Growth of shocked gaseous interfaces in a conical geometry

The results of experiments on Richtmyer-Meshkov instability growth of multimode initial perturbations on an air-sulfur hexafluoride (SF6) interface in a conical geometry are presented. The experiments are done in a relatively larger shock tube. A nominally planar interface is formed by sandwiching a polymeric membrane between wire-mesh frames. A single incident shock wave ruptures the membrane resulting in multimode perturbations. The instability develops from the action of baroclinically deposited vorticity at the interface. The visual thickness delta of the interface is measured from schlieren photographs obtained in each run. Data are presented for delta at times when the interface has become turbulent. The data are compared with the experiments of Vetter [Shock Waves 4, 247 (1995)] which were done in a straight test section geometry, to illustrate the effects of area convergence. It is found from schlieren images that the interface thickness grows about 40% to 50% more rapidly than in Vetter's experiments. Laser induced scattering is used to capture the air-helium interface at late times. Image processing of pictures is also used to determine the interface thickness in cases where it was not clear from the pictures and to obtain the dominant eddy-blob sizes in the mixing zone. Some computational studies are also presented to show the global geometry changes of the interface when it implodes into a conical geometry in both light-heavy and heavy-light cases

The Many Electron Ground State of the Adiabatic Holstein Model in Two and Three Dimensions

We present the complete ground state phase diagram of the Holstein model in two and three dimension considering the phonon variables to be classical. We first establish the overall structure of the phase diagram by using exact diagonalisation based Monte Carlo (ED-MC) on small lattices and then use a new ``travelling cluster'' approximation (TCA) for annealing the phonon degrees of freedom on large lattices. The phases that emerge include a Fermi liquid (FL), with no lattice distortions, an insulating polaron liquid (PL) at strong coupling, and a charge ordered insulating (COI) phase around half- filling. The COI phase is separated from the Fermi liquid by a regime of phase coexistence whose width grows with increasing electron-phonon coupling. We provide results on the electronic density of states, the COI order parameter, and the spatial organisation of polaronic states, for arbitrary density and electron-phonon coupling. The results highlight the crucial role of spatial correlations in this strong coupling problem.Comment: Final versio

Far-infrared study of K giants in the solar neighborhood: Connection between Li enrichment and mass-loss

We searched for a correlation between the two anomalous properties of K giants: Li enhancement and IR excess from an unbiased survey of a large sample of RGB stars. A sample of 2000 low-mass K giants with accurate astrometry from the Hipparcos catalog was chosen for which Li abundances have been determined from low-resolution spectra. Far-infrared data were collected from the $WISE$ and $IRAS$ catalogs. To probe the correlation between the two anomalies, we supplemented 15 Li-rich K giants discovered from this sample with 25 known Li-rich K giants from other studies. Dust shell evolutionary models and spectral energy distributions were constructed using the code DUSTY to estimate different dust shell properties, such as dust evolutionary time scales, dust temperatures, and mass-loss rates. Among 2000 K giants, we found about two dozen K giants with detectable far-IR excess, and surprisingly, none of them are Li-rich. Similarly, the 15 new Li-rich K giants that were identified from the same sample show no evidence of IR excess. Of the total 40 Li-rich K giants, only 7 show IR excess. Important is that K giants with Li enhancement and/or IR excess begin to appear only at the bump on the RGB. Results show that K giants with IR excess are very rare, similar to K giants with Li enhancement. This may be due to the rapid differential evolution of dust shell and Li depletion compared to RGB evolutionary time scales. We also infer from the results that during the bump evolution, giants probably undergo some internal changes, which are perhaps the cause of mass-loss and Li-enhancement events. However, the available observational results do not ascertain that these properties are correlated. That a few Li-rich giants have IR excess seems to be pure coincidence.Comment: Accepted for Publication in Astronomy & Astrophysics, 6 figures, 5 tables, 19 page

What Determines Firm Size?

Motivated by theories of the firm, which we classify as technological' or organizational,' we analyze the determinants of firm size across industries and across countries in a sample of 15 European countries. We find that, on average, firms facing larger markets are larger. At the industry level, we find firms in the utility sector are large, perhaps because they enjoy a natural, or officially sanctioned, monopoly. Capital intensive industries, high wage industries, and industries that do a lot of R&D have larger firms, as do industries that require little external financing. At the country level, the most salient findings are that countries with efficient judicial systems have larger firms, and, correcting for institutional development, there is little evidence that richer countries have larger firms. Interestingly, institutional development, such as greater judicial efficiency, seems to be correlated with lower dispersion in firm size within an industry. The effects of interactions (between an industry's characteristics and a country's environment) on size are perhaps the most novel results in the paper, and are best able to discriminate between theories. As the judicial system improves, the difference in size between firms in capital intensive industries and firms in industries that use little physical capital diminishes, a finding consistent with size of firms in industries dependent on external finance is larger in countries with better financial markets, suggesting that financial constraints limit average firm size.