arXiv subjects

V. Loreto

Publications and source records attributed to V. Loreto.

30 records · Page 2Linked to original sources

arXiv1999

Entropy for relaxation dynamics in granular media

We investigate the role of entropic concepts for the relaxation dynamics in granular systems. In these systems the existence of a geometrical frustration induces a drastic modification of the allowed phase space, which in its turn induces a dynamic behavior characterized by hierarchical relaxation phenomena with several time scales associated. In particular we show how, in the framework of a mean-field model introduced for the compaction phenomenon, there exists a free-energy-like functional which decreases along the trajectories of the dynamics and which allows to account for the asymptotic behavior: e.g. density profile, segregation phenomena. Also we are able to perform the continuous limit of the above mentioned model which turns out to be a diffusive limit. In this framework one can single out two separate physical ingredients: the free-energy-like functional that defines the phase-space and the asymptotic states and a diffusion coefficient $D(ρ)$ accounting for the velocity of approach to the asymptotic stationary states.

cond-mat.stat-mech↗

arXiv1999

Self-Structuring of Granular Media under Internal Avalanches

We study the phenomenon of internal avalanching within the context of recently proposed ``Tetris'' lattice models for granular media. We define a recycling dynamics under which the system reaches a steady state which is self-structured, i.e. it shows a complex interplay between textured internal structures and critical avalanche behavior. Furthermore we develop a general mean-field theory for this class of systems and discuss possible scenarios for the breakdown of universality.

cond-mat.stat-mech↗

arXiv1998

Internal avalanches in models of granular media

We study the phenomenon of internal avalanching within the context of recently introduced lattice models of granular media. The avalanche is produced by pulling out a grain at the base of the packing and studying how many grains have to rearrange before the packing is once more stable. We find that the avalanches are long-ranged, decaying as a power-law. We study the distriution of avalanches as a function of the density of the packing and find that the avalanche distribution is a very sensitive structural probe of the system.

cond-mat.stat-mech↗

arXiv1998

Shock propagation in a granular chain

We numerically solve the propagation of a shock wave in a chain of elastic beads with no restoring forces under traction (no-tension elasticity). We find a sequence of peaks of decreasing amplitude and velocity. Analyzing the main peak at different times we confirm a recently proposed scaling law for its decay.

cond-mat.stat-mech↗

arXiv1998

A kinetic approach to granular gases

We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the result of the balance between the dissipation and the random forces which inject energies. These models exhibit a genuine thermodynamic limit, i.e. at fixed density the mean values of kinetic energy and dissipated energy per particle are independent of the number $N$ of particles, for large values of $N$. One has two regimes: when the typical relaxation time $τ$ of the driving Brownian process is small compared with the mean collision time $τ_c$ the spatial density is nearly homogeneous and the velocity probability distribution is gaussian. In the opposite limit $τ\gg τ_c$ one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the gaussian one. Simulations performed in one and two dimensions under the {\it Stosszahlansatz} Boltzmann approximation confirm the scenario. Furthermore we analyze the instabilities bringing to the spatial and the velocity clusterization. Firstly, in the framework of a mean-field model, we explain how the existence of the inelasticity can bring to a spatial clusterization; on the other side we discuss, in the framework of a Langevin dynamics treating the collisions in a mean-field way, how a non-gaussian distribution of velocity can arise. The comparison between the numerical and the analytical results exhibits an excellent agreement.

cond-mat.stat-mech↗

arXiv1998

Clustering and Non-Gaussian Behavior in Granular Matter

We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy and the energy dissipation. When the typical relaxation time $τ$ associated with the Brownian process is small compared with the mean collision time $τ_c$ the spatial density is nearly homogeneous and the velocity probability distribution is gaussian. In the opposite limit $τ\gg τ_c$ one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the gaussian one.

cond-mat.stat-mech↗

arXiv1997

A ``Tetris''-like model for the Compaction of Dry Granular Media

We propose a two-dimensional geometrical model, based on the concept of geometrical frustration, conceived for the study of compaction in granular media. The dynamics exhibits an interesting inverse logarithmic law that is well known from real experiments. Moreover we present a simple dynamical model of $N$ planes exchanging particles with excluded volume problems, which allows to clarify the origin of the logarithmic relaxations and the stationary density distribution. A simple mapping allows us to cast this Tetris-like model in the form of an Ising-like spin systems with vacancies.

cond-mat↗

arXiv1996

Earthquake statistics and fractal faults

We introduce a Self-affine Asperity Model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles (fBm) that slide one over the other. An earthquake occurs when there is an overlap of the two profiles representing the two fault faces and its energy is assumed proportional to the overlap surface. The SAM exhibits the Gutenberg-Richter law with an exponent $β$ related to the roughness index of the profiles. Apart from being analytically treatable, the model exhibits a non-trivial clustering in the spatio-temporal distribution of epicenters that strongly resembles the experimentally observed one. A generalized and more realistic version of the model exhibits the Omori scaling for the distribution of the aftershocks. The SAM lies in a different perspective with respect to usual models for seismicity. In this case, in fact, the critical behaviour is not Self-Organized but stems from the fractal geometry of the faults, which, on its turn, is supposed to arise as a consequence of geological processes on very long time scales with respect to the seismic dynamics. The explicit introduction of the fault geometry, as an active element of this complex phenomenology, represents the real novelty of our approach.

cond-mat↗

arXiv1995

Characterization of chaos in random maps

We discuss the characterization of chaotic behaviours in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter is extracted at random at each time step by considering finite dimensional approximation of the Perron-Frobenius operator

chao-dyn↗

arXiv1995

Self-affine Asperity Model for earthquakes

A model for fault dynamics consisting of two rough and rigid brownian profiles that slide one over the other is introduced. An earthquake occurs when there is an intersection between the two profiles. The energy release is proportional to the overlap interval. Our model exhibits some specific features which follow from the fractal geometry of the fault: (1) non-universality of the exponent of the Gutenberg-Richter law for the magnitude distribution; (2) presence of local stress accumulation before a large seismic event; (3) non-trivial space-time clustering of the epicenters. These properties are in good agreement with various observations and lead to specific predictions that can be experimentally tested.

cond-mat↗

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

On the concept of complexity in random dynamical systems

We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In random dynamical system, this indicator coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. The meaning of K is discussed in the context of the information theory, and it is shown that it can be determined from real experimental data. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent computed considering two nearby trajectories evolving under the same randomness. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical computations for noisy maps and sandpile models.

cond-mat↗