1,097 research outputs found
Structural signatures of the unjamming transition at zero temperature
We study the pair correlation function for zero-temperature,
disordered, soft-sphere packings just above the onset of jamming. We find
distinct signatures of the transition in both the first and split second peaks
of this function. As the transition is approached from the jammed side (at
higher packing fraction) the first peak diverges and narrows on the small-
side to a delta-function. On the high- side of this peak, decays as a
power-law. In the split second peak, the two subpeaks are both singular at the
transition, with power-law behavior on their low- sides and step-function
drop-offs on their high- sides. These singularities at the transition are
reminiscent of empirical criteria that have previously been used to distinguish
glassy structures from liquid ones.Comment: 8 pages, 13 figure
Vibrations and diverging length scales near the unjamming transition
We numerically study the vibrations of jammed packings of particles
interacting with finite-range, repulsive potentials at zero temperature. As the
packing fraction is lowered towards the onset of unjamming at
, the density of vibrational states approaches a non-zero value in
the limit of zero frequency. For , there is a crossover
frequency, below which the density of states drops towards zero.
This crossover frequency obeys power-law scaling with .
Characteristic length scales, determined from the dominant wavevector
contributing to the eigenmode at , diverge as power-laws at the
unjamming transition.Comment: Submitted to PRL, 4 pages + 7 .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
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
Combining tomographic imaging and DEM simulations to investigate the structure of experimental sphere packings
We combine advanced image reconstruction techniques from computed X-ray micro
tomography (XCT) with state-of-the-art discrete element method simulations
(DEM) to study granular materials. This "virtual-laboratory" platform allows us
to access quantities, such as frictional forces, which would be otherwise
experimentally immeasurable.Comment: 20 pages, 17 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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