The influence of oscillations on energy estimates for damped wave models with time-dependent propagation speed and dissipation

The aim of this paper is to derive higher order energy estimates for solutions to the Cauchy problem for damped wave models with time-dependent propagation speed and dissipation. The model of interest is \begin{equation*} u_{tt}-\lambda^2(t)\omega^2(t)\Delta u +\rho(t)\omega(t)u_t=0, \quad u(0,x)=u_0(x), \,\, u_t(0,x)=u_1(x). \end{equation*} The coefficients $\lambda=\lambda(t)$ and $\rho=\rho(t)$ are shape functions and $\omega=\omega(t)$ is an oscillating function. If $\omega(t)\equiv1$ and $\rho(t)u_t$ is an "effective" dissipation term, then $L^2-L^2$ energy estimates are proved in [2]. In contrast, the main goal of the present paper is to generalize the previous results to coefficients including an oscillating function in the time-dependent coefficients. We will explain how the interplay between the shape functions and oscillating behavior of the coefficient will influence energy estimates.Comment: 37 pages, 2 figure

Strong relative intensity squeezing by 4-wave mixing in Rb vapor

We have measured -3.5 dB (-8.1 dB corrected for losses) relative intensity squeezing between the probe and conjugate beams generated by stimulated, nondegenerate four-wave mixing in hot rubidium vapor. Unlike early observations of squeezing in atomic vapors based on saturation of a two-level system, our scheme uses a resonant nonlinearity based on ground-state coherences in a three-level system. Since this scheme produces narrowband, squeezed light near an atomic resonance it is of interest for experiments involving cold atoms or atomic ensembles.Comment: Submitted to Optics Letter

V723 Cas (Nova Cassiopeiae 1995): MERLIN observations from 1996 to 2001

MERLIN observations of the unusually slow nova V723 Cas are presented. Nine epochs of 6-cm data between 1996 and 2001 are mapped, showing the initial expansion and brightening of the radio remnant, the development of structure and the final decline. A radio light curve is presented and fitted by the standard Hubble flow model for radio emission from novae in order to determine the values of various physical parameters for the shell. The model is consistent with the overall development of the radio emission. Assuming a distance of 2.39 (+/-0.38) kpc and a shell temperature of 17000 K, the model yields values for expansion velocity of 414 +/- 0.1 km s^-1 and shell mass of 1.13 +/- 0.04 * 10^-4 Msolar. These values are consistent with those derived from other observations although the ejected masses are rather higher than theoretical predictions. The structure of the shell is resolved by MERLIN and shows that the assumption of spherical symmetry in the standard model is unlikely to be correct.Comment: 6 pages, 6 figure

Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

The magnificent past of RR Lyrae variables

We briefly review the results obtained by using the times of maximum brightness of RR Lyrae variables. They cover more than 120 years and have been used to study the evolutionary changes of the pulsational periods, the different shapes of the Blazhko effect among Galactic RRab stars, and the interplay between pulsational and Blazhko periods in the eponym of the class, RR Lyr. The data are stored in the GEOS database, continuously fed by contributions from professional and amateur astronomers. <P /

Swift observations of the 2006 outburst of the recurrent nova RS Ophiuchi: I. Early X-ray emission from the shocked ejecta and red giant wind

RS Ophiuchi began its latest outburst on 2006 February 12. Previous outbursts have indicated that high velocity ejecta interact with a pre-existing red giant wind, setting up shock systems analogous to those seen in Supernova Remnants. However, in the previous outburst in 1985, X-ray observations did not commence until 55 days after the initial explosion. Here we report on Swift observations covering the first month of the 2006 outburst with the Burst Alert (BAT) and X-ray Telescope (XRT) instruments. RS Oph was clearly detected in the BAT 14-25 keV band from t=0 to $t\sim6$ days. XRT observationsfrom 0.3-10 keV, started at 3.17 days after outburst. The rapidly evolving XRT spectra clearly show the presence of both line and continuum emission which can be fitted by thermal emission from hot gas whose characteristic temperature, overlying absorbing column, $[N_H]_W$, and resulting unabsorbed total flux decline monotonically after the first few days. Derived shock velocities are in good agreement with those found from observations at other wavelengths. Similarly, $[N_H]_W$ is in accord with that expected from the red giant wind ahead of the forward shock. We confirm the basic models of the 1985 outburst and conclude that standard Phase I remnant evolution terminated by $t\sim10$ days and the remnant then rapidly evolved to display behaviour characteristic of Phase III. Around t=26 days however, a new, luminous and highly variable soft X-ray source began to appear whose origin will be explored in a subsequent paper.Comment: 20 pages, 4 figures (2 updated), accepted by Ap

The SSS phase of RS Ophiuchi observed with Chandra and XMM-Newton I.: Data and preliminary Modeling

The phase of Super-Soft-Source (SSS) emission of the sixth recorded outburst of the recurrent nova RS Oph was observed twice with Chandra and once with XMM-Newton. The observations were taken on days 39.7, 54.0, and 66.9 after outburst. We confirm a 35-sec period on day 54.0 and found that it originates from the SSS emission and not from the shock. We discus the bound-free absorption by neutral elements in the line of sight, resonance absorption lines plus self-absorbed emission line components, collisionally excited emission lines from the shock, He-like intersystem lines, and spectral changes during an episode of high-amplitude variability. We find a decrease of the oxygen K-shell absorption edge that can be explained by photoionization of oxygen. The absorption component has average velocities of -1286+-267 km/s on day 39.7 and of -771+-65 km/s on day 66.9. The wavelengths of the emission line components are consistent with their rest wavelengths as confirmed by measurements of non-self absorbed He-like intersystem lines. We have evidence that these lines originate from the shock rather than the outer layers of the outflow and may be photoexcited in addition to collisional excitations. We found collisionally excited emission lines that are fading at wavelengths shorter than 15A that originate from the radiatively cooling shock. On day 39.5 we find a systematic blue shift of -526+-114 km/s from these lines. We found anomalous He-like f/i ratios which indicates either high densities or significant UV radiation near the plasma where the emission lines are formed. During the phase of strong variability the spectral hardness light curve overlies the total light curve when shifted by 1000sec. This can be explained by photoionization of neutral oxygen in the line of sight if the densities of order 10^{10}-10^{11} cm^{-3}.Comment: 16 pages, 10 figures, 4 tables. Accepted by ApJ; v2: Co-author Woodward adde