Lattice Dynamics in the Half-Space, II. Energy Transport Equation

We consider the lattice dynamics in the half-space. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $\varepsilon^{-1}$. We establish two time regimes. For times of order $\varepsilon^{-\gamma}$, $0<\gamma<1$, locally the measure converges to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian, in general). For times of order $\varepsilon^{-1}$, this covariance changes in time and is governed by a semiclassical transport equation.Comment: 35 page

The Weak Blue Bump of H2106-099 and AGN De-Reddening

We present multi-frequency spectra of the Seyfert 1 galaxy H2106-099, from radio to hard X-rays, spanning over a decade of observations. The hard X-ray (2-20 keV) spectrum measured with Ginga had a Log slope of -0.80 +/- 0.02 on 1988 May 18 and -1.02 +/- 0.10 on 1988 May 22 / 23 UT, with no observed flux changes. Other measurements showed variability and unusual spectral features: The V band flux changed by a factor of 1.8 (> 10 sigma) in six weeks. Only moderate optical Fe II emission is present, but strong [FeVII] and [Fe X] lines are present in some epochs. The Balmer lines show > 25% variations in flux relative to the mean, and He I changed by more than 100% relative to the mean in <~ six years. The most surprising finds came from the composite UV through near-IR spectrum: If the spectrum is de-reddened by the galactic extinction value (from 21 cm observations), a residual 2175 Angstrom absorption feature is present. Additional de-reddening to correct the feature yields E(B-V)=0.07 mag due to material outside our galaxy, most probably associated with the AGN or its host galaxy. No other clear indications of reddening are observed in this object, suggesting that blue bump strength measurements in low and intermediate red-shift AGN could be incorrect if derived without UV observations of the region near 2175 Angstrom in the AGN frame. After all reddening corrections are performed, the log slope of H2106-099 from the near IR (~12500 Angstrom) to the UV (~1400 Angstrom), -0.94 +/- 0.05, is steep compared to other AGN, suggesting that the blue bump in this object is intrinsically weak. Weak blue bumps are, therefore, not always an artifact caused by reddening.Comment: Three parts: A. 33 pages text, B. one landscape table, C. 8 figure