arXiv subjects

Andrea Gabrielli

Publications and source records attributed to Andrea Gabrielli.

95 records · Page 6Linked to original sources

arXiv2000

Damaging and Cracks in Thin Mud Layers

We present a detailed study of a two-dimensional minimal lattice model for the description of mud cracking in the limit of extremely thin layers. In this model each bond of the lattice is assigned to a (quenched) breaking threshold. Fractures proceed through the selection of the part of the material with the smallest breaking threshold. A local damaging rule is also implemented, by using two different types of weakening of the neighboring sites, corresponding to different physical situations. Some analytical results are derived through a probabilistic approach known as Run Time Statistics. In particular, we find that the total time to break down the sample grows with the dimension $L$ of the lattice as $L^2$ even though the percolating cluster has a non trivial fractal dimension. Furthermore, a formula for the mean weakening in time of the whole sample is obtained.

cond-mat.stat-mech↗

arXiv2000

Persistent fluctuations and scaling properties in galaxy number counts

Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the large scale correlations in the galaxy spatial distribution. There are, in fact, no longer doubts since two decades of the existence of very large scale structures. The still remaining problem concerns the correct characterization of their statistical properties. We propose to study two properties of galaxy counts data, in order to discriminate between a small scale (~ 5 - 20 Mpc/h) homogeneous distribution, and a fractal structure on large scales (~ 20 - 300 Mpc/h). Firstly, the average slope of the counts which can be associated to an eventual fractal dimension in real space by simple arguments. Secondly, we propose to study fluctuations of counts around the average behavior as a function of apparent magnitude in the whole magnitude range B_j > 11. These fluctuations can discriminate between a genuine fractal distribution and a homogeneous one. In fact, they are related to the very statistical properties of the spatial distribution, independently on cosmological corrections. More specifically, in a fractal distribution one expects to find persistent scale-invariant fluctuations around the average behavior, which do not decay with apparent magnitude. On the other hand, in an homogeneous distribution, on large enough scales, the relative variance of the counts should decrease exponentially with apparent magnitude. Smooth cosmological corrections cannot change such a behavior.

astro-ph↗

arXiv2000

Biasing in Gaussian random fields and galaxy correlations

In this letter we show that in a Gaussian random field the correlation length, the typical size of correlated structures, does not change with biasing. We interpret the amplification of the correlation functions of subsets identified by different thresholds being due to the increasing sparseness of peaks over threshold. This clarifies an long-standing misconception in the literature. We also argue that this effect does not explain the observed increase of the amplitude of the correlation function xi(r) when galaxies of brighter luminosity or galaxy clusters of increasing richness are considered.

astro-ph↗

arXiv1999

Invasion Percolation with Temperature and the Nature of SOC in Real Systems

We show that the introduction of thermal noise in Invasion Percolation (IP) brings the system outside the critical point. This result suggests a possible definition of SOC systems as ordinary critical systems where the critical point correspond to set to 0 one of the parameters. We recover both IP and EDEN model, for $T \to 0$, and $T \to \infty$ respectively. For small $T$ we find a dynamical second order transition with correlation length diverging when $T \to 0$.

cond-mat.stat-mech↗

arXiv1997

Study of the disordered one-dimensional contact process

New theoretical and numerical analysis of the one-dimensional contact process with quenched disorder are presented. We derive new scaling relations, different from their counterparts in the pure model, which are valid not only at the critical point but also away from it due to the presence of generic scale invariance. All the proposed scaling laws are verified in numerical simulations. In addition we map the disordered contact process into a Non-Markovian contact process by using the so called Run Time Statistic, and write down the associated field theory. This turns out to be in the same universality class as one derived by Janssen for the quenched system with a Gaussian distribution of impurities. Our findings here support the lack of universality suggested by the field theoretical analysis: generic power-law behaviors are obtained, evidence is shown of the absence of a characteristic time away from the critical point, and the absence of universality is put forward. The intermediate sublinear regime predicted by Bramsom et al. is also found.

cond-mat↗