Minimal model for avalanches in granular systems

Enstrophy cascades in two-dimensional dense granular flows

Employing two-dimensional molecular dynamics simulations of dense granular materials under simple shear deformations, we investigate vortex structures of particle rearrangements. Introducing vorticity fields as a measure of local spinning motions of the particles, we observe their heterogeneous distributions, where statistics of vorticity fields exhibit the highly non-Gaussian behavior and typical domain sizes of vorticity fields significantly increase if the system is yielding under quasistatic deformations. In such dense granular flows, a power-law decay of vorticity spectra can be observed at mesoscopic scale, implying anomalous local structures of kinetic energy dissipation. We explain the power-law decay, or enstrophy cascades in dense granular materials, by a dimensional analysis, where the dependence of vorticity spectra not only on the wave number, but also on the shear rate, is well explained. From our dimensional analyses, the scaling of granular temperature and rotational kinetic energy is also predicted.

Dynamics of dry granular avalanches

A fine analysis of the statistics of dry granular avalanches in a rotating drum setup reveals that, beyond the fluctuations, the angle at which an avalanche ends is correlated experimentally to the angle at which the avalanche starts. This correlation resulting from inertia defines an intermediate "neutral" angle that characterizes the corresponding granular pile. In addition, an intensive study of the dynamics of the avalanche shows that the time duration of the avalanche is correlated to its amplitude, being smaller for higher amplitude. The time relaxation of the pile slope during any avalanche, governed by the deviation of the starting angle from the neutral angle, follows a master curve. A simple model recovers most of the results and contributes to a better understanding of the physics of the avalanche flow.

Stress in frictionless granular material: adaptive network simulations

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent theories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about 0.6 of the normal loading. The spatial distribution of contact forces shows strong concentration along "force chains." The probability of contact forces of magnitude f shows an exponential falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally.

Hysteretic transition between avalanches and continuous flow in rotated granular systems

Experiments in drums or cylinders partly filled with a granular system and rotated constantly about their horizontally aligned axis of symmetry show a hysteretic transition from discrete avalanches to continuous flow if the rotation rate is adiabatically changed. Herein, we show that this hysteresis can be explained by the impact of global Langevin-type fluctuations in a recently proposed minimal model for surface flow along granular piles. For too large magnitudes of the fluctuations corresponding to almost elastic grains, the hysteresis vanishes. This might explain why molecular dynamical simulations were not yet able to detect the hysteretic transition. (c) 1999 American Institute of Physics.

Bethe lattice representation for sandpiles

Avalanches in sandpiles are represented by a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches provide a better resemblance to the experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments performed by different authors are reconciled. Critical behavior is expressed here by the critical properties of percolation phenomena.