621 research outputs found

### Simulated three-component granular segregation in a rotating drum

Discrete particle simulations are used to model segregation in granular
mixtures of three different particle species in a horizontal rotating drum.
Axial band formation is observed, with medium-size particles tending to be
located between alternating bands of big and small particles. Partial radial
segregation also appears; it precedes the axial segregation and is
characterized by an inner core region richer in small particles. Axial bands
are seen to merge during the long simulation runs, leading to a coarsening of
the band pattern; the relocation of particles involved in one such merging
event is examined. Overall, the behavior is similar to experiment and
represents a generalization of what occurs in the simpler two-component
mixture.Comment: 7 pages, 11 figures (low resolution color figures only; originals at
author's website http://www.ph.biu.ac.il/~rapaport/research/granular.html)
[revised version contains extra figures

### Granular Packings: Nonlinear elasticity, sound propagation and collective relaxation dynamics

Experiments on isotropic compression of a granular assembly of spheres show
that the shear and bulk moduli vary with the confining pressure faster than the
1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of
contact elasticity. Moreover, the ratio between the moduli is found to be
larger than the prediction of the elastic theory by a constant value. The
understanding of these discrepancies has been a longstanding question in the
field of granular matter. Here we perform a test of the applicability of
elasticity theory to granular materials. We perform sound propagation
experiments, numerical simulations and theoretical studies to understand the
elastic response of a deforming granular assembly of soft spheres under
isotropic loading. Our results for the behavior of the elastic moduli of the
system agree very well with experiments. We show that the elasticity partially
describes the experimental and numerical results for a system under
compressional loads. However, it drastically fails for systems under shear
perturbations, particularly for packings without tangential forces and
friction. Our work indicates that a correct treatment should include not only
the purely elastic response but also collective relaxation mechanisms related
to structural disorder and nonaffine motion of grains.Comment: 21 pages, 13 figure

### Rheology and Contact Lifetime Distribution in Dense Granular Flows

We study the rheology and distribution of interparticle contact lifetimes for
gravity-driven, dense granular flows of non-cohesive particles down an inclined
plane using large-scale, three dimensional, granular dynamics simulations.
Rather than observing a large number of long-lived contacts as might be
expected for dense flows, brief binary collisions predominate. In the hard
particle limit, the rheology conforms to Bagnold scaling, where the shear
stress is quadratic in the strain rate. As the particles are made softer,
however, we find significant deviations from Bagnold rheology; the material
flows more like a viscous fluid. We attribute this change in the collective
rheology of the material to subtle changes in the contact lifetime distribution
involving the increasing lifetime and number of the long-lived contacts in the
softer particle systems.Comment: 4 page

### Scale separation in granular packings: stress plateaus and fluctuations

It is demonstrated, by numerical simulations of a 2D assembly of polydisperse
disks, that there exists a range (plateau) of coarse graining scales for which
the stress tensor field in a granular solid is nearly resolution independent,
thereby enabling an `objective' definition of this field. Expectedly, it is not
the mere size of the the system but the (related) magnitudes of the gradients
that determine the widths of the plateaus. Ensemble averaging (even over
`small' ensembles) extends the widths of the plateaus to sub-particle scales.
The fluctuations within the ensemble are studied as well. Both the response to
homogeneous forcing and to an external compressive localized load (and gravity)
are studied. Implications to small solid systems and constitutive relations are
briefly discussed.Comment: 4 pages, 4 figures, RevTeX 4, Minor corrections to match the
published versio

### Effective boundary conditions for dense granular flows

We derive an effective boundary condition for granular flow taking into
account the effect of the heterogeneity of the force network on sliding
friction dynamics. This yields an intermediate boundary condition which lies in
the limit between no-slip and Coulomb friction; two simple functions relating
wall stress, velocity, and velocity variance are found from numerical
simulations. Moreover, we show that this effective boundary condition
corresponds to Navier slip condition when GDR MiDi's model is assumed to be
valid, and that the slip length depends on the length scale that characterises
the system, \emph{viz} the particle diameter.Comment: 4 pages, 5 figure

