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Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears 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
The Cape Floral Region (CFR) in southwestern South Africa is one of the most diverse in the world, with >9,000 plant species, 70% of which are endemic, in an area of only ~90,000 km2. Many have suggested that the CFR's heterogeneous environment, with respect to landscape gradients, vegetation, rainfall, elevation, and soil fertility, is responsible for the origin and maintenance of this biodiversity. While studies have struggled to link species diversity with these features, no study has attempted to associate patterns of gene flow with environmental data to determine how CFR biodiversity evolves on different scales. Here, a molecular population genetic data is presented for a widespread CFR plant, Leucadendron salignum, across 51 locations with 5-kb of chloroplast (cpDNA) and 6-kb of unlinked nuclear (nuDNA) DNA sequences in a dataset of 305 individuals. In the cpDNA dataset, significant genetic structure was found to vary on temporal and spatial scales, separating Western and Eastern Capes - the latter of which appears to be recently derived from the former - with the highest diversity in the heart of the CFR in a central region. A second study applied a statistical model using vegetation and soil composition and found fine-scale genetic divergence is better explained by this landscape resistance model than a geographic distance model. Finally, a third analysis contrasted cpDNA and nuDNA datasets, and revealed very little geographic structure in the latter, suggesting that seed and pollen dispersal can have different evolutionary genetic histories of gene flow on even small CFR scales. These three studies together caution that different genomic markers need to be considered when modeling the geographic and temporal origin of CFR groups. From a greater perspective, the results here are consistent with the hypothesis that landscape heterogeneity is one driving influence in limiting gene flow across the CFR that can lead to species diversity on fine-scales. Nonetheless, while this pattern may be true of the widespread L. salignum, the extension of this approach is now warranted for other CFR species with varying ranges and dispersal mechanisms to determine how universal these patterns of landscape genetic diversity are.
ContributorsTassone, Erica (Author) / Verrelli, Brian C (Thesis advisor) / Dowling, Thomas (Committee member) / Cartwright, Reed (Committee member) / Rosenberg, Michael S. (Committee member) / Wojciechowski, Martin (Committee member) / Arizona State University (Publisher)
Created2013
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
Triops (Branchiopoda: Notostraca) and Streptocephalus (Branchiopoda: Anostraca) are two crustaceans which cohabitate in ephemeral freshwater pools. They both lay desiccation resistant eggs that disperse passively to new hydrologically isolated environments. The extent of genetic distance among regions and populations is of perennial interest in animals that live in such isolated habitats. Populations in six natural ephemeral pool habitats located in two different regions of the Sonoran Desert and a transition area between the Sonoran and Chihuahuan Deserts were sampled. Sequences from Genbank were used for reference points in the determination of species as well as to further identify regional genetic distance within species. This study estimated the amount of within and between genetic distance of individuals from each region and population through the use of a neutral marker, cytochrome oxidase I (COI). We concluded that, although the method of passive dispersal may differ between the two genera, the differences do not results in different patterns of genetic distances between regions and populations. Furthermore, we only found the putative species, Triops longicaudatus "short", with enough distinct speciation. Although Triops longicaudatus "long" and Triops newberryi may be in the early stages of speciation, this study does not find enough support to conclude that they have separated.
ContributorsMurphy Jr., Patrick Joseph (Author) / Rutowski, Ronald (Thesis director) / Cartwright, Reed (Committee member) / Lessios, Nikos (Committee member) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The evolution of blindness in cave animals has been heavily studied; however, little research has been done on the interaction of migration and drift on the development of blindness in these populations. In this study, a model is used to compare the effect that genetic drift has on the fixation of a blindness allele for varying amounts of migration and selection. For populations where the initial frequency is quite low, genetic drift plays a much larger role in the fixation of blindness than populations where the initial frequency is high. In populations where the initial frequency is high, genetic drift plays almost no role in fixation. Our results suggest that migration plays a greater role in the fate of the blindness allele than selection.
ContributorsMerry, Alexandra Leigh (Author) / Cartwright, Reed (Thesis director) / Rosenberg, Michael (Committee member) / Schwartz, Rachel (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2014-05
Description
The modern web presents an opportunity for educators and researchers to create tools that are highly accessible. Because of the near-ubiquity of modern web browsers, developers who hope to create educational and analytical tools can reach a large au- dience by creating web applications. Using JavaScript, HTML, and other modern web development technologies, Genie was developed as a simulator to help educators in biology, genetics, and evolution classrooms teach their students about population genetics. Because Genie was designed for the modern web, it is highly accessible to both educators and students, who can access the web application using any modern web browser on virtually any device. Genie demonstrates the efficacy of web devel- opment technologies for demonstrating and simulating complex processes, and it will be a unique educational tool for educators who teach population genetics.
