Matching Items (81)
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
The atomization of a liquid jet by a high speed cross-flowing gas has many applications such as gas turbines and augmentors. The mechanisms by which the liquid jet initially breaks up, however, are not well understood. Experimental studies suggest the dependence of spray properties on operating conditions and nozzle geom- etry. Detailed numerical simulations can offer better understanding of the underlying physical mechanisms that lead to the breakup of the injected liquid jet. In this work, detailed numerical simulation results of turbulent liquid jets injected into turbulent gaseous cross flows for different density ratios is presented. A finite volume, balanced force fractional step flow solver to solve the Navier-Stokes equations is employed and coupled to a Refined Level Set Grid method to follow the phase interface. To enable the simulation of atomization of high density ratio fluids, we ensure discrete consistency between the solution of the conservative momentum equation and the level set based continuity equation by employing the Consistent Rescaled Momentum Transport (CRMT) method. The impact of different inflow jet boundary conditions on different jet properties including jet penetration is analyzed and results are compared to those obtained experimentally by Brown & McDonell(2006). In addition, instability analysis is performed to find the most dominant insta- bility mechanism that causes the liquid jet to breakup. Linear instability analysis is achieved using linear theories for Rayleigh-Taylor and Kelvin- Helmholtz instabilities and non-linear analysis is performed using our flow solver with different inflow jet boundary conditions.
ContributorsGhods, Sina (Author) / Herrmann, Marcus (Thesis advisor) / Squires, Kyle (Committee member) / Chen, Kangping (Committee member) / Huang, Huei-Ping (Committee member) / Tang, Wenbo (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
The OMFIT (One Modeling Framework for Integrated Tasks) modeling environment and the BRAINFUSE module have been deployed on the PPPL (Princeton Plasma Physics Laboratory) computing cluster with modifications that have rendered the application of artificial neural networks (NNs) to the TRANSP databases for the JET (Joint European Torus), TFTR (Tokamak Fusion Test Reactor), and NSTX (National Spherical Torus Experiment) devices possible through their use. This development has facilitated the investigation of NNs for predicting heat transport profiles in JET, TFTR, and NSTX, and has promoted additional investigations to discover how else NNs may be of use to scientists at PPPL. In applying NNs to the aforementioned devices for predicting heat transport, the primary goal of this endeavor is to reproduce the success shown in Meneghini et al. in using NNs for heat transport prediction in DIII-D. Being able to reproduce the results from is important because this in turn would provide scientists at PPPL with a quick and efficient toolset for reliably predicting heat transport profiles much faster than any existing computational methods allow; the progress towards this goal is outlined in this report, and potential additional applications of the NN framework are presented.
ContributorsLuna, Christopher Joseph (Author) / Tang, Wenbo (Thesis director) / Treacy, Michael (Committee member) / Orso, Meneghini (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2015-05
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
In the digital humanities, there is a constant need to turn images and PDF files into plain text to apply analyses such as topic modelling, named entity recognition, and other techniques. However, although there exist different solutions to extract text embedded in PDF files or run OCR on images, they typically require additional training (for example, scholars have to learn how to use the command line) or are difficult to automate without programming skills. The Giles Ecosystem is a distributed system based on Apache Kafka that allows users to upload documents for text and image extraction. The system components are implemented using Java and the Spring Framework and are available under an Open Source license on GitHub (https://github.com/diging/).
ContributorsLessios-Damerow, Julia (Contributor) / Peirson, Erick (Contributor) / Laubichler, Manfred (Contributor) / ASU-SFI Center for Biosocial Complex Systems (Contributor)
Created2017-09-28
Description
Because collective cognition emerges from local signaling among group members, deciphering communication systems is crucial to understanding the underlying mechanisms. Alarm signals are widespread in the social insects and can elicit a variety of behavioral responses to danger, but the functional plasticity of these signals has not been well studied. Here we report an alarm pheromone in the ant Temnothorax rugatulus that elicits two different behaviors depending on context. When an ant was tethered inside an unfamiliar nest site and unable to move freely, she released a pheromone from her mandibular gland that signaled other ants to reject this nest as a potential new home, presumably to avoid potential danger. When the same pheromone was presented near the ants' home nest, they were instead attracted to it, presumably to respond to a threat to the colony. We used coupled gas chromatography/mass spectrometry to identify candidate compounds from the mandibular gland and tested each one in a nest choice bioassay. We found that 2,5-dimethylpyrazine was sufficient to induce rejection of a marked new nest and also to attract ants when released at the home nest. This is the first detailed investigation of chemical communication in the leptothoracine ants. We discuss the possibility that this pheromone's deterrent function can improve an emigrating colony's nest site selection performance.
ContributorsSasaki, Takao (Author) / Hoelldobler, Bert (Author) / Millar, Jocelyn G. (Author) / Pratt, Stephen (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / ASU-SFI Center for Biosocial Complex Systems (Contributor) / Center for Social Dynamics and Complexity (Contributor)
Created2014-09-01