Slow logarithmic relaxation in models with hierarchically constrained dynamics.

A general kind of model with hierarchically constrained dynamics is shown to exhibit logarithmic anomalous relaxation similar to a variety of complex strongly interacting materials. The logarithmic behavior describes most of the decay of the response function.

Glasslike dynamical behavior in hierarchical models submitted to continuous cooling and heating processes.

The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature processes. In cooling processes, a phenomenon analogous to the laboratory glass transition appears. The residual properties are analytically evaluated, and the concept of fictive temperature is discussed on a physical basis. The evolution of the system in heating processes is governed by the existence of a normal solution of the evolution equations, which is approached by all the other solutions. This trend of the system is directly related to the glassy hysteresis effects shown by these systems. The existence of the normal solution is not restricted to the linear regime around equilibrium, but it is defined for any arbitrary, far-from-equilibrium, situation.

Linear response of vibrated granular systems to sudden changes in the vibration intensity.

The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of "anomalous" and "normal" responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this paper and previous studies is discussed.

Hydrodynamics of an open vibrated granular system.

Using the hydrodynamic description and molecular dynamics simulations, the steady state of a fluidized granular system in the presence of gravity is studied. For an open system, the density profile exhibits a maximum, while the temperature profile goes through a minimum at high altitude, beyond that the temperature increases with the height. The existence of the minimum is explained by the hydrodynamic equations if the presence of a collisionless boundary layer is taken into account. The energy dissipated by interparticle collisions is also computed. A good agreement is found between theory and simulation. The relationship with previous works is discussed.

Origin of density clustering in a freely evolving granular gas.

The physical mechanisms leading to the development of density inhomogeneities in a freely evolving low density granular gas are investigated. By means of the direct simulation Monte Carlo method, numerical solutions of the inelastic Boltzmann equation are constructed for both a perturbed system and also for an initially homogeneous state. Analysis of the Fourier components of the fields indicates that the nonlinear coupling contributions of the transversal velocity play a crucial role in the initial setup of clustering. A simple hydrodynamic model is proposed to describe what is observed in the simulations. Finally, the nature of the inhomogeneous state is briefly discussed.

Simple model with facilitated dynamics for granular compaction.

A simple lattice model is used to study compaction in granular media. As in real experiments, we consider a series of taps separated by large enough waiting times. The relaxation of the density exhibits the characteristic inverse logarithmic law. Moreover, we have been able to identify analytically the relevant time scale, leading to a relaxation law independent of the specific values of the parameters. Also, an expression for the asymptotic density reached in the compaction process has been derived. The theoretical predictions agree fairly well with the results from the Monte Carlo simulation.

Brownian motion in a granular gas.

The dynamics of a heavy particle in a gas of much lighter particles is studied via the Boltzmann-Lorentz equation with inelastic collisions among all particles. A formal expansion in the ratio of gas to tagged particle mass transforms the Boltzmann-Lorentz equation into a Fokker Planck equation. The predictions of the latter are tested here using direct Monte Carlo simulation of the Boltzmann-Lorentz equation. Excellent agreement is obtained for the approach to a homogeneous cooling state, the temperature of that state, approach to diffusion, and the dependence of the diffusion constant on dissipation parameters. Some results from molecular-dynamics simulations are also presented and shown to agree with the theoretical predictions.