Matching Items (90)
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
It is important to consider factors that contribute to successful fertilization and the development of viable offspring. Better understanding the factors that contribute to infertility can be used to assist in the development of viable offspring, especially for human beings looking to successfully reproduce. Identifying paternal effect genes, genes that come from the father, introduces more targets that can be manipulated to produce specific reproductive effects. Use of Drosophila melanogaster as a model to study reproduction has increased, in part, due to the use of the GAL4 system. In this system, the GAL4 gene encodes an 881 amino acid protein that binds to the 4-site Upstream Activating Sequence (UAS) to induce transcription of the gene of interest. These sequences constitute the two components of the system: the driver (GAL4) and the responder (gene of interest) \u2014 each of which is maintained as a separate parental line. Effects of the GAL4 driver line "driving" transcription of the responder can be assessed by examining the offspring. One of the more common uses of the GAL4 system involves analyzing phenotypic effects of reducing or eliminating expression of a target gene through the induction of RNAi transcription, which often results in toxicity, lethality, or reduced viability. Utilizing these principles, we strove to demonstrate the effect of knocking down the expression of testis-specific sperm-leucyl-aminopeptidases gene CG13340 on progeny by inducing expression of RNAi with two distinct GAL4 driver lines - one with a nonspecific actin-binding activation sequence and the other with a testis-specific activation sequence. Comparison of both GAL4 driver lines to crosses using N01 wild type ("wt") flies verify that inducing RNAi transcription using the GAL4 system results in reduction of proper offspring development. Further studies using D. melanogaster and the GAL4 system can improve knowledge of factors contributing to male fertility and also be applied to better understand mammalian, specifically human, fertility.
ContributorsEvans, Donna Marie (Author) / Karr, Timothy L. (Thesis director) / Roland, Kenneth (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor) / Department of English (Contributor)
Created2014-05
Description
The development of stab-resistant Kevlar armor has been an ongoing field of research
since the late 1990s, with the ultimate goal of improving the multi-threat capabilities of
traditional soft-body armor while significantly improving its protective efficiency - the amount
of layers of armor material required to defeat threats. To create a novel, superior materials
system to reinforce Kevlar armor for the Norica Capstone project, this thesis set out to
synthesize, recover, and characterize zinc oxide nanowire colloids.
The materials synthesized were successfully utilized in the wider Capstone effort to
dramatically enhance the protective abilities of Kevlar, while the data obtained on the 14
hydrothermal synthesis attempts and numerous challenges at recovery provided critical
information on the synthesis parameters involved in the reliable, scalable mass production of the
nanomaterial additive. Additionally, recovery was unconventionally facilitated in the absence of
a vacuum filtration apparatus with nanoscale filters by intentionally inducing electrostatic
agglomeration of the nanowires during standard gravity filtration. The subsequent application of
these nanowires constituted a pioneering use in the production of nanowire-reinforced
STF-based Kevlar coatings, and support the future development and, ultimately, the
commercialization of lighter and more-protective soft armor systems.
since the late 1990s, with the ultimate goal of improving the multi-threat capabilities of
traditional soft-body armor while significantly improving its protective efficiency - the amount
of layers of armor material required to defeat threats. To create a novel, superior materials
system to reinforce Kevlar armor for the Norica Capstone project, this thesis set out to
synthesize, recover, and characterize zinc oxide nanowire colloids.
The materials synthesized were successfully utilized in the wider Capstone effort to
dramatically enhance the protective abilities of Kevlar, while the data obtained on the 14
hydrothermal synthesis attempts and numerous challenges at recovery provided critical
information on the synthesis parameters involved in the reliable, scalable mass production of the
nanomaterial additive. Additionally, recovery was unconventionally facilitated in the absence of
a vacuum filtration apparatus with nanoscale filters by intentionally inducing electrostatic
agglomeration of the nanowires during standard gravity filtration. The subsequent application of
these nanowires constituted a pioneering use in the production of nanowire-reinforced
STF-based Kevlar coatings, and support the future development and, ultimately, the
commercialization of lighter and more-protective soft armor systems.
ContributorsDurso, Michael Nathan (Author) / Tongay, Sefaattin (Thesis director) / Zhuang, Houlong (Committee member) / Materials Science and Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
With renewable energy on the rise, researchers have turned their funding and their focus towards new solar cell technologies, and perovskites are a major source of interest. This class of materials is particularly interesting due to their quick, simple synthesis as well as their physical and electrical superiority when compared to current silicon-based solar cells. Through this thesis, we will explore the synthesis of various types of perovskites and their subsequent characterization, which includes optical microscopy, photoluminescence spectroscopy, Raman microscopy, and X-ray diffraction. Analyzing two different perovskites both before and after a two-week period of storage revealed that while synthesis is indeed experiment-friendly, these materials have a concerning lack of stability even in ideal conditions.
