman, David (Thesis director) / Kodibagkar, Vikram (Committee member) / Harrington Bioengineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Over 5.8 million people are currently living with Alzheimer’s disease (AD), with the sixth highest mortality rate in the United States. No known cure or substantially life-extending treatment exists. With the growing aging population these numbers are only expected to increase to about 13.8 million by the year 2050. Alzheimer’s is a multifactorial disease, giving rise to two main types: familial AD (FAD) and sporadic AD (SAD). Although there are different factors associated with each type of the disease, both FAD and SAD result in neuronal and synaptic loss and remain difficult to model in-vitro and treat overall.
Current advances in cellular models of neurodegenerative diseases overcome a variety of limitations possessed in animal and post-mortem human models. Human-induced pluripotent stem cells (hiPSCs) provide a platform with cells that can self-renew and differentiate into mature and functional cell types. HiPSCs are at the forefront of neurodegenerative disease research because of their ability to differentiate into neural cell types. Apolipoprotein E (ApoE) is a protein encoded by the APOE gene found on chromosome 19 of the human genome. There are three common polymorphisms in the APOE gene, resulting from a single amino acid change in the protein. The presence of these polymorphisms are studied as associated risk factors of developing AD. Different combinations of these alleles closely relate to the risk a patient has in developing Alzheimer’s disease. The risk associated effects of this gene are primarily investigated, however the protective effects are not examined to the same extent.
This research aims to overcome the existing limitations in cell differentiations and improve cell population purity that limits the variables present in the culture. To do this, this study optimized a differentiation protocol by separating and purifying neuronal cell populations to study the potential protective effects associated with ApoE, a risk factor seen in SAD. This platform aims to use a purified cell population to effectively analyze cell type specific affects of the ApoE risk factor, specifically in neurons.
Current advances in cellular models of neurodegenerative diseases overcome a variety of limitations possessed in animal and post-mortem human models. Human-induced pluripotent stem cells (hiPSCs) provide a platform with cells that can self-renew and differentiate into mature and functional cell types. HiPSCs are at the forefront of neurodegenerative disease research because of their ability to differentiate into neural cell types. Apolipoprotein E (ApoE) is a protein encoded by the APOE gene found on chromosome 19 of the human genome. There are three common polymorphisms in the APOE gene, resulting from a single amino acid change in the protein. The presence of these polymorphisms are studied as associated risk factors of developing AD. Different combinations of these alleles closely relate to the risk a patient has in developing Alzheimer’s disease. The risk associated effects of this gene are primarily investigated, however the protective effects are not examined to the same extent.
This research aims to overcome the existing limitations in cell differentiations and improve cell population purity that limits the variables present in the culture. To do this, this study optimized a differentiation protocol by separating and purifying neuronal cell populations to study the potential protective effects associated with ApoE, a risk factor seen in SAD. This platform aims to use a purified cell population to effectively analyze cell type specific affects of the ApoE risk factor, specifically in neurons.
ContributorsFrisch, Carlye Arin (Author) / Brafman, David (Thesis director) / Tian, Xiaojun (Committee member) / Harrington Bioengineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05