116 research outputs found
Stability analysis of cosmological models through Liapunov's method
We investigate the general asymptotic behaviour of Friedman-Robertson-Walker
(FRW) models with an inflaton field, scalar-tensor FRW cosmological models and
diagonal Bianchi-IX models by means of Liapunov's method. This method provides
information not only about the asymptotic stability of a given equilibrium
point but also about its basin of attraction. This cannot be obtained by the
usual methods found in the literature, such as linear stability analysis or
first order perturbation techniques. Moreover, Liapunov's method is also
applicable to non-autonomous systems. We use this advantadge to investigate the
mechanism of reheating for the inflaton field in FRW models.Comment: Latex file, 8 pages, no figures, accepted for publication in Class. &
Quant. Gra
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
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