Doubly-periodic array of bubbles in a Hele-Shaw cell

Exact solutions are presented for a doubly-periodic array of steadily moving bubbles in a Hele-Shaw cell when surface tension is neglected. It is assumed that the bubbles either are symmetrical with respect to the channel centreline or have fore-and-aft symmetry, or both, so that the relevant flow domain can be reduced to a simply connected region. By using conformal mapping techniques, a general solution with any number of bubbles per unit cell is obtained in integral form. Several examples are given, including solutions for multi-file arrays of bubbles in the channel geometry and doubly-periodic solutions in an unbounded cell.Comment: 15 pages, 12 figure

Joint Formation of QSOs and Spheroids: QSOs as clocks of star formation in Spheroids

Direct and indirect observational evidence leads to the conclusion that high redshift QSOs did shine in the core of early type proto-galaxies during their main episode of star formation. Exploting this fact, we derive the rate of formation of this kind of stellar systems at high redshift by using the QSO Luminosity Function. The elemental proportions in elliptical galaxies, the descendents of the QSO hosts, suggest that the star formation was more rapid in more massive objects. We show that this is expected to occur in Dark Matter haloes, when the processes of cooling and heating is considered. This is also confirmed by comparing the observed sub-mm counts to those derived by coupling the formation rate and the star formation rate of the spheroidal galaxies with a detailed model for their SED evolution. In this scenario SCUBA galaxies and Lyman Break Galaxies are early type proto-galaxies forming the bulk of their stars before the onset of QSO activity.Comment: 13 pages, 8 figures, accepted by MNRAS, major revision of the formalis

Panchromatic models of galaxies: GRASIL

We present here a model for simulating the panchromatic spectral energy distribution of galaxies, which aims to be a complete tool to study the complex multi-wavelength picture of the universe. The model take into account all important components that concur to the SED of galaxies at wavelengths from X-rays to the radio. We review the modeling of each component and provide several applications, interpreting observations of galaxy of different types at all the wavelengths.Comment: 10 pages, 4 figures, invited talk, to appear in the proceedings of: "The Spectral Energy Distribution of Gas-Rich Galaxies: Confronting Models with Data", Heidelberg, 4-8 Oct. 2004, eds. C.C. Popescu and R.J. Tuffs, AIP Conf. Ser., in pres