Generic stability of dissipative non-relativistic and relativistic fluids

The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium is asymptotically stable in both cases due to purely thermodynamic restrictions; the only requirements are the thermodynamic stability and the nonnegativity of the transport coefficients.Comment: 22 page

An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Fake Superpotential for Large and Small Extremal Black Holes

We consider the fist order, gradient-flow, description of the scalar fields coupled to spherically symmetric, asymptotically flat black holes in extended supergravities. Using the identification of the fake superpotential with Hamilton's characteristic function we clarify some of its general properties, showing in particular (besides reviewing the issue of its duality invariance) that W has the properties of a Liapunov's function, which implies that its extrema (associated with the horizon of extremal black holes) are asymptotically stable equilibrium points of the corresponding first order dynamical system (in the sense of Liapunov). Moreover, we show that the fake superpotential W has, along the entire radial flow, the same flat directions which exist at the attractor point. This allows to study properties of the ADM mass also for small black holes where in fact W has no critical points at finite distance in moduli space. In particular the W function for small non-BPS black holes can always be computed analytically, unlike for the large black-hole case.Comment: 30 pages, LaTeX source. Discussion on the radial evolution of the scalar fields, in relation to the symmetries of the W-function, extended. Table 1 added. Typos correcte

Kinetical systems

summary:The aim of the paper is to give some preliminary information concerning a class of nonlinear differential equations often used in physical chemistry and biology. Such systems are often very large and it is well known that where studying properties of such systems difficulties rapidly increase with their dimension. One way how to get over the difficulties is to use special forms of such systems

A case of informal encounter between theories and practices

Supported by CNRConsiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Past and future spatio-temporal variability of rainfall of the Bani catchment in West Africa.

6 pagesInternational audienceSince 1970, on the Bani, main tributary of the upper Niger, annual discharges have decreased by 69% while annual rainfall has decreased only by 15% to 25% over the catchment. Among the possible causes for this very strong discharge decrease changes of precipitation patterns must be explored. Four different methods of spatial interpolation of rainfall fields were compared on intra-seasonal indices (number of dry days, the dry spells, EDI, SPI, etc.) for the period 1950-2006. This study was also conducted on simulated pluviometric data generated by a regional climatic model (WRF) for the 2032-2041 period. The pluviometric deficit is explained by a conjunction of many factors: an earlier end of rainy season, less precipitation during the core of it and an increase of the number of dry spells. The climatic model envisages an increase of annual precipitation amounts compared to the 1981-1990 period, fewer dry spells and shorter droughts