The spontaneous symmetry breaking in a vibro-fluidized low-density granular gas in three connected compartments is investigated. When the total number of particles in the system becomes large enough, particles distribute themselves unequally among the three compartments. Particles tend to concentrate in one of the compartments, the other two having the (relatively small) same average number of particles. A hydrodynamical model that accurately predicts the bifurcation diagram of the system is presented. The theory can be easily extended to the case of an arbitrary number of connected compartments.
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.
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.
A granular gas may be modeled as a set of hard-spheres undergoing inelastic collisions; its microscopic dynamics is thus strongly irreversible. As pointed out in several experimental works bearing on turbulent flows or granular materials, the power injected in a dissipative system to sustain a steady-state over an asymptotically large time window is a central observable. We describe an analytic approach allowing us to determine the full distribution of the power injected in a granular gas within a steady-state resulting from subjecting each particle independently either to a random force (stochastic thermostat) or to a deterministic force proportional to its velocity (Gaussian thermostat). We provide an analysis of our results in the light of the relevance, for other types of systems, of the injected power to fluctuation relations.
We consider a dilute gas of inelastic hard spheres enclosed in a slab under the action of gravity along the longitudinal direction. In addition, the gas is subject to a white-noise stochastic force that mimics the effect of external vibrations customarily used in experiments to compensate for the collisional cooling. The system is described by means of a kinetic model of the inelastic Boltzmann equation and its steady-state solution is derived through second order in gravity. This solution differs from the Navier-Stokes description in that the hydrostatic pressure is not uniform, normal stress differences are present, a component of the heat flux normal to the thermal gradient exists, and the temperature profile includes a positive quadratic term. As in the elastic case, this new term is responsible for a bimodal shape of the temperature profile. The results show that, except for high inelasticities, the effect of inelasticity on the profiles is to slightly decrease the quantitative deviations from the Navier-Stokes results.
The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anti-correlation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the plate.
J. Javier Brey
,R. Garcia-Rojo
,F. Moreno
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(2007)
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"Symmetry breaking and clustering in a vibrated granular gas with several macroscopically connected compartments"
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Maria J. Ruiz-Montero
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