ContributorsRoos, Benjamin Hirsch (Author) / Cartwright, Reed (Thesis director) / Wilson Sayres, Melissa (Committee member) / Mayron, Liam (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor)
Created2015-05
Description
Background
Improvements in sequencing technology now allow easy acquisition of large datasets; however, analyzing these data for phylogenetics can be challenging. We have developed a novel method to rapidly obtain homologous genomic data for phylogenetics directly from next-generation sequencing reads without the use of a reference genome. This software, called SISRS, avoids the time consuming steps of de novo whole genome assembly, multiple genome alignment, and annotation.
Results
For simulations SISRS is able to identify large numbers of loci containing variable sites with phylogenetic signal. For genomic data from apes, SISRS identified thousands of variable sites, from which we produced an accurate phylogeny. Finally, we used SISRS to identify phylogenetic markers that we used to estimate the phylogeny of placental mammals. We recovered eight phylogenies that resolved the basal relationships among mammals using datasets with different levels of missing data. The three alternate resolutions of the basal relationships are consistent with the major hypotheses for the relationships among mammals, all of which have been supported previously by different molecular datasets.
Conclusions
SISRS has the potential to transform phylogenetic research. This method eliminates the need for expensive marker development in many studies by using whole genome shotgun sequence data directly. SISRS is open source and freely available at https://github.com/rachelss/SISRS/releases.
Improvements in sequencing technology now allow easy acquisition of large datasets; however, analyzing these data for phylogenetics can be challenging. We have developed a novel method to rapidly obtain homologous genomic data for phylogenetics directly from next-generation sequencing reads without the use of a reference genome. This software, called SISRS, avoids the time consuming steps of de novo whole genome assembly, multiple genome alignment, and annotation.
Results
For simulations SISRS is able to identify large numbers of loci containing variable sites with phylogenetic signal. For genomic data from apes, SISRS identified thousands of variable sites, from which we produced an accurate phylogeny. Finally, we used SISRS to identify phylogenetic markers that we used to estimate the phylogeny of placental mammals. We recovered eight phylogenies that resolved the basal relationships among mammals using datasets with different levels of missing data. The three alternate resolutions of the basal relationships are consistent with the major hypotheses for the relationships among mammals, all of which have been supported previously by different molecular datasets.
Conclusions
SISRS has the potential to transform phylogenetic research. This method eliminates the need for expensive marker development in many studies by using whole genome shotgun sequence data directly. SISRS is open source and freely available at https://github.com/rachelss/SISRS/releases.
ContributorsSchwartz, Rachel (Author) / Harkins, Kelly (Author) / Stone, Anne (Author) / Cartwright, Reed (Author) / Biodesign Institute (Contributor) / Center for Evolution and Medicine (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / School of Life Sciences (Contributor)
Created2015-06-11
Description
Callithrix penicillata, also known as the Black-tufted marmoset primarily lives in the Brazilian highlands and has had little research conducted on it. For this project I performed a genome curation on the newly assembled genome of this species. The scaffolds obtained by the Dovetail Genomics reads were organized and labeled into chromosomes using the 2014 Callithrix jacchus genome as a reference. Then, using that same genome as a reference, 13 of the chromosomes were reverse complimented to be continuous with the 2014 Callithrix jacchus genome. The N50 statistics of the assembly were calculated and found to be 124 Mb. Quality scores were run for the final genome using referee and visualized with a bar plot, with 99% of sites scoring above 0. Heterozygosity was also calculated and found to be 0.3%. Finally, the final version of the genome was visually compared to the 2017 Callithrix jacchus genome and the GRCh38 human genome. This genome was submitted to the NCBIs database to await further approval.
ContributorsJohnson, Joelle Genevieve (Author) / Cartwright, Reed (Thesis director) / Stone, Anne (Committee member) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-12
Description
Since its discovery in 1524, many people have characterized the vermiform appendix. Charles Darwin considered the human appendix to be a vestige and a useless structure. Others at the time opposed this hypothesis. However, Darwin's hypothesis became prevalent one until recently when there became a renewed interest in the appendix because of advancements in microscopes, knowledge of the immune system, and phylogenetics. In this review, I will argue that the vermiform appendix, although still not completely understood, has important functions. First, I will give the anatomy of the appendix. I will discuss the comparative anatomy between different animals and also primates. I will address the effects of appendicitis and appendectomy. I will give background on vestigial structures and will discuss if the appendix is a vestige. Following, I will review the evolution of the appendix. Finally, I will argue that the function of the appendix is as an immune organ, including discussion of gut-associated lymphoid tissue (GALT), development of lymphoid follicles in GALT and their comparison within different organs, Immunoglobulin A (IgA) function in the gut, biofilms as evidence that the appendix is a safe-house for beneficial bacteria, re-inoculation of the bowel, and protection against recurring infection. I will conclude with future studies that should be conducted to further our understanding of the vermiform appendix.
ContributorsPrestwich, Shelby Elizabeth (Author) / Cartwright, Reed (Thesis director) / Lynch, John (Committee member) / Furstenau, Tara (Committee member) / School of Geographical Sciences and Urban Planning (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05