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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
In the middle of the COVID-19 epidemic, flaws in the SARS-CoV-2 diagnostic
test were identified by the impending supply shortages of nasopharyngeal swabs and nucleic acid isolation and purification kits. The ASU Biodesign Clinical Testing Lab (ABCTL), which converted from a research lab to SARS-CoV-2 testing lab, was not an exception to these shortages, but the consequences were greater due to its significant testing load in the state of Arizona. In response to the shortages, researchers at The Department of Epidemiology of Microbial Diseases, at the Yale School of Public Health created SalivaDirect method, which is an epidemic effective test, that accounts for limitations of materials, accessibility to specialized lab equipment, time per test, and cost per test. SalivaDirect simplified the diagnostic process by collecting samples via saliva and skipping the nucleic acid extraction and purification, and did it in a way that resulted in a highly sensitive limit of detection of 6-12 SARS-CoV-2 copies/μL with a minimal decrease in positive test agreement.
ContributorsBreshears, Scott (Co-author) / Anderson, Laura (Co-author) / Majhail, Kajol (Co-author) / Raun, Ellen (Co-author) / Smetanick, Jennifer (Co-author) / Compton, Carolyn (Thesis director) / Magee, Mitch (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The ASU Biodesign Clinical Testing Laboratory began in March 2020 after the severe acute respiratory syndrome, coronavirus 2, began spreading throughout the world. ASU worked towards implementing its own efficient way of testing for the virus, in order to assist the university but also keep the communities around it safe. By developing its own strategy for COVID-19 testing, ASU was on the forefront of research by developing new ways to test for the virus. This process began when research labs at ASU were quickly converted into clinical testing laboratories, which used saliva testing to develop swift COVID-19 diagnostic tests for the Arizona community. The lab developed more accurate and time efficient results, while also converting Nasopharyngeal tests to saliva tests. Not only did this allow for fewer amounts of resources required, but more individuals were able to get tested at faster rates. The ASU Biodesign Clinical Testing Laboratory (ABCTL) was able to accomplish this through the adaptation of previous machines and personnel to fit the testing needs of the community. In the future, the ABCTL will continue to adapt to the ever-changing needs of the community in regards to the unprecedented COVID-19 pandemic. The research collected throughout the past year following the breakout of the COVID-19 pandemic is a reflection of the impressive strategy ASU has created to keep its communities safe, while continuously working towards improving not only the testing sites and functions, but also the ways in which an institution approaches and manages an unfortunate impact on diverse communities.
ContributorsMajhail, Kajol (Co-author) / Smetanick, Jennifer (Co-author) / Anderson, Laura (Co-author) / Ruan, Ellen (Co-author) / Shears, Scott (Co-author) / Compton, Carolyn (Thesis director) / Magee, Mitch (Committee member) / School of Life Sciences (Contributor) / School of Human Evolution & Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
This thesis project is part of a larger collaboration documenting the history of the ASU Biodesign Clinical Testing Laboratory (ABCTL). There are many different aspects that need to be considered when transforming to a clinical testing laboratory. This includes the different types of tests performed in the laboratory. In addition to the diagnostic polymerase chain reaction (PCR) test that is performed detecting the presence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), antibody testing is also performed in clinical laboratories. Antibody testing is used to detect a previous infection. Antibodies are produced as part of the immune response against SARS-CoV-2. There are many different forms of antibody tests and their sensitives and specificities have been examined and reviewed in the literature. Antibody testing can be used to determine the seroprevalence of the disease which can inform policy decisions regarding public health strategies. The results from antibody testing can also be used for creating new therapeutics like vaccines. The ABCTL recognizes the shifting need of the community to begin testing for previous infections of SARS-CoV-2 and is developing new forms of antibody testing that can meet them.
