Caloric curve of star clusters

Self-gravitating systems, like globular clusters or elliptical galaxies, are the prototypes of many-body systems with long-range interactions, and should be the natural arena where to test theoretical predictions on the statistical behaviour of long-range-interacting systems. Systems of classical self-gravitating particles can be studied with the standard tools of equilibrium statistical mechanics, provided the potential is regularized at small length scales and the system is confined in a box. The confinement condition looks rather unphysical in general, so that it is natural to ask whether what we learn with these studies is relevant to real self-gravitating systems. In order to provide a first answer to this question we consider a basic, simple, yet effective model of globular clusters, the King model. This model describes a self-consistently confined system, without the need of any external box, but the stationary state is a non-thermal one. In particular, we consider the King model with a short-distance cutoff on the interactions and we discuss how such a cutoff affects the caloric curve, i.e. the relation between temperature and energy. We find that the cutoff stabilizes a low-energy phase which is absent in the King model without cutoff; the caloric curve of the model with cutoff turns out to be very similar to that of previously studied confined and regularized models, but for the absence of a high-energy gas-like phase. We briefly discuss the possible phenomenological as well as theoretical implications of these results.Comment: 21 pages, 13 figure

The Impact of Internet on the Market for Daily Newspapers in Italy

Recent years have seen a surge in websites that provide news for free and, up to the end of 2001, daily newspapers in Italy have shown a growing trend towards making available online for free; the exact articles published on paper. To assess whether on-line news and traditional daily newspapers are substitute, complement or independent goods, I model the choice between different daily newspapers as a discrete choice among differentiated products. Considering the availability of a website as a newspaper characteristic and controlling for other observable and unobservable characteristics of newspapers and of the outside good, I estimate a logit model of demand on market level data from 1976 to 2001 for the main national daily newspapers in Italy. Results suggest that opening a website had a negative impact both on the sales of the newspaper who opened it and on those of its rivals. I calculate the implied short-run and approximated long-run losses in both sales and profits and provide some evidence of the additional negative effect stemming from the general availability of Internet and on-line news. Results also contribute to explaining why, starting from the end of 2001, many publishers introduced a fee to read on-line the paper edition of the newspaper.daily newspapers, Internet, websites, substitution, discrete choice models, product differentiation, dynamics, market level data

Geometric approach to Hamiltonian dynamics and statistical mechanics

This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of freedom of interest for statistical mechanics. The first part of the paper concerns the applications of methods used in classical differential geometry to study the chaotic dynamics of Hamiltonian systems. Starting from the identity between the trajectories of a dynamical system and the geodesics in its configuration space, a geometric theory of chaotic dynamics can be developed, which sheds new light on the origin of chaos in Hamiltonian systems. In fact, it appears that chaos can be induced not only by negative curvatures, as was originally surmised, but also by positive curvatures, provided the curvatures are fluctuating along the geodesics. In the case of a system with a large number of degrees of freedom it is possible to give an analytical estimate of the largest Lyapunov exponent by means of a geometric model independent of the dynamics. In the second part of the paper the phenomenon of phase transitions is addressed and it is here that topology comes into play. In fact, when a system undergoes a phase transition, the fluctuations of the configuration-space curvature exhibit a singular behavior at the phase transition point, which can be qualitatively reproduced using geometric models. In these models the origin of the singular behavior of the curvature fluctuations appears to be caused by a topological transition in configuration space. This leads us to put forward a Topological Hypothesis (TH). The content of the TH is that phase transitions would be related at a deeper level to a change in the topology of the configuration space of the system.Comment: REVTeX, 81 pages, 36 ps/eps figures (some low-quality figures to save space); review article submitted to Physics Report