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Some general dynamical properties of models for compaction of granular media based on master equations are analyzed. In particular, a one-dimensional lattice model with short-ranged dynamical constraints is considered. The stationary state is consistent with Edwards theory of powders. The system is submitted to processes in which the tapping strength is monotonically increased and decreased. In such processes the behavior of the model resembles the reversible-irreversible branches which have been recently obaserved in experiments. This behavior is understood in terms of the general dynamical properties of the model, and related to the hysteresis cycles exhibited by structural glasses in thermal cycles. The existence of a normal solution, i.e., a solution of the master equation which is monotonically approached by all the other solutions, plays a fundamental role in the understanding of the hysteresis effects.
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A laser facility based on a linear image sensor with a sampling period of 100microseconds allows to investigate the dissipative dynamics of a vibrated granular matter under gravity. The laser reveals the vertical movement of an individual Zirconia-Ytria stabilized 2mm ball at the surface of a weakly excited 3D granular matter bed. The stochastic realizations are measured from the top of the container. Then, power spectra measurements reveal the different cooperative dynamics of the fluidized gap. We also carried out measurements for one steel ball and many balls in 1D and 3D systems. We fit the measured different regimes with generalized Langevin pictures. We introduce a fractional temporal operator to characterize the ensemble of dissipative particles which cannot be represented by a single Langevin particle in a complex fluid.
The granular Leidenfrost effect (B. Meerson et al, Phys. Rev. Lett. {bf 91}, 024301 (2003), P. Eshuis et al, Phys. Rev. Lett. {bf 95}, 258001 (2005)) is the levitation of a mass of granular matter when a wall below the grains is vibrated giving rise to a hot granular gas below the cluster. We find by simulation that for a range of parameters the system is bistable: the levitated cluster can occasionally break and give rise to two clusters and a hot granular gas above and below. We use techniques from the theory of rare events to compute the mean transition time for breaking to occur. This requires the introduction of a two-component reaction coordinate.
We study experimentally the particle velocity fluctuations in an electrostatically driven dilute granular gas. The experimentally obtained velocity distribution functions have strong deviations from Maxwellian form in a wide range of parameters. We have found that the tails of the distribution functions are consistent with a stretched exponential law with typical exponents of the order 3/2. Molecular dynamic simulations shows qualitative agreement with experimental data. Our results suggest that this non-Gaussian behavior is typical for most inelastic gases with both short and long range interactions.
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