Logarithmic Relaxations in a Random Field Lattice Gas Subject to Gravity

A simple lattice gas model with random fields and gravity is introduced to describe a system of grains moving in a disordered environment. Off equilibrium relaxations of bulk density and its two time correlation functions are numerically found to show logarithmic time dependences and "aging" effects. Similitudes with dry granular media are stressed. The connections with off equilibrium dynamics in others kinds of "frustrated" lattice models in presence of a directional driving force (gravity) are discussed to single out the appearance of universal features in the relaxation process.Comment: 15 pages, latex, 7 figures include

Memory effects in response functions of driven vortex matter

Vortex flow in driven type II superconductors shows strong memory and history dependent effects. Here, we study a schematic microscopic model of driven vortices to propose a scenario for a broad set of these kind of phenomena ranging from ``rejuvenation'' and ``stiffening'' of the system response, to ``memory'' and ``irreversibility'' in I-V characteristics

Aging and multiscaling in out of equilibrium dynamical processes in granular media

In the framework of recently introduced frustrated lattice gas models, we study the out of equilibrium dynamical processes during the compaction process in granular media. We find irreversible-reversible cycles in agreement with recent experimental observations. Moreover in analogy with the phenomenology of the glass transition we find aging effects during the compaction process In particular we find that the two time density correlation function $C(t,t')$ asymptotically scales as a function of the single variable $\ln(t')/\ln(t)$. This result is interpreted in terms of multiscaling properties of the system.Comment: 4 page

Dynamical response functions in models of vibrated granular media

In recently introduced schematic lattice gas models for vibrated dry granular media, we study the dynamical response of the system to small perturbations of shaking amplitudes and its relations with the characteristic fluctuations. Strong off equilibrium features appear and a generalized version of the fluctuation dissipation theorem is introduced. The relations with thermal glassy systems and the role of Edwards' compactivity are discussed.Comment: 12 pages, 2 postscript figure

A cellular automaton for the factor of safety field in landslides modeling

Landslide inventories show that the statistical distribution of the area of recorded events is well described by a power law over a range of decades. To understand these distributions, we consider a cellular automaton to model a time and position dependent factor of safety. The model is able to reproduce the complex structure of landslide distribution, as experimentally reported. In particular, we investigate the role of the rate of change of the system dynamical variables, induced by an external drive, on landslide modeling and its implications on hazard assessment. As the rate is increased, the model has a crossover from a critical regime with power-laws to non power-law behaviors. We suggest that the detection of patterns of correlated domains in monitored regions can be crucial to identify the response of the system to perturbations, i.e., for hazard assessment.Comment: 4 pages, 3 figure

The jamming transition of Granular Media

We briefly review the basics ideas and results of a recently proposed statistical mechanical approach to granular materials. Using lattice models from standard Statistical Mechanics and results from a mean field replica approach and Monte Carlo simulations we find a jamming transition in granular media closely related to the glass transition in super-cooled liquids. These models reproduce the logarithmic relaxation in granular compaction and reversible-irreversible lines, in agreement with experimental data. The models also exhibit aging effects and breakdown of the usual fluctuation dissipation relation. It is shown that the glass transition may be responsible for the logarithmic relaxation and may be related to the cooperative effects underlying many phenomena of granular materials such as the Reynolds transition.Comment: 18 pages with 6 postscript figures. to appear in J.Phys: Cond. Ma

Off equilibrium magnetic properties in a model for vortices in superconductors

We study the properties of a simple lattice model of repulsive particles diffusing in a pinning landscape. The behaviour of the model is very similar to the observed physics of vortices in superconductors. We compare and discuss the equilibrium phase diagram, creep dynamics, the Bean state profiles, hysteresis of magnetisation loops (including the second peak feature), and, in particular, ``off equilibrium'' relaxations. The model is analytically tractable in replica mean field theory and numerically via Monte Carlo simulations. It offers a comprehensive schematic framework of the observed phenomenology

Aging and memory phenomena in magnetic and transport properties of vortex matter: a brief review

There is mounting experimental evidence that strong off-equilibrium phenomena, such as ``memory'' or ``aging'' effects, play a crucial role in the physics of vortices in type II superconductors. We give a short review, based on a recently introduced schematic vortex model, of current progresses in understanding out of equilibrium vortex behaviours. We develop a unified description of ``memory'' phenomena in magnetic and transport properties, such as magnetisation loops and their ``anomalous'' 2nd peak, logarithmic creep, ``anomalous'' finite creep rate in the limit of vanishing temperature, ``memory'' and ``irreversibility'' in I-V characteristics, time dependent critical currents, ``rejuvenation'' and ``aging'' of the system response.Comment: updated versio

Two-phase densification of cohesive granular aggregates

When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressed upon with a ram, these aggregates densify by particle rearrangement. Here we introduce experimental evidence to the effect that particle rearrangement is a spatially heterogeneous phenomenon, which occurs in the form of a phase transformation between two configurational phases of the granular aggregate. We then show that the energy landscape associated with particle rearrangement is consistent with our interpretation of the experimental results. Besides affording insight into the physics of the granular state, our conclusions are relevant to many engineering processes and natural phenomena.Comment: 7 pages, 3 figure

Dynamics and thermodynamics of the spherical frustrated Blume-Emery-Griffiths model

We introduce a spherical version of the frustrated Blume-Emery-Griffiths model and solve exactly the statics and the Langevin dynamics for zero particle-particle coupling (K=0). In this case the model exhibits an equilibrium transition from a disordered to a spin glass phase which is always continuous for nonzero temperature. The same phase diagram results from the study of the dynamics. Furthermore, we notice the existence of a nonequilibrium time regime in a region of the disordered phase, characterized by aging as occurs in the spin glass phase. Due to a finite equilibration time, the system displays in this region the pattern of interrupted aging.Comment: 19 pages, 8 figure