arXiv subjects

L. Pietronero

Publications and source records attributed to L. Pietronero.

93 records · Page 6Linked to original sources

arXiv1995

Renormalization group approach to the critical behavior of the forest fire model

We introduce a Renormalization scheme for the one and two dimensional Forest-Fire models in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. This model is therefore critical in the usual sense because the control parameter has to be tuned to its critical value in order to get criticality. It turns out that this is not just the condition for a time scale separation. The critical exponents are computed analytically and we obtain $ν=1.0$, $τ=1.0$ and $ν=0.65$, $τ=1.16$ respectively for the one and two dimensional case, in very good agreement with numerical simulations.

cond-mat↗

arXiv1995

Stochastic aggregation model for the multifractal distribution of matter

Two main features of the observable distribution of visible matter are the space correlations of galaxy positions and the mass function of galaxies. As discussed in Pietronero and Sylos Labini on this issue ([1], see also [2],[3]), the concept of multifractal (MF) distribution (including the masses) naturally unifies these two properties. Hence with the knowledge of the whole MF spectrum one obtains information on the correlations in space as well as on the mass function. From a theoretical point of view one would like to identify the dynamical process that leads to such a MF distribution. In order to gain some insight into this complex problem we have developed a simple stochastic model that includes some of the basic properties of aggregation process and allows us to pose a variety of interesting question concerning the possible dynamical origin of the MF distribution. The dynamics is characterised by some parameters, that have a direct physical meaning in term of cosmological processes. In this way we can relate the input parameters of the dynamics to the properties of the final configuration and produce a sort of phase diagram.

astro-ph↗

arXiv1995

Cosmological Principle and the debate about Large Scale Structures distribution

The basic hypothesis of a post-Copernican Cosmological theory is that {\em all the points} of the Universe have to be essentially equivalent: this hypothesis is required in order to avoid any privileged {\em observer}. This assumption has been implemented by Einstein in the so-called Cosmological Principles (CP): {\em all the positions} in the Universe have to be essentially equivalent, so that the Universe is homogeneous. This situation implies also the condition of spherical symmetry about every point, so that the Universe in also Isotropic. There is a hidden assumption in the formulation of the CP in regard to the hypothesis that all the points are equivalent In fact, the condition that all the occupied points are statistically equivalent with respect to their environment correspond to the property of of Local Isotropy. It is generally believed that the Universe cannot be isotropic about every point without being also homogeneous [1]. Actually Local Isotropy does not necessarily implies homogeneity; in fact a topology theorem states that homogeneity is implied by the condition of local isotropy together with {\em the assumption of the analyticity or regularity} for the distribution of matter. Up to the seventies analyticity was an obvious implicit assumption in any physical problem. Recently however we have learned about intrinsically irregular structures for which analyticity should be considered as a property to be tested with appropriate analysis of experiment.

astro-ph↗