1,203 research outputs found
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
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
Fractal dimensions of jammed packings with power-law particle size distributions in two and three dimensions
Static structure factors are computed for large-scale, mechanically stable,
jammed packings of frictionless spheres (three dimensions) and disks (two
dimensions) with broad, power-law size dispersity characterized by the exponent
. The static structure factor exhibits diverging power-law behavior for
small wavenumbers, allowing us to identify a structural fractal dimension,
. In three dimensions, for ,
such that each of the structure factors can be collapsed onto a universal
curve. In two dimensions, we instead find for
. Furthermore, we show that the fractal behavior
persists when rattler particles are removed, indicating that the long
wavelength structural properties of the packings are controlled by the large
particle backbone conferring mechanical rigidity to the system. A numerical
scheme for computing structure factors for triclinic unit cells is presented
and employed to analyze the jammed packings.Comment: 5 figures, 1 tabl
Granular packing simulation protocols: tap, press and relax
Granular matter takes many paths to pack. Gentle compression, compaction or
repetitive tapping can happen in natural and industrial processes. The path
influences the packing microstructure, and thus macroscale properties,
particularly for frictional grains. We perform discrete element modeling
simulations to construct packings of frictional spheres implementing a range of
stress-controlled protocols with 3D periodic boundary conditions. A
volume-controlled over-compression method is compared to four stress-controlled
methods, including over-compression and release, gentle under-compression and
cyclical compression and release. The packing volume fraction of each method
depends on the pressure, initial kinetic energy and protocol parameters. A
non-monotonic pressure dependence in the volume fraction, but not the
coordination number occurs when dilute particles initialized with a non-zero
kinetic energy are compressed, but can be reduced with the inclusion of drag.
The fraction of frictional contacts correlates with the volume fraction
minimum. Packings were cyclically compressed 1000 times. Response to
compression depends on pressure; low pressure packings have a constant volume
fraction regime, while high pressure packings continue to get dense with number
of cycles. The capability of stress-controlled, bulk-like particle simulations
to capture different protocols is showcased, and the ability to pack at low
pressures demonstrates unexpected behavior
Partially fluidized shear granular flows: Continuum theory and MD simulations
The continuum theory of partially fluidized shear granular flows is tested
and calibrated using two dimensional soft particle molecular dynamics
simulations. The theory is based on the relaxational dynamics of the order
parameter that describes the transition between static and flowing regimes of
granular material. We define the order parameter as a fraction of static
contacts among all contacts between particles. We also propose and verify by
direct simulations the constitutive relation based on the splitting of the
shear stress tensor into a``fluid part'' proportional to the strain rate
tensor, and a remaining ``solid part''. The ratio of these two parts is a
function of the order parameter. The rheology of the fluid component agrees
well with the kinetic theory of granular fluids even in the dense regime. Based
on the hysteretic bifurcation diagram for a thin shear granular layer obtained
in simulations, we construct the ``free energy'' for the order parameter. The
theory calibrated using numerical experiments with the thin granular layer is
applied to the surface-driven stationary two dimensional granular flows in a
thick granular layer under gravity.Comment: 20 pages, 19 figures, submitted to Phys. Rev.
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