Exponential decay for the damped wave equation in unbounded domains

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilisation and control

Predicted FeII Emission-Line Strengths from Active Galactic Nuclei

We present theoretical FeII emission line strengths for physical conditions typical of Active Galactic Nuclei with Broad-Line Regions. The FeII line strengths were computed with a precise treatment of radiative transfer using extensive and accurate atomic data from the Iron Project. Excitation mechanisms for the FeII emission included continuum fluorescence, collisional excitation, self-fluorescence amoung the FeII transitions, and fluorescent excitation by Lyman-alpha and Lyman-beta. A large FeII atomic model consisting of 827 fine structure levels (including states to E ~ 15 eV) was used to predict fluxes for approximately 23,000 FeII transitions, covering most of the UV, optical, and IR wavelengths of astrophysical interest. Spectral synthesis for wavelengths from 1600 Angstroms to 1.2 microns is presented. Applications of present theoretical templates to the analysis of observations are described. In particular, we discuss recent observations of near-IR FeII lines in the 8500 Angstrom -- 1 micron region which are predicted by the Lyman-alpha fluorescence mechanism. We also compare our UV spectral synthesis with an empirical iron template for the prototypical, narrow-line Seyfert galaxy I Zw 1. The theoretical FeII template presented in this work should also applicable to a variety of objects with FeII spectra formed under similar excitation conditions, such as supernovae and symbiotic stars.Comment: 33 pages, 15 postscript figure

Derivation of the Zakharov equations

This paper continues the study of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for well-prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic estimate that describes solutions of the Euler-Maxwell equations in terms of WKB approximate solutions which leading terms are solutions of the Zakharov equations. Because of transparency properties of the Euler-Maxwell equations, this study is led in a supercritical (highly nonlinear) regime. In such a regime, resonances between plasma waves, electromagnetric waves and acoustic waves could create instabilities in small time. The key of this work is the control of these resonances. The proof involves the techniques of geometric optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of pseudodifferential operators, and a semiclassical, paradifferential calculus

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

Curvature tensors on distorted Killing horizons and their algebraic classification

We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned on the horizon. It is also pointed out that results obtained in the tetrad adjusted to a static observer in general differ from those obtained in a free-falling frame. This is connected to the fact that a static observer becomes null on the horizon. It is also shown that finiteness of the Kretschmann scalar on the horizon is compatible with the divergence of the Weyl component $\Psi_{3}$ or $\Psi_{4}$ in the freely falling frame. Furthermore finiteness of $\Psi_{4}$ is compatible with divergence of curvature invariants constructed from second derivatives of the Riemann tensor. We call the objects with finite Krestschmann scalar but infinite $\Psi_{4}$ ``truly naked black holes''. In the (ultra)extremal versions of these objects the structure of the Einstein tensor on the horizon changes due to extra terms as compared to the usual horizons, the null energy condition being violated at some portions of the horizon surface. The demand to rule out such divergencies leads to the constancy of the factor that governs the leading term in the asymptotics of the lapse function and in this sense represents a formal analog of the zeroth law of mechanics of non-extremal black holes. In doing so, all extra terms in the Einstein tensor automatically vanish.Comment: 21 pages, To appear in Class. Quant. Gra

A Systematic Analysis of Fe II Emission in Quasars: Evidence for Inflow to the Central Black Hole

Broad Fe II emission is a prominent feature of the optical and ultraviolet spectra of quasars. We report on a systematical investigation of optical Fe II emission in a large sample of 4037 z < 0.8 quasars selected from the Sloan Digital Sky Survey. We have developed and tested a detailed line-fitting technique, taking into account the complex continuum and narrow and broad emission-line spectrum. Our primary goal is to quantify the velocity broadening and velocity shift of the Fe II spectrum in order to constrain the location of the Fe II-emitting region and its relation to the broad-line region. We find that the majority of quasars show Fe II emission that is redshifted, typically by ~ 400 km/s but up to 2000 km/s, with respect to the systemic velocity of the narrow-line region or of the conventional broad-line region as traced by the Hbeta line. Moreover, the line width of Fe II is significantly narrower than that of the broad component of Hbeta. We show that the magnitude of the Fe II redshift correlates inversely with the Eddington ratio, and that there is a tendency for sources with redshifted Fe II emission to show red asymmetry in the Hbeta line. These characteristics strongly suggest that Fe II originates from a location different from, and most likely exterior to, the region that produces most of Hbeta. The Fe II-emitting zone traces a portion of the broad-line region of intermediate velocities whose dynamics may be dominated by infall.Comment: 20 pages, 14 figures, accepted for publication in Ap

Doppler optical frequency domain reflectometry for remote fiber sensing

Coherent optical frequency domain reflectometry has been widely used to locate static reflectors with high spatial resolution. Here, we present a new type of Doppler optical frequency domain reflectometry that offers simultaneous measurement of the position and speed of moving objects. The system is exploited to track optically levitated "flying" particles inside a hollow-core photonic crystal fiber. As an example, we demonstrate distributed temperature sensing with sub-mm-scale spatial resolution and a standard deviation of similar to 10 degrees C up to 200 degrees C. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreemen

