Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure

We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and V\'azquez, where the pressure is obtained as a Riesz potential associated to the density. We take advantage of the displacement convexity of the Riesz potential in one dimension to show a functional inequality involving the entropy, entropy dissipation, and the Euclidean transport distance. An argument by approximation shows that this functional inequality is enough to deduce the exponential convergence of solutions in self-similar variables to the unique steady states

The UNAM-KIAS Catalog of Isolated Galaxies

A new catalog of isolated galaxies from The Sloan Digital Sky Survey (DR5) is presented. 1520 isolated galaxies were found in 1.4 steradians of sky. The selection criteria in this so called UNAM-KIAS catalog was implemented from a variation on the criteria developed by Karachentseva 1973 including full redshift information. Through an image processing pipeline that takes advantage from the high resolution (~ 0.4 ''/pix) and high dynamic range of the SDSS images, a uniform g band morphological classification for all these galaxies is presented. We identify 80% (SaSm) spirals (50% later than Sbc types) on one hand, and a scarce population of early-type E(6.5%) and S0(8%) galaxies amounting to 14.5% on the other hand. This magnitude-limited catalog is ~ 80% complete at 16.5, 15.6, 15.0, 14.6 and 14.4 magnitudes in the ugriz bands respectively. Some representative physical properties including SDSS magnitudes and color distributions, color-color diagrams, absolute magnitude-color, and concentration-color diagrams as a function of morphological type are presented. The UNAM-KIAS Morphological Atlas is also released along with this paper. For each galaxy of type later than Sa, a mosaic is presented that includes: (1) a g-band logarithmic image, (2) a g band filtered-enhanced image where a Gaussian kernel of various sizes was applied and (3) an RGB color image from the SDSS database. For E/S0/Sa galaxies, in addition to the images in (1), (2) and (3), plots of r band surface brightness and geometric profiles (ellipticity, Position Angle PA and A4/B4 coefficients of the Fourier series expansions of deviations of a pure ellipse) are provided...Comment: 40 pages, 17 figures and 3 table

The UNAM-KIAS Catalog of Isolated Galaxies

A new catalog of isolated galaxies from The Sloan Digital Sky Survey (DR5) is presented. 1520 isolated galaxies were found in 1.4 steradians of sky. The selection criteria in this so called UNAM-KIAS catalog was implemented from a variation on the criteria developed by Karachentseva 1973 including full redshift information. Through an image processing pipeline that takes advantage from the high resolution (~ 0.4 ''/pix) and high dynamic range of the SDSS images, a uniform g band morphological classification for all these galaxies is presented. We identify 80% (SaSm) spirals (50% later than Sbc types) on one hand, and a scarce population of early-type E(6.5%) and S0(8%) galaxies amounting to 14.5% on the other hand. This magnitude-limited catalog is ~ 80% complete at 16.5, 15.6, 15.0, 14.6 and 14.4 magnitudes in the ugriz bands respectively. Some representative physical properties including SDSS magnitudes and color distributions, color-color diagrams, absolute magnitude-color, and concentration-color diagrams as a function of morphological type are presented. The UNAM-KIAS Morphological Atlas is also released along with this paper. For each galaxy of type later than Sa, a mosaic is presented that includes: (1) a g-band logarithmic image, (2) a g band filtered-enhanced image where a Gaussian kernel of various sizes was applied and (3) an RGB color image from the SDSS database. For E/S0/Sa galaxies, in addition to the images in (1), (2) and (3), plots of r band surface brightness and geometric profiles (ellipticity, Position Angle PA and A4/B4 coefficients of the Fourier series expansions of deviations of a pure ellipse) are provided...Comment: 40 pages, 17 figures and 3 table

Solid flow drives surface nanopatterning by ion-beam irradiation

Ion Beam Sputtering (IBS) is known to produce surface nanopatterns over macroscopic areas on a wide range of materials. However, in spite of the technological potential of this route to nanostructuring, the physical process by which these surfaces self-organize remains poorly under- stood. We have performed detailed experiments of IBS on Si substrates that validate dynamical and morphological predictions from a hydrodynamic description of the phenomenon. Our results elucidate flow of a nanoscopically thin and highly viscous surface layer, driven by the stress created by the ion-beam, as a description of the system. This type of slow relaxation is akin to flow of macroscopic solids like glaciers or lead pipes, that is driven by defect dynamics.Comment: 12 pages, 4 figure