Kolmogorov-Sinai entropy of a generalized Markov shift

In this paper we calculate Kolmogorov-Sinai entropy $h_M(S)$ of the generalized Markov shift associated with a contractive Markov system (CMS) \cite{Wer1} using the coding map constructed in \cite{Wer3}. We show that $$h_M(S)=-\sum\limits_{e\in E}\int\limits_{K_{i(e)}} p_e\log p_ed\mu$$ where $\mu$ is a unique invariant Borel probability measure of the CMS. I. Werner, Contractive Markov systems, J. London Math. Soc. (2005) 236-258. I. Werner, Coding map for a contractive Markov system, Math. Proc. Camb. Phil. Soc. to appear 140 (2), March 2006

Radiation Hydrodynamics of Line-Driven Winds

Dimtri Mihalas' textbooks in the 70's and 80's on "Stellar Atmospheres" and "Foundations of Radiation Hydrodynamics" helped lay the early groundwork for understanding the moving atmospheres and winds of massive, luminous stars. Indeed, the central role of the momentum of stellar radiation in driving the mass outflow makes such massive-star winds key prototypes for radiation hydrodynamical processes. This paper reviews the dynamics of such radiative driving, building first upon the standard CAK model, and then discussing subtleties associated with the development and saturation of instabilities, and wind initiation near the sonic point base. An overall goal is to illuminate the rich physics of radiative driving and the challenges that lie ahead in developing dynamical models that can explain the broad scaling of mass loss rate and flow speed with stellar properties, as well as the often complex structure and variability observed in massive-star outflows.Comment: 14 pages. to appear in "Recent Directions in Astrophysical Quantitative Spectroscopy and Radiation Hydrodynamics

Including All the Lines

I present a progress report on including all the lines in the linelists, including all the lines in the opacities, including all the lines in the model atmosphere and spectrum synthesis calculations, producing high-resolution, high-signal-to-noise atlases that show (not quite) all the lines, so that finally we can determine the properties of stars from a few of the lines.Comment: 9 pages, no figures. Presented at "Dimitrifest" conference in Boulder, Colorado, March 30 - April 3, 200