Exposure in utero to maternal diabetes leads to glucose intolerance and high blood pressure with no major effects on lipid metabolism

AIM: Recent evidence shows that adult metabolic disease may originate from an adverse fetal environment that can alter organ development and function in postnatal life. This study aimed to analyze the effect of exposure in utero to maternal diabetes on the development of the metabolic syndrome in the offspring. METHODS: Pregnant rats were made diabetic (blood glucose was 20mM) with a single streptozotocin injection on day 0 of gestation. Offspring from diabetic mothers (DMO) and control mothers (CMO) were followed from birth to 12 months of age. In these animals, metabolic parameters, such as glucose tolerance, insulin sensitivity and plasma lipid levels, as well as pancreatic insulin and morphology were studied. RESULTS: Compared with controls, DMO offspring had normal birth weights, but impaired postnatal growth that persisted throughout life. Metabolic tests revealed that DMO offspring also showed impaired glucose tolerance at six months associated with decreased insulin sensitivity and low insulin secretion. In older animals (12 months old), this phenotype persisted, but to a lesser extent. The DMO offspring also presented with high blood pressure and decreased levels of fasting plasma triglycerides, but normal plasma NEFA, and HDL and total cholesterol. CONCLUSION: Altogether, these results show that our model of exposure in utero to maternal diabetes led to normal birth weights, and induced transient glucose intolerance and increased blood pressure with no major effects on lipid metabolism. It also suggests that a hyperglycaemic fetal environment may be able to \u27programme\u27 hypertension and glucose intolerance, but not alter lipid metabolism

An Empirical Ultraviolet Template for Iron Emission in Quasars as Derived from I Zw 1

We present an empirical template spectrum suitable for fitting/subtracting and studying the FeII and FeIII line emission in the restframe UV spectra of active galatic nuclei (AGNs), the first empirical UV iron template to cover the full 1250 - 3090 A range. Iron emission is often a severe contaminant in optical--UV spectra of AGNs. Its presence complicates and limits the accuracy of measurements of both strong and weak emission lines and the continuum emission, affecting studies of line and continuum interrelations, the ionization structure, and elemental abundances in AGNs. Despite the wealth of work on modeling the AGN FeII emission and the need to account for it in observed AGN spectra, there is no UV template electronically available to aid this process. The iron template we present is based on HST spectra of the Narrow Line Seyfert 1, IZw1. Its intrinsic narrow lines (~900 km/s) and rich iron spectrum make the template particularly suitable for use with most AGN spectra. The iron emission spectrum and the line identifications and measurements are presented and compared with the work of Laor et al. We illustrate the application of the derived FeII and FeIII templates by fitting and subtracting the iron emission from UV spectra of four high-z quasars and of the nearby quasar, 3C273. We briefly discuss the small discrepancies between this observed iron emission and the UV template, and compare the template with previously published ones. We discuss the advantages and limitations of the templates and of the template fitting method. We conclude that the templates work sufficiently well to be a valuable and important tool for eliminating and studying the iron emission in AGNs, at least until accurate theoretical iron emission models are developed. (Abridged)Comment: 73 pages including 7 figures, 6 tables. To appear in ApJS. Preprint is also available at http://www.astronomy.ohio-state.edu/~vester/IronEmission

The UV Properties of the Narrow Line Quasar I Zwicky 1

I Zw 1 is the prototype narrow line quasar. We report here the results of our study of the UV emission of I Zw 1 using a high S/N (50-120) spectrum obtained with the HST FOS. The following main new results are obtained: 1. The Mg II and Al III doublets are partially/fully resolved. The measured doublet ratios verify theoretical predictions that the lines are thermalized in the BLR. 2. A weak associated UV absorption system is detected in N~V, and possibly also in C IV and Lya, suggesting an outflow with a velocity of 1870 km/s and velocity dispersion <300 km/s. 3. Lines from ions of increasing ionization level show increasing excess blue wing flux, and an increasing line peak velocity shift, reaching a maximum blueshift of about 2000 km/s for He II 1640. This may indicate an out-flowing component in the BLR, where the ionization level increases with velocity, and which is visible only in the approaching direction. The highest velocity part of this outflow may produce the associated UV absorption system. 4. The small C III] 1909 EW, and the small C III] 1909/Lya and C III] 1909/Si III] 1892 flux ratios indicate a typical BLR density of 10^11, i.e. about an order of magnitude larger than implied by C III] 1909 in most quasars. A BLR component of a higher density is implied by the EW and doublet ratio of the Al III 1857 doublet. 5. Prominent Fe II UV 191 emission is seen, together with weaker line emission at 1294 and 1871 A. These three features have been proposed as evidence for significant Lya pumping of the 8-10 eV levels of Fe II. 6. Significant Fe III emission is present. The Fe III UV 34 and UV 48 multiplets are clearly resolved, and Fe III UV 1, UV 47, UV 50, and UV 68 may also be present. (Shortened version)Comment: 28 pages, 1 table and 7 figures included. Uses aas2pp4.sty. Scheduled for the Astrophysical Journal November 10, 1997 issue, Vol. 48