Global well-posedness for KdV in Sobolev Spaces of negative index

The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in H^s({\mathbb{R}), -3/10<s.Comment: 5 pages. Electronic Journal of Differential equations (submitted

Concerning the Wave equation on Asymptotically Euclidean Manifolds

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on $(\R^d, \mathfrak{g})$, $d \geq 3$, when metric $\mathfrak{g}$ is non-trapping and approaches the Euclidean metric like $x ^{- \rho}$ with $\rho>0$. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for $\rho> 1$ and $d=3$. Also, we establish the Strauss conjecture when the metric is radial with $\rho>0$ for $d= 3$.Comment: Final version. To appear in Journal d'Analyse Mathematiqu

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction

Recent Developments in Smart Adaptive Structures for Solar Sailcraft

The "Smart Adaptive Structures for Solar Sailcraft" development activity at MSFC has investigated issues associated with understanding how to model and scale the subsystem and multi-body system dynamics of a gossamer solar sailcraft with the objective of designing sailcraft attitude control systems. This research and development activity addressed three key tasks that leveraged existing facilities and core competencies of MSFC to investigate dynamics and control issues of solar sails. Key aspects of this effort included modeling and testing of a 30 m deployable boom; modeling of the multi-body system dynamics of a gossamer sailcraft; investigation of control-structures interaction for gossamer sailcraft; and development and experimental demonstration of adaptive control technologies to mitigate control-structures interaction

Spatially-Resolved Spectra of the "Teacup" AGN: Tracing the History of a Dying Quasar

The Sloan Digital Sky Survey (SDSS) Galaxy Zoo project has revealed a number of spectacular galaxies possessing Extended Emission-Line Regions (EELRs), the most famous being Hanny's Voorwerp galaxy. We present another EELR object discovered in the SDSS endeavor: the Teacup Active Galactic Nucleus (AGN), nicknamed for its EELR, which has a handle like structure protruding 15 kpc into the northeast quadrant of the galaxy. We analyze physical conditions of this galaxy with long-slit ground based spectroscopy from Lowell, Lick, and KPNO observatories. With the Lowell 1.8m Perkin's telescope we took multiple observations at different offset positions, allowing us to recover spatially resolved spectra across the galaxy. Line diagnostics indicate the ionized gas is photoionized primarily by the AGN. Additionally we are able to derive the hydrogen density from the [S II] 6716/6731 ratio. We generated two-component photoionization models for each spatially resolved Lowell spectrum. These models allow us to calculate the AGN bolometric luminosity seen by the gas at different radii from the nuclear center of the Teacup. Our results show a drop in bolometric luminosity by more than two orders of magnitude from the EELR to the nucleus, suggesting that the AGN has decreased in luminosity by this amount in a continuous fashion over 46,000 years, supporting the case for a dying AGN in this galaxy independent of any IR based evidence. We demonstrate that spatially resolved photoionization modeling could be applied to EELRs to investigate long time scale variability.Comment: 38 pages, 11 figures, accepted for publication in the Astrophysical Journa