arXiv subjects

Andrea Baldassarri

Publications and source records attributed to Andrea Baldassarri.

23 records · Page 2Linked to original sources

arXiv2003

Velocity fluctuations in cooling granular gases

We study the formation and the dynamics of correlations in the velocity field for 1D and 2D cooling granular gases with the assumption of negligible density fluctuations (``Homogeneous Velocity-correlated Cooling State'', HVCS). It is shown that the predictions of mean field models fail when velocity fluctuations become important. The study of correlations is done by means of molecular dynamics and introducing an Inelastic Lattice Maxwell Models. This lattice model is able to reproduce all the properties of the Homogeneous Cooling State and several features of the HVCS. Moreover it allows very precise measurements of structure functions and other crucial statistical indicators. The study suggests that both the 1D and the 2D dynamics of the velocity field are compatible with a diffusive dynamics at large scale with a more complex behavior at small scale. In 2D the issue of scale separation, which is of interest in the context of kinetic theories, is addressed.

cond-mat.stat-mech↗

arXiv2003

Self-Organized Percolation Power Laws with and without Fractal Geometry in the Etching of Random Solids

Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for which the frontier of the infinite cluster is no more fractal. In particular the exponent 7/4 which was recently demonstrated to be the exact value for the dimension of the so-called "hull" or external perimeter of the incipient percolation cluster, controls the width and length of gradient percolation frontiers whatever the gradient magnitude. This behavior is extended to previous model studies of etching by a finite volume of etching solution in contact with a disordered solid. In such a model, the dynamics stop spontaneously on an equilibrium self-similar surface similar to the fractal frontier of gradient percolation. It is shown that the power laws describing the system geometry involves also the fractal dimension of the percolation hull, whatever the value of the dynamically generated gradient, i.e. even for a non-fractal frontier. The comparison between numerical results and the exact results that can be obtained analytically for extreme values of the gradient suggests that there exist a unique power law valid from the smallest possible scale up to infinity. These results suggest the possible existence of an underlying conservation law, relating the length and the statistical width of percolation gradient frontiers.

cond-mat.stat-mech↗

arXiv2003

The average shape of a fluctuation: universality in excursions of stochastic processes

We study the average shape of a fluctuation of a time series x(t), that is the average value _T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law of the form _T = T^αf(t/T) is obeyed. The scaling function f(s) is to a large extent independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.

cond-mat.stat-mech↗

arXiv2000

Analytical results for generalized persistence properties of smooth processes

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the diffusion equation evolving from random initial conditions, one of the simplest coarsening systems. Exact results are obtained in certain limits, and rely on a new method to deal with constrained multiplicative processes. An excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found.

cond-mat.stat-mech↗

arXiv1996

Non-equilibrium Monte Carlo dynamics of the Sherrington-Kirkpatrick mean field spin glass model

We present a numerical study of the non-equilibrium dynamics of the Sherrington-Kirkpatrick model. We analize the overlap distribution between the configurations visited at the time t and in particular its scaling behaviour with the size of the system. We find two different non-equilibrium dynamical regimes. The first is a proper Out of Equilibrium Regime, that is the relevant regime for the dynamics of an infinite system. The second is an Intermediate Regime that separates the Out of Equilibrium Regime from equilibrium. After studying the crossover beetween the two regimes, we focus on the Out of Equilibrium Regime and we reveal some of the geometrical features of phase space. According to recent analitical work, we find that the asymptotic out of equilibrium energy density is the equilibrium one. The same happens to the staggered-magnetisation, suggesting there is a deep geometrical similarity between equilibrium and out of equilibrium configurations. A procedure, that we call clonation, shows that the dynamics follows sort of canyons, as opposed to a system of independent traps.

cond-mat↗