Density Waves in Granular Flow: A Kinetic Wave Approach

It was recently observed that sand flowing down a vertical tube sometimes forms a traveling density pattern in which a number of regions with high density are separated from each other by regions of low density. In this work, we consider this behavior from the point of view of kinetic wave theory. Similar density patterns are found in molecular dynamic simulations of the system, and a well defined relationship is observed between local flux and local density -- a strong indicator of the presence of kinetic waves. The equations of motion for this system are also presented, and they allow kinetic wave solutions. Finally, the pattern formation process is investigated using a simple model of interacting kinetic waves.Comment: RevTeX, HLRZ preprint 46/93, 4 figures available upon reques

A Model for the Propagation of Sound in Granular Materials

This paper presents a simple ball-and-spring model for the propagation of small amplitude vibrations in a granular material. In this model, the positional disorder in the sample is ignored and the particles are placed on the vertices of a square lattice. The inter-particle forces are modeled as linear springs, with the only disorder in the system coming from a random distribution of spring constants. Despite its apparent simplicity, this model is able to reproduce the complex frequency response seen in measurements of sound propagation in a granular system. In order to understand this behavior, the role of the resonance modes of the system is investigated. Finally, this simple model is generalized to include relaxation behavior in the force network -- a behavior which is also seen in real granular materials. This model gives quantitative agreement with experimental observations of relaxation.Comment: 21 pages, requires Harvard macros (9/91), 12 postscript figures not included, HLRZ preprint 6/93, (replacement has proper references included

Asymptotic behavior of the density of states on a random lattice

We study the diffusion of a particle on a random lattice with fluctuating local connectivity of average value q. This model is a basic description of relaxation processes in random media with geometrical defects. We analyze here the asymptotic behavior of the eigenvalue distribution for the Laplacian operator. We found that the localized states outside the mobility band and observed by Biroli and Monasson (1999, J. Phys. A: Math. Gen. 32 L255), in a previous numerical analysis, are described by saddle point solutions that breaks the rotational symmetry of the main action in the real space. The density of states is characterized asymptotically by a series of peaks with periodicity 1/q.Comment: 11 pages, 2 figure

Force Distribution in a Granular Medium

We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of monodisperse glass beads show that this distribution is nearly uniform for forces below the mean force and decays exponentially for forces greater than the mean. The shape of the distribution and the value of the exponential decay constant are unaffected by changes in the system preparation history or in the boundary conditions. An empirical functional form for the distribution is proposed that provides an excellent fit over the whole force range measured and is also consistent with recent computer simulation data.Comment: 6 pages. For more information, see http://mrsec.uchicago.edu/granula

Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations

The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the wavelength of the sollicitation is smaller than a characteristic length of approximately 30 molecular sizes. Due to this surprisingly large effect ensembles containing up to N=40,000 particles have been required in two dimensions to yield a convincing match with the classical continuum predictions for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk systems. The existence of an effective length scale \xi is confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the {\em non-affine} part of the displacement fields under imposed elongation and shear. Similar correlations (vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table

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

Power-Laws in Nonlinear Granular Chain under Gravity

The signal generated by a weak impulse propagates in an oscillatory way and dispersively in a gravitationally compacted granular chain. For the power-law type contact force, we show analytically that the type of dispersion follows power-laws in depth. The power-law for grain displacement signal is given by $h^{-1/4(1-1/p)}$ where $h$ and $p$ denote depth and the exponent of contact force, and the power-law for the grain velocity is $h^{-1/4({1/3}+1/p)}$. Other depth-dependent power-laws for oscillation frequency, wavelength, and period are given by combining above two and the phase velocity power-law $h^{1/2(1-1/p)}$. We verify above power-laws by comparing with the data obtained by numerical simulations.Comment: 12 pages, 3 figures; Changed conten