Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales are explicitly considered: i) the Stokes time, accounting for the inertia of the particles, ii) the mean collision time among the grains, iii) the typical time scale of the flow, and iv) the inverse of the Lyapunov exponent of the chaotic flow, which gives a typical time for the separation of two initially close parcels of fluid. Depending on the relative values of these different times a complex scenario appears for the long-time steady spatial distribution of particles, where clusters of particles may or not appear.Comment: 4 pages, 3 figure

Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime

We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity $\omega$, the system undergoes a hysteresis cycle between an intermittent and a continuous flow regimes. In the intermittent flow regime, and approaching the transition, the avalanche duration exhibits critical slowing down with a temporal power-law divergence. Upon adding a white noise term, and close to the transition, the distribution of avalanche durations is also a power-law. The hysteresis, as well as the statistics of avalanche durations, are in good qualitative agreement with recent experiments in partly filled rotating cylinders.Comment: 4 pages, RevTeX 3.0, postscript figures 1, 3 and 4 appended

Generation of Porous Particle Structures using the Void Expansion Method

The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller "void-particles". Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles' mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure

Projectile-shape dependence of impact craters in loose granular media

We report on the penetration of cylindrical projectiles dropped from rest into a dry, noncohesive granular medium. The cylinder length, diameter, density, and tip shape are all explicitly varied. For deep penetrations, as compared to the cylinder diameter, the data collapse onto a single scaling law that varies as the 1/3 power of the total drop distance, the 1/2 power of cylinder length, and the 1/6 power of cylinder diameter. For shallow penetrations, the projectile shape plays a crucial role with sharper objects penetrating deeper.Comment: 3 pages, 3 figures; experimen

A Model for Granular Texture with Steric Exclusion

We propose a new method to characterize the geometrical texture of a granular packing at the particle scale including the steric hindrance effect. This method is based on the assumption of a maximum disorder (entropy) compatible both with strain-induced anisotropy of the contact network and steric exclusions. We show that the predicted statistics for the local configurations is in a fairly agreement with our numerical data.Comment: 9 pages, 5 figure

Slow relaxation in granular compaction

Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as $N=\rho/(1-\rho)$, and the density increase rate is drastically reduced by a factor $e^{-N}$. Consequently, a logarithmically slow approach to the final state is found $\rho_{\infty}-\rho(t)\cong 1/\ln t$.Comment: revtex, 4 pages, 3 figures, also available from http://arnold.uchicago.edu/~ebn

Velocity Fluctuations in Electrostatically Driven Granular Media

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.Comment: 4 pages, 4 figure

Density waves in dry granular media falling through a vertical pipe

We report experimental measurements of density waves in granular materials flowing down in a capillary tube. The density wave regime occurs at intermediate flow rates between a low density free fall regime and a high compactness slower flow.Comment: LaTeX file, 17 pages, 6 EPS figures, Phys.Rev.E (Feb.1996

Symmetry-breaking instability in a prototypical driven granular gas

Symmetry-breaking instability of a laterally uniform granular cluster (strip state) in a prototypical driven granular gas is investigated. The system consists of smooth hard disks in a two-dimensional box, colliding inelastically with each other and driven, at zero gravity, by a "thermal" wall. The limit of nearly elastic particle collisions is considered, and granular hydrodynamics with the Jenkins-Richman constitutive relations is employed. The hydrodynamic problem is completely described by two scaled parameters and the aspect ratio of the box. Marginal stability analysis predicts a spontaneous symmetry breaking instability of the strip state, similar to that predicted recently for a different set of constitutive relations. If the system is big enough, the marginal stability curve becomes independent of the details of the boundary condition at the driving wall. In this regime, the density perturbation is exponentially localized at the elastic wall opposite to the thermal wall. The short- and long-wavelength asymptotics of the marginal stability curves are obtained analytically in the dilute limit. The physics of the symmetry-breaking instability is discussed.Comment: 11 pages, 14 figure

Velocity correlations in dense granular gases

We report the statistical properties of spherical steel particles rolling on an inclined surface being driven by an oscillating wall. Strong dissipation occurs due to collisions between the particles and rolling and can be tuned by changing the number density. The velocities of the particles are observed to be correlated over large distances comparable to the system size. The distribution of velocities deviates strongly from a Gaussian. The degree of the deviation, as measured by the kurtosis of the distribution, is observed to be as much as four times the value corresponding to a Gaussian, signaling a significant breakdown of the assumption of negligible velocity correlations in a granular system.Comment: 4 pages, 4 Figure