1,294 research outputs found
Temporally heterogeneous dynamics in granular flows
Granular simulations are used to probe the particle scale dynamics at short,
intermediate, and long time scales for gravity driven, dense granular flows
down an inclined plane. On approach to the angle of repose, where motion
ceases, the dynamics become intermittent over intermediate times, with strong
temporal correlations between particle motions -- temporally heterogeneous
dynamics. This intermittency is characterised through large scale structural
events whereby the contact network periodically spans the system. A
characteristic time scale associated with these processes increases as the
stopped state is approached. These features are discussed in the context of the
dynamics of supercooled liquids near the glass transition.Comment: Under review PRL, 4 pages + 9 .eps figure
Confined granular packings: structure, stress, and forces
The structure and stresses of static granular packs in cylindrical containers
are studied using large-scale discrete element molecular dynamics simulations
in three dimensions. We generate packings by both pouring and sedimentation and
examine how the final state depends on the method of construction. The vertical
stress becomes depth-independent for deep piles and we compare these stress
depth-profiles to the classical Janssen theory. The majority of the tangential
forces for particle-wall contacts are found to be close to the Coulomb failure
criterion, in agreement with the theory of Janssen, while particle-particle
contacts in the bulk are far from the Coulomb criterion. In addition, we show
that a linear hydrostatic-like region at the top of the packings unexplained by
the Janssen theory arises because most of the particle-wall tangential forces
in this region are far from the Coulomb yield criterion. The distributions of
particle-particle and particle-wall contact forces exhibit
exponential-like decay at large forces in agreement with previous studies.Comment: 11 pages, 11 figures, submitted to PRE (v2) added new references,
fixed typo
Granular flow down a rough inclined plane: transition between thin and thick piles
The rheology of granular particles in an inclined plane geometry is studied
using molecular dynamics simulations. The flow--no-flow boundary is determined
for piles of varying heights over a range of inclination angles . Three
angles determine the phase diagram: , the angle of repose, is the
angle at which a flowing system comes to rest; , the maximum angle
of stability, is the inclination required to induce flow in a static system;
and is the maximum angle for which stable, steady state flow is
observed. In the stable flow region , three
flow regimes can be distinguished that depend on how close is to
: i) : Bagnold rheology, characterized by a
mean particle velocity in the direction of flow that scales as
, for a pile of height , ii)
: the slow flow regime, characterized by a linear
velocity profile with depth, and iii) : avalanche flow
characterized by a slow underlying creep motion combined with occasional free
surface events and large energy fluctuations. We also probe the physics of the
initiation and cessation of flow. The results are compared to several recent
experimental studies on chute flows and suggest that differences between
measured velocity profiles in these experiments may simply be a consequence of
how far the system is from jamming.Comment: 19 pages, 14 figs, submitted to Physics of Fluid
Velocity correlations in dense granular flows
Velocity fluctuations of grains flowing down a rough inclined plane are
experimentally studied. The grains at the free surface exhibit fluctuating
motions, which are correlated over few grains diameters. The characteristic
correlation length is shown to depend on the inclination of the plane and not
on the thickness of the flowing layer. This result strongly supports the idea
that dense granular flows are controlled by a characteristic length larger than
the particle diameter
Isostaticity in two dimensional pile of rigid disks
We study the static structure of piles made of polydisperse disks in the
rigid limit with and without friction using molecular dynamic simulations for
various elasticities of the disks and pile preparation procedures. The
coordination numbers are calculated to examine the isostaticity of the pile
structure. For the frictionless pile, it is demonstrated that the coordination
number converges to 4 in the rigid limit, which implies that the structure of
rigid disk pile is isostatic. On the other hand, for the frictional case with
the infinite friction constant, the coordination number depends on the
preparation procedure of the pile, but we find that the structure becomes very
close to isostatic with the coordination number close to 3 in the rigid limit
when the pile is formed through the process that tends to make a pile of random
configuration.Comment: 3 pages, 3 figures, Submitted to J. Phys. Soc. Jp
Normal Modes in Model Jammed Systems in Three Dimensions
Vibrational spectra and normal modes of mechanically stable particle packings
in three dimensions are analyzed over a range of compressions, from near the
jamming transition, where the packings lose their rigidity, to far above it. At
high frequency, the normal modes are localized at all compressions. At low
frequency, the nature of the modes depends somewhat on compression. At large
compressions, far from the transition, the lowest-frequency normal modes have
some plane-wave character, though less than one would expect for a crystalline
or isotropic solid. At low compressions near the jamming transition, the
lowest-frequency modes are neither plane-wave-like nor localized. We
characterize these differences, highlighting the unusual dispersion behavior
that emerges for marginally jammed solids.Comment: Under review at Phys. Rev. E. Lower resolution figures her
Geometric origin of excess low-frequency vibrational modes in amorphous solids
Glasses have a large excess of low-frequency vibrational modes in comparison
with crystalline solids. We show that such a feature is a necessary consequence
of the geometry generic to weakly connected solids. In particular, we analyze
the density of states of a recently simulated system, comprised of weakly
compressed spheres at zero temperature. We account for the observed a)
constancy of the density of modes with frequency, b) appearance of a
low-frequency cutoff, and c) power-law increase of this cutoff with
compression. We predict a length scale below which vibrations are very
different from those of a continuous elastic body.Comment: 4 pages, 2 figures. Argument rewritten, identical result
Statistics of the contact network in frictional and frictionless granular packings
Simulated granular packings with different particle friction coefficient mu
are examined. The distribution of the particle-particle and particle-wall
normal and tangential contact forces P(f) are computed and compared with
existing experimental data. Here f equivalent to F/F-bar is the contact force F
normalized by the average value F-bar. P(f) exhibits exponential-like decay at
large forces, a plateau/peak near f = 1, with additional features at forces
smaller than the average that depend on mu. Computations of the force-force
spatial distribution function and the contact point radial distribution
function indicate that correlations between forces are only weakly dependent on
friction and decay rapidly beyond approximately three particle diameters.
Distributions of the particle-particle contact angles show that the contact
network is not isotropic and only weakly dependent on friction. High
force-bearing structures, or force chains, do not play a dominant role in these
three dimensional, unloaded packings.Comment: 11 pages, 13 figures, submitted to PR
Fragility and hysteretic creep in frictional granular jamming
The granular jamming transition is experimentally investigated in a
two-dimensional system of frictional, bi-dispersed disks subject to
quasi-static, uniaxial compression at zero granular temperature. Currently
accepted results show the jamming transition occurs at a critical packing
fraction . In contrast, we observe the first compression cycle exhibits
{\it fragility} - metastable configuration with simultaneous jammed and
un-jammed clusters - over a small interval in packing fraction (). The fragile state separates the two conditions that define
with an exponential rise in pressure starting at and an exponential
fall in disk displacements ending at . The results are explained
through a percolation mechanism of stressed contacts where cluster growth
exhibits strong spatial correlation with disk displacements. Measurements with
several disk materials of varying elastic moduli and friction coefficients
, show friction directly controls the start of the fragile state, but
indirectly controls the exponential slope. Additionally, we experimentally
confirm recent predictions relating the dependence of on . Under
repetitive loading (compression), the system exhibits hysteresis in pressure,
and the onset increases slowly with repetition number. This friction
induced hysteretic creep is interpreted as the granular pack's evolution from a
metastable to an eventual structurally stable configuration. It is shown to
depend upon the quasi-static step size which provides the only
perturbative mechanism in the experimental protocol, and the friction
coefficient which acts to stabilize the pack.Comment: 12 pages, 10 figure
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
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