ContributorsBuzas, Benjamin Joseph (Author) / Tongay, Sefaattin (Thesis director) / Muhich, Christopher (Committee member) / Materials Science and Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Graphene is a very strong two-dimensional material with a lot of potential applications in microelectromechanical systems (MEMS). In this research, graphene is being optimized for use in a 5 m x 5 m graphene resonator. To work properly, this graphene resonator must have a uniform strain across all manufactured devices. To reduce strain induced in graphene sheets grown for use in these resonators, evaporated platinum has been used in this investigation due to its relatively lower surface roughness compared to copper films. The final goal is to have the layer of ultrathin platinum (<=200 nm) deposited on the MEMS graphene resonator and used to grow graphene directly onto the devices to remove the manual transfer step due to its inscalability. After growth, graphene is coated with polymer and the platinum is then etched. This investigation concentrated on the transfer process of graphene onto Si/SiO2 substrate from the platinum films. It was determined that the ideal platinum etchant was aqua regia at a volumetric ratio of 6:3:1 (H2O:HCl:HNO3). This concentration was dilute enough to preserve the polymer and graphene layer, but strong enough to etch within a day. Type and thickness of polymer support layers were also investigated. PMMA at a thickness of 200 nm was ideal because it was easy to remove with acetone and strong enough to support the graphene during the etch process. A reference growth recipe was used in this investigation, but now that the transfer has been demonstrated, growth can be optimized for even thinner films.
ContributorsCayll, David Richard (Author) / Tongay, Sefaattin (Thesis director) / Lee, Hyunglae (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Solid-state lithium-ion batteries are a major area of research due to their increased safety characteristics over conventional liquid electrolyte batteries. Lithium lanthanum zirconate (LLZO) is a promising garnet-type ceramic for use as a solid-state electrolyte due to its high ionic conductivity. The material exists in two dierent phases, one that is cubic in structure and one that is tetragonal. One potential synthesis method that results in LLZO in the more useful, cubic phase, is electrospinning, where a mat of nanowires is spun and then calcined into LLZO. A phase containing lanthanum zirconate (LZO) and amorphous lithium occursas an intermediate during the calcination process. LZO has been shown to be a sintering aid for LLZO, allowing for lower sintering temperatures. Here it is shown the eects of internal LZO on the sintered pellets. This is done by varying the 700C calcination time to transform diering amounts of LZO and LLZO in electrospun nanowires, and then using the same sintering parameters for each sample. X-ray diraction was used to get structural and compositional analysis of both the calcined powders and sintered pellets. Pellets formed from wires calcined at 1 hour or longer contained only LLZO even if the calcined powder had only undergone the rst phase transformation. The relative density of the pellet with no initial LLZO of 61.0% was higher than that of the pellet with no LZO, which had a relative density of 57.7%. This allows for the same, or slightly higher, quality material to be synthesized with a shorter amount of processing time.
ContributorsLondon, Nathan Harry (Author) / Chan, Candace (Thesis director) / Tongay, Sefaattin (Committee member) / Department of Physics (Contributor) / Materials Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
ContributorsCole, Alexandra Shea (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / School of International Letters and Cultures (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
In the Rare-earth-Tri-telluride family, (RTe3s) [R=La, Ce, Nd, Sm, Gd, Tb, Dy, Er, Ho, Tm] the emergence of Charge Density Waves, (CDW) has been under investigation for a long time due to broadly tunable properties by either chemical substitution or pressure application. These quasi 2D Layered materials RTe3s undergo Fermi Surface Nesting leading to CDW instability. CDWs are electronic instabilities found in low-dimensional materials with highly anisotropic electronic structures. Since the CDW is predominantly driven by Fermi-surface (FS) nesting, it is especially sensitive to pressure-induced changes in the electronic structure. The FS of RTe3s is a function of p-orbitals of Tellurium atoms, which are arranged in two adjacent planes in the crystal structure. Although the FS and electronic structure possess a nearly four-fold symmetry, RTe3s form an incommensurate CDW.This dissertation is structured as follows: Chapter 1 includes basic ideas of Quantum materials, followed by an introduction to CDW and RTe3s. In Chapter 2, there are fundamentals of crystal growth by Chemical Vapor Transport, including various precursors, transport agent, temperature gradient, and rate of the reaction. After the growth, the crystals were confirmed for lattice vibrations by Raman, for composition by Energy Dispersive Spectroscopy; crystal structure and orientation were confirmed by X-ray Diffraction; magnetic ordering was established by Vibrating sample measurement. Detailed CDW study was done on various RTe3s by Raman spectroscopy. The basic mechanism and instrumentations used in these characterizations are explained in Chapter 3. Chapter 4 includes experimental data for crystal growth and results of these characterizations for Parent RTe3s. Chapter 5 includes fundamental insights on Cationic alloying of RTe3s, along with one alloy system’s crystal growth and characterization. This work tries to explain the behavior of CDW by a Temperature-dependent Raman study of RTe3s established the CDW transition temperature accompanied by Phonon softening; Angle-resolved Raman data confirming the nearly four-fold symmetry; thickness-dependent Raman spectroscopy resulting in the conclusion that as thickness decreases CDW transition temperature increases. Also, CDW transition is analyzed as a function of alloying.
ContributorsAttarde, Yashika (Author) / Tongay, Sefaattin (Thesis advisor) / Botana, Antia (Committee member) / Alford, Terry (Committee member) / Arizona State University (Publisher)
Created2021