ContributorsRuan, Ellen (Co-author) / Smetanick, Jennifer (Co-author) / Majhail, Kajol (Co-author) / Anderson, Laura (Co-author) / Breshears, Scott (Co-author) / Compton, Carolyn (Thesis director) / Magee, Mitch (Committee member) / School of Life Sciences (Contributor, Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Surface plasmon resonance (SPR) has emerged as a popular technique for elucidating subtle signals from biological events in a label-free, high throughput environment. The efficacy of conventional SPR sensors, whose signals are mass-sensitive, diminishes rapidly with the size of the observed target molecules. The following work advances the current SPR sensor paradigm for the purpose of small molecule detection. The detection limits of two orthogonal components of SPR measurement are targeted: speed and sensitivity. In the context of this report, speed refers to the dynamic range of measured kinetic rate constants, while sensitivity refers to the target molecule mass limitation of conventional SPR measurement. A simple device for high-speed microfluidic delivery of liquid samples to a sensor surface is presented to address the temporal limitations of conventional SPR measurement. The time scale of buffer/sample switching is on the order of milliseconds, thereby minimizing the opportunity for sample plug dispersion. The high rates of mass transport to and from the central microfluidic sensing region allow for SPR-based kinetic analysis of binding events with dissociation rate constants (kd) up to 130 s-1. The required sample volume is only 1 μL, allowing for minimal sample consumption during high-speed kinetic binding measurement. Charge-based detection of small molecules is demonstrated by plasmonic-based electrochemical impedance microscopy (P-EIM). The dependence of surface plasmon resonance (SPR) on surface charge density is used to detect small molecules (60-120 Da) printed on a dextran-modified sensor surface. The SPR response to an applied ac potential is a function of the surface charge density. This optical signal is comprised of a dc and an ac component, and is measured with high spatial resolution. The amplitude and phase of local surface impedance is provided by the ac component. The phase signal of the small molecules is a function of their charge status, which is manipulated by the pH of a solution. This technique is used to detect and distinguish small molecules based on their charge status, thereby circumventing the mass limitation (~100 Da) of conventional SPR measurement.
ContributorsMacGriff, Christopher Assiff (Author) / Tao, Nongjian (Thesis advisor) / Wang, Shaopeng (Committee member) / LaBaer, Joshua (Committee member) / Chae, Junseok (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
In this thesis, we present the study of several physical properties of relativistic mat- ters under extreme conditions. We start by deriving the rate of the nonleptonic weak processes and the bulk viscosity in several spin-one color superconducting phases of quark matter. We also calculate the bulk viscosity in the nonlinear and anharmonic regime in the normal phase of strange quark matter. We point out several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. In the corresponding study, we take into account the interplay between the non- leptonic and semileptonic weak processes. The results can be important in order to relate accessible observables of compact stars to their internal composition. We also use quantum field theoretical methods to study the transport properties in monolayer graphene in a strong magnetic field. The corresponding quasi-relativistic system re- veals an anomalous quantum Hall effect, whose features are directly connected with the spontaneous flavor symmetry breaking. We study the microscopic origin of Fara- day rotation and magneto-optical transmission in graphene and show that their main features are in agreement with the experimental data.
ContributorsWang, Xinyang, Ph.D (Author) / Shovkovy, Igor (Thesis advisor) / Belitsky, Andrei (Committee member) / Easson, Damien (Committee member) / Peng, Xihong (Committee member) / Vachaspati, Tanmay (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation investigates the condition of skeletal muscle insulin resistance using bioinformatics and computational biology approaches. Drawing from several studies and numerous data sources, I have attempted to uncover molecular mechanisms at multiple levels. From the detailed atomistic simulations of a single protein, to datamining approaches applied at the systems biology level, I provide new targets to explore for the research community. Furthermore I present a new online web resource that unifies various bioinformatics databases to enable discovery of relevant features in 3D protein structures.
