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- Creators: Novak, Gail (Pianist)
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
ContributorsKierum, Caitlin (Contributor) / Novak, Gail (Pianist) (Performer) / Liang, Jack (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-11
ContributorsLougheed, Julia (Performer) / Novak, Gail (Pianist) (Performer) / Bayer, Elizabeth Kennedy (Performer) / Clifton-Armenta, Tyler (Performer) / Park, Julie (Performer) / Javier de Alba, Francisco (Performer) / Vientos Dulces (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-07
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
ContributorsCoffey, Brennan (Performer) / Novak, Gail (Pianist) (Performer) / ASU Library. Music Library (Publisher)
Created2021-04-26
ContributorsHolly, Sean (Performer) / Wright, Aaron (Performer) / Novak, Gail (Pianist) (Performer) / ASU Library. Music Library (Publisher)
Created2021-04-29
ContributorsBreeden, Katherine (Performer) / German, Lindsey (Performer) / Novak, Gail (Pianist) (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-13
Description
ABSTRACT Many musicians, both amateur and professional alike, are continuously seeking to expand and explore their performance literature and repertory. Introducing new works into the standard repertory is an exciting endeavor for any active musician. Establishing connections, commissioning new works, and collaborating on performances can all work together toward the acceptance and success of a composer's music within an instrument community. For the flute, one such composer is Daniel Dorff (b. 1956). Dorff, a Philadelphia-based composer, has written for symphony orchestra, clarinet, contrabassoon, and others; however, his award-winning works for flute and piccolo are earning him much recognition. He has written works for such illustrious flutists as Mimi Stillman, Walfrid Kujala, and Gary Schocker; his flute works have been recorded by Laurel Zucker, Pamela Youngblood and Lois Bliss Herbine; and his pieces have been performed and premiered at each of the National Flute Association Conventions from 2004 to 2009. Despite this success, little has been written about Dorff's life, compositional style, and contributions to the flute repertory. In order to further promote the flute works of Daniel Dorff, the primary focus of this study is the creation of a compact disc recording of Dorff's most prominent works for flute: April Whirlwind, 9 Walks Down 7th Avenue, both for flute and piano, and Nocturne Caprice for solo flute. In support of this recording, the study also provides biographical information regarding Daniel Dorff, discusses his compositional methods and ideology, and presents background information, description, and performance notes for each piece. Interviews with Daniel Dorff regarding biographical and compositional details serve as the primary source for this document. Suggestions for the performance of the three flute works were gathered through interviews with prominent flutists who have studied and performed Dorff's pieces. Additional performance suggestions for Nocturne Caprice were gathered through a coaching session between the author and the composer. This project is meant to promote the flute works of Daniel Dorff and to help establish their role in the standard flute repertory.
ContributorsRich, Angela Marie (Contributor) / Novak, Gail (Pianist) (Performer) / Buck, Elizabeth Y (Thesis advisor) / Hill, Gary W. (Committee member) / Holbrook, Amy (Committee member) / Schuring, Martin (Committee member) / Arizona State University (Publisher)
Created2010
ContributorsBroome-Robinson, Julia (Performer) / Novak, Gail (Pianist) (Performer) / Glick, Philip (Performer) / Lynch, Paul (Performer) / Ryall, Blake (Performer) / ASU Library. Music Library (Publisher)
Created2018-10-19