Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011)

The distribution of the poles of branches of the Painleve' VI transcendents associated to semi-simple Frobenius manifolds is determined close to a critical point. It is shown that the poles accumulate at the critical point, asymptotically along two rays. The example of the Frobenius manifold given by the quantum cohomology of the two-dimensional complex projective space is also considered.Comment: 35 pages, 10 figures; Physica D (2012

Solving the Sixth Painleve' Equation: Towards the Classification of all the Critical Behaviours and the Connection Formulae (October 2010)

The critical behavior of a three real parameter class of solutions of the sixth Painlev\'e equation is computed, and parametrized in terms of monodromy data of the associated $2\times 2$ matrix linear Fuchsian system of ODE. The class may contain solutions with poles accumulating at the critical point. The study of this class closes a gap in the description of the transcendents in one to one correspondence with the monodromy data. These transcendents are reviewed in the paper. Some formulas that relate the monodromy data to the critical behaviors of the four real (two complex) parameter class of solutions are missing in the literature, so they are computed here. A computational procedure to write the full expansion of the four and three real parameter class of solutions is proposed.Comment: 53 pages, 2 figure

Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces

We compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves.Comment: 50 pages, 6 Postscript figure

Gravitational waves from inflation

The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power-spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio $r$ and tensor spectral index $n_{\rm T}$. In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized.Comment: 85 pages, 4 tables, 9 figures; table 2 added, references added; matches published versio

Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)

The critical and asymptotic behaviors of solutions of the sixth Painlev\'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.Comment: 30 pages, 1 figure; Nonlinearity 201

Information system on hydrological and geomorphological catastrophes in Italy (SICI): a tool for managing landslide and flood hazards

International audienceSince 1990, we have maintained a database of historical information on landslides and floods in Italy, known as the National Research Council's AVI (Damaged Urban Areas) archive. The database was originally designed to respond to a request of the Minister of Civil Protection, and was aimed at helping the regional assessment of landslide and flood risk in Italy. The database was compiled in 1991-1992 to cover the period 1917 to 1990, and then updated to cover systematically the period 1917 to 2000, and non-systematically the periods 1900 to 1916 and 2001 to 2002. The database currently contains information on more than 32000 landslide events occurred at more than 21000 sites, and on more than 29000 flood events occurred at more than 14000 sites. Independently from the AVI archive, we have obtained other databases containing information on damage caused by mass movements and inundations, daily discharge measurements and solid-transport measurements at selected gauging stations, bibliographical and reference information on landslides and inundations, and a catalogue of National legislation on hydrological and geological hazards and risk in Italy. The databases are part of an information system known as SICI (an Italian acronym for Sistema Informativo sulle Catastrofi Idrogeologiche, Information System on Hydrological and Geomorphological Catastrophes), which is currently the largest single repository of historical information on landslides and floods in Italy. After an outline of the history and evolution of the AVI Project archive, we present and discuss: (a) the structure of the SICI information system, including the hardware and software solutions adopted to maintain, manage, update, use and disseminate the information stored in the various databases, (b) the type and amount of information stored in each database, including an estimate of their completeness, and (c) examples of recent applications of the information system, including a web-based GIS system to show the location of sites historically affected by landslides and floods, and an estimate of geo-hydrological (i.e. landslide and flood) risk in Italy based on the available historical information