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ContributorsLovelady, Alexis (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-08
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
ContributorsAle, Lea (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-07
ContributorsASU Library. Music Library (Publisher)
Created2018-04-09
ContributorsZhang, Ziyang (Performer) / Chen, Neilson (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-12
Description
The goal of this project was to design and create a genetic construct that would allow for <br/>tumor growth to be induced in the center of the wing imaginal disc of Drosophila larvae, the <br/>R85E08 domain, using a heat shock. The resulting transgene would be combined with other <br/>transgenes in a single fly that would allow for simultaneous expression of the oncogene and, in <br/>the surrounding cells, other genes of interest. This system would help establish Drosophila as a <br/>more versatile and reliable model organism for cancer research. Furthermore, pilot studies were <br/>performed, using elements of the final proposed system, to determine if tumor growth is possible <br/>in the center of the disc, which oncogene produces the best results, and if oncogene expression <br/>induced later in development causes tumor growth. Three different candidate genes were <br/>investigated: RasV12, PvrACT, and Avli.
ContributorsSt Peter, John Daniel (Author) / Harris, Rob (Thesis director) / Varsani, Arvind (Committee member) / School of Molecular Sciences (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
ContributorsKierum, Caitlin (Contributor) / Novak, Gail (Pianist) (Performer) / Liang, Jack (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-11
ContributorsLee, Jun (Performer) / Kim, Rina (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-08
ContributorsArch, Nathan (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-18
ContributorsBurton, Charlotte (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-08