### Coefficient of tangential restitution for the linear dashpot model

The linear dashpot model for the inelastic normal force between colliding
spheres leads to a constant coefficient of normal restitution,
$\epsilon_n=$const., which makes this model very popular for the investigation
of dilute and moderately dense granular systems. For two frequently used models
for the tangential interaction force we determine the coefficient of tangential
restitution $\epsilon_t$, both analytically and by numerical integration of
Newton's equation. Although $\epsilon_n=$const. for the linear-dashpot model,
we obtain pronounced and characteristic dependencies of the tangential
coefficient on the impact velocity $\epsilon_t=\epsilon_t(\vec{g})$. The
results may be used for event-driven simulations of granular systems of
frictional particles.Comment: 12 pages, 12 figure

### Measurements of the Yield Stress in Frictionless Granular Systems

We perform extensive molecular dynamics simulations of 2D frictionless
granular materials to determine whether these systems can be characterized by a
single static yield shear stress. We consider boundary-driven planar shear at
constant volume and either constant shear force or constant shear velocity.
Under steady flow conditions, these two ensembles give similar results for the
average shear stress versus shear velocity. However, near jamming it is
possible that the shear stress required to initiate shear flow can differ
substantially from the shear stress required to maintain flow. We perform
several measurements of the shear stress near the initiation and cessation of
flow. At fixed shear velocity, we measure the average shear stress
$\Sigma_{yv}$ in the limit of zero shear velocity. At fixed shear force, we
measure the minimum shear stress $\Sigma_{yf}$ required to maintain steady flow
at long times. We find that in finite-size systems $\Sigma_{yf} > \Sigma_{yv}$,
which implies that there is a jump discontinuity in the shear velocity from
zero to a finite value when these systems begin flowing at constant shear
force. However, our simulations show that the difference $\Sigma_{yf} -
\Sigma_{yv}$, and thus the discontinuity in the shear velocity, tend to zero in
the infinite system size limit. Thus, our results indicate that in the large
system limit, frictionless granular systems are characterized by a single
static yield shear stress. We also monitor the short-time response of these
systems to applied shear and show that the packing fraction of the system and
shape of the velocity profile can strongly influence whether or not the shear
stress at short times overshoots the long-time average value.Comment: 7 pages and 6 figure

### Piling and avalanches of magnetized particles

We performed computer simulations based on a two-dimensional Distinct Element
Method to study granular systems of magnetized spherical particles. We measured
the angle of repose and the surface roughness of particle piles, and we studied
the effect of magnetization on avalanching. We report linear dependence of both
angle of repose and surface roughness on the ratio $f$ of the magnetic dipole
interaction and the gravitational force (\emph{interparticle force ratio}).
There is a difference in avalanche formation at small and at large
interparticle force ratios. The transition is at $f_c \approx 7$. For $f < f_c$
the particles forming the avalanches leave the system in a quasi-continuous
granular flow (\emph{granular regime}), while for $f > f_c$ the avalanches are
formed by long particle clusters (\emph{correlated regime}). The transition is
not sharp. We give plausible estimates for $f_c$ based on stability criteria.Comment: 9 pages, 7 figure

### Microscopic origin of granular ratcheting

Numerical simulations of assemblies of grains under cyclic loading exhibit
``granular ratcheting'': a small net deformation occurs with each cycle,
leading to a linear accumulation of deformation with cycle number. We show that
this is due to a curious property of the most frequently used models of the
particle-particle interaction: namely, that the potential energy stored in
contacts is path-dependent. There exist closed paths that change the stored
energy, even if the particles remain in contact and do not slide. An
alternative method for calculating the tangential force removes granular
ratcheting.Comment: 13 pages, 18 figure

### Phase transition in inelastic disks

This letter investigates the molecular dynamics of inelastic disks without
external forcing. By introducing a new observation frame with a rescaled time,
we observe the virtual steady states converted from asymptotic energy
dissipation processes. System behavior in the thermodynamic limit is carefully
investigated. It is found that a phase transition with symmetry breaking occurs
when the magnitude of dissipation is greater than a critical value.Comment: 9 pages, 6 figure

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