The two membranes problem for different operators

We study the two membranes problem for different operators, possibly nonlocal. We prove a general result about the H\"older continuity of the solutions and we develop a viscosity solution approach to this problem. Then we obtain $C^{1,\gamma}$ regularity of the solutions provided that the orders of the two operators are different. In the special case when one operator coincides with the fractional Laplacian, we obtain the optimal regularity and a characterization of the free boundary

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

Controlled Shock Shells and Intracluster Fusion Reactions in the Explosion of Large Clusters

The ion phase-space dynamics in the Coulomb explosion of very large ($\sim 10^6 - 10^7$ atoms) deuterium clusters can be tailored using two consecutive laser pulses with different intensities and an appropriate time delay. For suitable sets of laser parameters (intensities and delay), large-scale shock shells form during the explosion, thus highly increasing the probability of fusion reactions within the single exploding clusters. In order to analyze the ion dynamics and evaluate the intracluster reaction rate, a one-dimensional theory is used, which approximately accounts for the electron expulsion from the clusters. It is found that, for very large clusters (initial radius $\sim$ 100 nm), and optimal laser parameters, the intracluster fusion yield becomes comparable to the intercluster fusion yield. The validity of the results is confirmed with three-dimensional particle-in-cell simulations.Comment: 25 pages, 11 figures, to appear in Physical Review