73 research outputs found
A 2-D asymmetric exclusion model for granular flows
A 2-D version of the asymmetric exclusion model for granular sheared flows is
presented. The velocity profile exhibits two qualitatively different behaviors,
dependent on control parameters. For low friction, the velocity profile follows
an exponential decay while for large friction the profile is more accurately
represented by a Gaussian law. The phase transition occurring between these two
behavior is identified by the appearance of correlations in the cluster size
distribution. Finally, a mean--field theory gives qualitative and quantitative
good agreement with the numerical results.Comment: 13 pages, 5 figures; typos added, one definition change
Pre-avalanche instabilities in a granular pile
We investigate numerically the transition between static equilibrium and
dynamic surface flow of a 2D cohesionless granular system driven by a
continuous gravity loading. This transition is characterized by intermittent
local dynamic rearrangements and can be described by an order parameter defined
as the density of critical contacts, e.g. contacts where the friction is fully
mobilized. Analysis of the spatial correlations of critical contacts shows the
occurence of ``fluidized'' clusters which exhibit a power-law divergence in
size at the approach of the stability limit. The results are compatible with
recent models that describe the granular system during the static/dynamic
transition as a multi-phase system.Comment: 9 pages, 6 figures, submitted to Phys. Rev. Let
Statistical Mechanics of Stress Transmission in Disordered Granular Arrays
We give a statistical-mechanical theory of stress transmission in disordered
arrays of rigid grains with perfect friction. Starting from the equations of
microscopic force and torque balance we derive the fundamental equations of
stress equilibrium. We illustrate the validity of our approach by solving the
stress distribution of a homogeneous and isotropic array.Comment: 4 pages, to be published in PR
Creep motion in a granular pile exhibiting steady surface flow
We investigate experimentally granular piles exhibiting steady surface flow.
Below the surface flow, it has been believed exisitence of a `frozen' bulk
region, but our results show absence of such a frozen bulk. We report here that
even the particles in deep layers in the bulk exhibit very slow flow and that
such motion can be detected at an arbitrary depth. The mean velocity of the
creep motion decays exponentially with depth, and the characteristic decay
length is approximately equal to the particle-size and independent of the flow
rate. It is expected that the creep motion we have seeen is observable in all
sheared granular systems.Comment: 3 pages, 4 figure
Strain versus stress in a model granular material: a Devil's staircase
The series of equilibrium states reached by disordered packings of rigid,
frictionless discs in two dimensions, under gradually varying stress, are
studied by numerical simulations. Statistical properties of trajectories in
configuration space are found to be independent of specific assumptions ruling
granular dynamics, and determined by geometry only. A monotonic increase in
some macroscopic loading parameter causes a discrete sequence of
rearrangements. For a biaxial compression, we show that, due to the statistical
importance of such events of large magnitudes, the dependence of the resulting
strain on stress direction is a Levy flight in the thermodynamic limit.Comment: REVTeX, 4 pages, 5 included PostScript figures. New version altered
throughout text, very close to published pape
Granular Rheology in Zero Gravity
We present an experimental investigation on the rheological behavior of model
granular media made of nearly elastic spherical particles. The experiments are
performed in a cylindrical Couette geometry and the experimental device is
placed inside an airplane undergoing parabolic flights to cancel the effect of
gravity. The corresponding curves, shear stress versus shear rate, are
presented and a comparison with existing theories is proposed. The quadratic
dependence on the shear rate is clearly shown and the behavior as a function of
the solid volume fraction of particles exhibits a power law function. It is
shown that theoretical predictions overestimate the experiments. We observe, at
intermediate volume fractions, the formation of rings of particles regularly
spaced along the height of the cell. The differences observed between
experimental results and theoretical predictions are discussed and related to
the structures formed in the granular medium submitted to the external shear.Comment: 10 pages, 6 figures to be published in Journal of Physics : Condensed
Matte
Deformation and flow of a two-dimensional foam under continuous shear
We investigate the flow properties of a two-dimensional aqueous foam
submitted to a quasistatic shear in a Couette geometry. A strong localization
of the flow (shear banding) at the edge of the moving wall is evidenced,
characterized by an exponential decay of the average tangential velocity.
Moreover, the analysis of the rapid velocity fluctuations reveals self-similar
dynamical structures consisting of clusters of bubbles rolling as rigid bodies.
To relate the instantaneous (elastic) and time-averaged (plastic) components of
the strain, we develop a stochastic model where irreversible rearrangements are
activated by local stress fluctuations originating from the rubbing of the
wall. This model gives a complete description of our observations and is also
consistent with data obtained on granular shear bands by other groups.Comment: 5 pages, 2 figure
Packing of Compressible Granular Materials
3D Computer simulations and experiments are employed to study random packings
of compressible spherical grains under external confining stress. Of particular
interest is the rigid ball limit, which we describe as a continuous transition
in which the applied stress vanishes as (\phi-\phi_c)^\beta, where \phi is the
(solid phase) volume density. This transition coincides with the onset of shear
rigidity. The value of \phi_c depends, for example, on whether the grains
interact via only normal forces (giving rise to random close packings) or by a
combination of normal and friction generated transverse forces (producing
random loose packings). In both cases, near the transition, the system's
response is controlled by localized force chains. As the stress increases, we
characterize the system's evolution in terms of (1) the participation number,
(2) the average force distribution, and (3) visualization techniques.Comment: 4 pages, 7 figures, to appear in Phys. Rev. Let
Density of states in random lattices with translational invariance
We propose a random matrix approach to describe vibrational excitations in
disordered systems. The dynamical matrix M is taken in the form M=AA^T where A
is some real (not generally symmetric) random matrix. It guaranties that M is a
positive definite matrix which is necessary for mechanical stability of the
system. We built matrix A on a simple cubic lattice with translational
invariance and interaction between nearest neighbors. We found that for certain
type of disorder phonons cannot propagate through the lattice and the density
of states g(w) is a constant at small w. The reason is a breakdown of affine
assumptions and inapplicability of the elasticity theory. Young modulus goes to
zero in the thermodynamic limit. It strongly reminds of the properties of a
granular matter at the jamming transition point. Most of the vibrations are
delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil.
Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure
Cooperativity in sandpiles: statistics of bridge geometries
Bridges form dynamically in granular media as a result of spatiotemporal
inhomogeneities. We classify bridges as linear and complex, and analyse their
geometrical characteristics. In particular, we find that the length
distribution of linear bridges is exponential. We then turn to the analysis of
the orientational distribution of linear bridges and find that, in three
dimensions, they are {\it vertically diffusive but horizontally
superdiffusive}; thus, when they exist, long linear bridges form `domes'. Our
results are in good accord with Monte Carlo simulations of bridge structure; we
make predictions for quantities that are experimentally accessible, and suggest
that bridges are very closely related to force chains.Comment: 15 pages, 10 figures. Minor changes and update
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