From non-symmetric particle systems to non-linear PDEs on fractals

We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging to a non-linear heat equation. We discuss a joint density-current law of large numbers and a corresponding large deviations principle.Comment: v2: 10 pages, 1 figure. To appear in the proceedings for the 2016 conference "Stochastic Partial Differential Equations & Related Fields" in honor of Michael R\"ockner's 60th birthday, Bielefel

Dynamical Masses in Luminous Infrared Galaxies

We have studied the dynamics and masses of a sample of ten nearby luminous and ultraluminous infrared galaxies (LIRGS and ULIRGs), using 2.3 micron CO absorption line spectroscopy and near-infrared H- and Ks-band imaging. By combining velocity dispersions derived from the spectroscopy, disk scale-lengths obtained from the imaging, and a set of likely model density profiles, we calculate dynamical masses for each LIRG. For the majority of the sample, it is difficult to reconcile our mass estimates with the large amounts of gas derived from millimeter observations and from a standard conversion between CO emission and H_2 mass. Our results imply that LIRGs do not have huge amounts of molecular gas (10^10-10^11 Msolar) at their centers, and support previous indications that the standard conversion of CO to H_2 probably overestimates the gas masses and cannot be used in these environments. This in turn suggests much more modest levels of extinction in the near-infrared for LIRGs than previously predicted (A_V~10-20 versus A_V~100-1000). The lower gas mass estimates indicated by our observations imply that the star formation efficiency in these systems is very high and is triggered by cloud-cloud collisions, shocks, and winds rather than by gravitational instabilities in circumnuclear gas disks.Comment: 14 pages, 2 figures, accepted to Ap