K-Theory for group C^*-algebras

These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C^*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjecture.Comment: 22 pages, 2 figures, to be published in Springer Lecture Note

Some results on thermal stress of layered plates and shells by using Unified Formulation

This work presents some results on two-dimensional modelling of thermal stress problems in multilayered structures. The governing equations are written by referring to the Unified Formulation (UF) introduced by the first author. These equations are obtained in a compact form, that doesn't depend on the order of expansion of variables in the thickness direction or the variable description (layer-wise models and equivalent single layers models). Classical and refined theories based on the Principle of Virtual Displacements (PVD) and advanced mixed theories based on the Reissner Mixed Variational Theorem (RMVT) are both considered. As a result, a large variety of theories are derived and compared. The temperature profile along the thickness of the plate/shell is calculated by solving the Fourier's heat conduction equation. Alternatively, thermo-mechanical coupling problems can be considered, in which the thermal variation is influenced by mechanical loading. Exact closed-form solutions are provided for plates and shells, but also the applications of the Ritz method and the Finite Element Method (FEM) are presented

X-ray sources as tracers of the large-scale structure in the Universe

We review the current status of studies of large-scale structure in the X-ray Universe. After motivating the use X-rays for cosmological purposes, we discuss the various approaches used on different angular scales including X-ray background multipoles, cross-correlations of the X-ray background with galaxy catalogues, clustering of X-ray selected sources and small-scale fluctuations and anisotropies in the X-ray background. We discuss the implications of the above studies for the bias parameter of X-ray sources, which is likely to be moderate for X-ray selected AGN and the X-ray background (~1-2). We finally outline how all-sky X-ray maps at hard X-rays and medium surveys with large sky coverage could provide important tests for the cosmological models.Comment: Invited review presented at the Workshop X-ray Astronomy'99: Stellar endpoints, AGN and the diffuse X-ray background (Astrophys Lett and Comm

RETRASO, a code for modeling reactive transport in saturated and unsaturated porous media

The code RETRASO (REactive TRAnsport of SOlutes) simulates reactive transport of dissolved and gaseous species in non-isothermal saturated or unsaturated problems. Possible chemical reactions include aqueous complexation (including redox reactions), sorption, precipitation-dissolution of minerals and gas dissolution. Various models for sorption of solutes on solids are available, from experimental relationships (linear KD, Freundlich and Langmuir isotherms) to cation exchange and surface complexation models (constant capacitance, diffuse layer and triple layer models). Precipitation-dissolution and aqueous complexation can be modelled in equilibrium or according to kinetic laws. For the numerical solution of the reactive transport equations it uses the Direct Substitution Approach. The use of the code is demonstrated by three examples. The first example models various sorption processes in a smectite barrier. The second example models a complex chemical system in a two dimensional cross-section. The last example models pyrite weathering in an unsaturated medium

On the arcmin structure of the X-ray Universe

We present the angular correlation function of the X-ray population of 1063 XMM-Newton observations at high Galactic latitudes, comprising up to ~30000 sources over a sky area of ~125 sq. degrees in the energy bands: soft (0.5-2 keV) and hard (2-10 keV). This is the largest sample of serendipitous X-ray sources ever used for clustering analysis purposes to date and the results have been determined with unprecedented accuracy. We detect significant clustering signals in the soft and hard bands (~10 sigma and ~5 sigma, respectively). We deproject the angular correlation function via Limber's equation and calculate the typical spatial lengths. We infer that AGN at redshifts ~1 are embedded in dark matter halos with typical masses of log M ~ 12.6/h Msol and lifetimes in the range ~3-5 x 10^8 years, which indicates that AGN activity is a transient phase in the life of galaxies.Comment: 4 pages, 1 figure. Proc. of the conference "X-ray Astronomy 2009: Present status, multiwavelength approach and future perspectives", September 2009, Bologna. To appear in AIP Conf. Proc. (editors: A. Comastri, M. Cappi, L. Angelini)

Relativistic reflection in the average X-ray spectrum of AGN in the V\'eron-Cetty & V\'eron catalogue

The X-ray spectra of active galactic nuclei (AGN) unveil properties of matter around the super massive black hole (SMBH). We investigate the X-ray spectra of AGN focusing on Compton reflection and fluorescence, important processes of interaction between primary radiation and circum-nuclear material. Unresolved emission lines (most notably the Fe line) in the X-ray spectra of AGN indicate that this material is located far away from the SMBH. Contributions from the inner accretion disk, affected by relativistic effects, have also been detected in several cases. We studied the average X-ray spectrum of a sample of 263 X-ray unabsorbed AGN that yield 419023 counts in the 2-12 keV rest-frame band distributed among 388 XMM-Newton spectra. We fitted the average spectrum using a (basically) unabsorbed power law (primary radiation). From second model that represents the interaction of the primary radiation with matter located far away from the SMBH, we found that it was very significantly detected. Finally, we added a contribution from interaction with neutral material in the accretion disk close to the central SMBH, which is therefore smeared by relativistic effects, which improved the fit at 6 sigma. The reflection factors are 0.65 for the accretion disk and 0.25 for the torus. Replacing the neutral disk-reflection with low-ionisation disk reflection, also relativistically smeared, fits the data equally well, suggesting that we do not find evidence for a significant ionisation of the accretion disk. We detect distant neutral reflection in the average spectrum of unabsorbed AGN with z=0.8. Adding the disk-reflection component associated with a relativistic Fe line improves the data description at 6 sigma confidence level, suggesting that both reflection components are present. The disk-reflection component accounts for about 70 % of the total reflected flux.Comment: Accepted by A&A. 10 pages, 7 figure