ContributorsMielke, Clinton (Author) / Mandarino, Lawrence (Committee member) / LaBaer, Joshua (Committee member) / Magee, D. Mitchell (Committee member) / Dinu, Valentin (Committee member) / Willis, Wayne (Committee member) / Arizona State University (Publisher)
Created2013
Description
Numerical simulations are very helpful in understanding the physics of the formation of structure and galaxies. However, it is sometimes difficult to interpret model data with respect to observations, partly due to the difficulties and background noise inherent to observation. The goal, here, is to attempt to bridge this gap between simulation and observation by rendering the model output in image format which is then processed by tools commonly used in observational astronomy. Images are synthesized in various filters by folding the output of cosmological simulations of gasdynamics with star-formation and dark matter with the Bruzual- Charlot stellar population synthesis models. A variation of the Virgo-Gadget numerical simulation code is used with the hybrid gas and stellar formation models of Springel and Hernquist (2003). Outputs taken at various redshifts are stacked to create a synthetic view of the simulated star clusters. Source Extractor (SExtractor) is used to find groupings of stellar populations which are considered as galaxies or galaxy building blocks and photometry used to estimate the rest frame luminosities and distribution functions. With further refinements, this is expected to provide support for missions such as JWST, as well as to probe what additional physics are needed to model the data. The results show good agreement in many respects with observed properties of the galaxy luminosity function (LF) over a wide range of high redshifts. In particular, the slope (alpha) when fitted to the standard Schechter function shows excellent agreement both in value and evolution with redshift, when compared with observation. Discrepancies of other properties with observation are seen to be a result of limitations of the simulation and additional feedback mechanisms which are needed.
ContributorsMorgan, Robert (Author) / Windhorst, Rogier A (Thesis advisor) / Scannapieco, Evan (Committee member) / Rhoads, James (Committee member) / Gardner, Carl (Committee member) / Belitsky, Andrei (Committee member) / Arizona State University (Publisher)
Created2012
Description
Understanding the temperature structure of protoplanetary disks (PPDs) is paramount to modeling disk evolution and future planet formation. PPDs around T Tauri stars have two primary heating sources, protostellar irradiation, which depends on the flaring of the disk, and accretional heating as viscous coupling between annuli dissipate energy. I have written a "1.5-D" radiative transfer code to calculate disk temperatures assuming hydrostatic and radiative equilibrium. The model solves for the temperature at all locations simultaneously using Rybicki's method, converges rapidly at high optical depth, and retains full frequency dependence. The likely cause of accretional heating in PPDs is the magnetorotational instability (MRI), which acts where gas ionization is sufficiently high for gas to couple to the magnetic field. This will occur in surface layers of the disk, leaving the interior portions of the disk inactive ("dead zone"). I calculate temperatures in PPDs undergoing such "layered accretion." Since the accretional heating is concentrated far from the midplane, temperatures in the disk's interior are lower than in PPDs modeled with vertically uniform accretion. The method is used to study for the first time disks evolving via the magnetorotational instability, which operates primarily in surface layers. I find that temperatures in layered accretion disks do not significantly differ from those of "passive disks," where no accretional heating exists. Emergent spectra are insensitive to active layer thickness, making it difficult to observationally identify disks undergoing layered vs. uniform accretion. I also calculate the ionization chemistry in PPDs, using an ionization network including multiple charge states of dust grains. Combined with a criterion for the onset of the MRI, I calculate where the MRI can be initiated and the extent of dead zones in PPDs. After accounting for feedback between temperature and active layer thickness, I find the surface density of the actively accreting layers falls rapidly with distance from the protostar, leading to a net outward flow of mass from ~0.1 to 3 AU. The clearing out of the innermost zones is possibly consistent with the observed behavior of recently discovered "transition disks."
ContributorsLesniak, Michael V., III (Author) / Desch, Steven J. (Thesis advisor) / Scannapieco, Evan (Committee member) / Timmes, Francis (Committee member) / Starrfield, Sumner (Committee member) / Belitsky, Andrei (Committee member) / Arizona State University (Publisher)
Created2012