Double Greedy Algorithms: Reduced Basis Methods for Transport Dominated Problems

The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov $n$-widths of the solution sets. The central ingredient is the construction of computationally feasible "tight" surrogates which in turn are based on deriving a suitable well-conditioned variational formulation for the parameter dependent problem. The theoretical results are illustrated by numerical experiments for convection-diffusion and pure transport equations. In particular, the latter example sheds some light on the smoothness of the dependence of the solutions on the parameters

Extended Molecular Gas in the Nearby Starburst Galaxy Maffei 2

We present a 9'x9' fully-sampled map of the CO J=1-0 emission in the nearby starburst galaxy Maffei 2 obtained at the Five College Radio Astronomy Observatory. The map reveals previously known strong CO emission in the central starburst region as well as an extended asymmetric distribution with bright CO lines at the ends of the bar and in a feature at the north-east edge of the molecular disk. This northern feature, proposed previously to be an interacting companion galaxy, could be a dwarf irregular galaxy, although the CO data are also consistent with the feature being simply an extension of one of the spiral arms. We estimate the total molecular gas mass of Maffei 2 to be (1.4-1.7)x10^9 Mo or ~3-4% of its dynamical mass. Adopting the recently determined lower value for the CO-to-H2 conversion factor in the central region, our data lead to the surprising result that the largest concentrations of molecular gas in Maffei 2 lie at the bar ends and in the putative dwarf companion rather than in the central starburst. A gravitational stability analysis reveals that the extended disk of Maffei 2 lies above the critical density for star formation; however, whether the central region is also gravitationally unstable depends both on the details of the rotation curve and the precise value of the CO-to-H2 conversion factor in this region.Comment: accepted to ApJ (Sept 10 2004 issue

Modeling fast pyrolysis of waste biomass: Improving predictive capability

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CH 3 GHz Observations of the Galactic Center

A 3 $\times$ 3 map of the Galactic Center was made at 9\arcmin resolution and 10\arcmin spacing in the CH $^2\Pi_{1/2}$, J=1/2, F=1-1 transition at 3335 MHz. The CH emission shows a velocity extent that is nearly that of the CO(1-0) line, but the CH line profiles differ markedly from the CO. The 3335 MHz CH transition primarily traces low-density molecular gas and our observations indicate that the mass of this component within $\sim$ 30 pc of the Galactic Center is $\sim$ 9 $\times$ 10$^6$ M$_\odot$. The CO-H$_2$ conversion factor obtained for the low-density gas in the mapped region is greater than that thought to apply to the dense molecular gas at the Galactic Center. In addition to tracing the low-density molecular gas at the Galactic Center, the CH spectra show evidence of emission from molecular clouds along the line of sight both in the foreground and background. The scale height of these clouds ranges from 27 - 109 pc, consistent with previous work based on observations of molecular clouds in the inner Galaxy.Comment: 29 pages, 12 figure