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We describe the results of 3D numerical simulations of oxygen shell burning and hydrogen core burning in a 23 M stellar model. A detailed comparison is made to stellar mixing-length theory (MLT) for the shell-burning model. Simulations in 2D are significantly different from 3D, in terms of both flow morphology and velocity amplitude. Convective mixing regions are better predicted using a dynamic boundary condition based on the bulk Richardson number than by purely local, static criteria like Schwarzschild or Ledoux. MLT gives a good description of the velocity scale and temperature gradient for shell convection; however, there are other important effects that it does not capture, mostly related to the dynamical motion of the boundaries between convective and nonconvective regions. There is asymmetry between upflows and downflows, so the net kinetic energy flux is not zero. The motion of convective boundaries is a source of gravity waves; this is a necessary consequence of the deceleration of convective plumes. Convective ''overshooting'' is best described as an elastic response by the convective boundary, rather than ballistic penetration of the stable layers by turbulent eddies. The convective boundaries are rife with internal and interfacial wave motions, and a variety of instabilities arise that induce mixing through a process best described as turbulent entrainment. We find that the rate at which material entrainment proceeds at the boundaries is consistent with analogous laboratory experiments and simulation and observation of terrestrial atmospheric mixing. In particular, the normalized entrainment rate E ¼ u E / H is well described by a power-law dependence on the bulk Richardson number Ri B ¼ ÁbL/ 2 H for the conditions studied, 20 P Ri B P 420. We find E ¼ ARi Àn B , with best-fit values log A ¼ 0:027 AE 0:38 and n ¼ 1:05 AE 0:21. We discuss the applicability of these results to stellar evolution calculations.

Prepared by the LSST Science Collaborations, with contributions from the LSST Project. PrefaceMajor advances in our understanding of the Universe over the history of astronomy have often arisen from dramatic improvements in our ability to observe the sky to greater depth, in previously unexplored wavebands, with higher precision, or with improved spatial, spectral, or temporal resolution. Aided by rapid progress in information technology, current sky surveys are again changing the way we view and study the Universe, and the next-generation instruments, and the surveys that will be made with them, will maintain this revolutionary progress. Substantial progress in the important scientific problems of the next decade (determining the nature of dark energy and dark matter, studying the evolution of galaxies and the structure of our own Milky Way, opening up the time domain to discover faint variable objects, and mapping both the inner and outer Solar System) all require wide-field repeated deep imaging of the sky in optical bands.The wide-fast-deep science requirement leads to a single wide-field telescope and camera which can repeatedly survey the sky with deep short exposures. The Large Synoptic Survey Telescope (LSST), a dedicated telecope with an effective aperture of 6.7 meters and a field of view of 9.6 deg 2 , will make major contributions to all these scientific areas and more. It will carry out a survey of 20,000 deg 2 of the sky in six broad photometric bands, imaging each region of sky roughly 2000 times (1000 pairs of back-to-back 15-sec exposures) over a ten-year survey lifetime.The LSST project will deliver fully calibrated survey data to the United States scientific community and the public with no proprietary period. Near real-time alerts for transients will also be provided worldwide. A goal is worldwide participation in all data products. The survey will enable comprehensive exploration of the Solar System beyond the Kuiper Belt, new understanding of the structure of our Galaxy and that of the Local Group, and vast opportunities in cosmology and galaxy evolution using data for billions of distant galaxies. Since many of these science programs will involve the use of the world's largest non-proprietary database, a key goal is maximizing the usability of the data. Experience with previous surveys is that often their most exciting scientific results were unanticipated at the time that the survey was designed; we fully expect this to be the case for the LSST as well.The purpose of this Science Book is to examine and document in detail science goals, opportunities, and capabilities that will be provided by the LSST. The book addresses key questions that will be confronted by the LSST survey, and it poses new questions to be addressed by future study. It contains previously available material (including a number of White Papers submitted to the ASTRO2010 Decadal Survey) as well as new results from a year-long campaign of study and evaluation. This book does not attempt to be complete; there are many ...

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