1,101 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
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
Gravity-driven Dense Granular Flows
We report and analyze the results of numerical studies of dense granular
flows in two and three dimensions, using both linear damped springs and
Hertzian force laws between particles. Chute flow generically produces a
constant density profile that satisfies scaling relations suggestive of a
Bagnold grain inertia regime. The type of force law has little impact on the
behavior of the system. Bulk and surface flows differ in their failure criteria
and flow rheology, as evidenced by the change in principal stress directions
near the surface. Surface-only flows are not observed in this geometry.Comment: 4 pages, RevTeX 3.0, 4 PostScript figures (5 files) embedded with
eps
Stability of Monomer-Dimer Piles
We measure how strong, localized contact adhesion between grains affects the
maximum static critical angle, theta_c, of a dry sand pile. By mixing dimer
grains, each consisting of two spheres that have been rigidly bonded together,
with simple spherical monomer grains, we create sandpiles that contain strong
localized adhesion between a given particle and at most one of its neighbors.
We find that tan(theta_c) increases from 0.45 to 1.1 and the grain packing
fraction, Phi, decreases from 0.58 to 0.52 as we increase the relative number
fraction of dimer particles in the pile, nu_d, from 0 to 1. We attribute the
increase in tan(theta_c(nu_d)) to the enhanced stability of dimers on the
surface, which reduces the density of monomers that need to be accomodated in
the most stable surface traps. A full characterization and geometrical
stability analysis of surface traps provides a good quantitative agreement
between experiment and theory over a wide range of nu_d, without any fitting
parameters.Comment: 11 pages, 12 figures consisting of 21 eps files, submitted to PR
Patterns and Collective Behavior in Granular Media: Theoretical Concepts
Granular materials are ubiquitous in our daily lives. While they have been a
subject of intensive engineering research for centuries, in the last decade
granular matter attracted significant attention of physicists. Yet despite a
major efforts by many groups, the theoretical description of granular systems
remains largely a plethora of different, often contradicting concepts and
approaches. Authors give an overview of various theoretical models emerged in
the physics of granular matter, with the focus on the onset of collective
behavior and pattern formation. Their aim is two-fold: to identify general
principles common for granular systems and other complex non-equilibrium
systems, and to elucidate important distinctions between collective behavior in
granular and continuum pattern-forming systems.Comment: Submitted to Reviews of Modern Physics. Full text with figures (2Mb
pdf) avaliable at
http://mti.msd.anl.gov/AransonTsimringReview/aranson_tsimring.pdf Community
responce is appreciated. Comments/suggestions send to [email protected]
Stress response inside perturbed particle assemblies
The effect of structural disorder on the stress response inside three
dimensional particle assemblies is studied using computer simulations of
frictionless sphere packings. Upon applying a localised, perturbative force
within the packings, the resulting {\it Green's} function response is mapped
inside the different assemblies, thus providing an explicit view as to how the
imposed perturbation is transmitted through the packing. In weakly disordered
arrays, the resulting transmission of forces is of the double-peak variety, but
with peak widths scaling linearly with distance from the source of the
perturbation. This behaviour is consistent with an anisotropic elasticity
response profile. Increasing the disorder distorts the response function until
a single-peak response is obtained for fully disordered packings consistent
with an isotropic description.Comment: 8 pages, 7 figure captions To appear in Granular Matte
Microscopic elasticity of complex systems
Lecture Notes for the Erice Summer School 2005 Computer Simulations in
Condensed Matter: from Materials to Chemical Biology. Perspectives in
celebration of the 65th Birthday of Mike Klein organized by Kurt Binder,
Giovanni Ciccotti and Mauro Ferrari
Sparse random matrices and vibrational spectra of amorphous solids
A random matrix approach is used to analyze the vibrational properties of
amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative
eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n
independent non-zero elements in each row. The average values =0 and
dispersion =V^2 for all non-zero elements. The density of vibrational
states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle
law with radius independent of N. We argue that for n^2 << N this model can be
used to describe the interaction of atoms in amorphous solids. The level
statistics of matrix M is well described by the Wigner surmise and corresponds
to repulsion of eigenfrequencies. The participation ratio for the major part of
vibrational modes in three dimensional system is about 0.2 - 0.3 and
independent of N. Together with term repulsion it indicates clearly to the
delocalization of vibrational excitations. We show that these vibrations spread
in space by means of diffusion. In this respect they are similar to diffusons
introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous
silicon. Our results are in a qualitative and sometimes in a quantitative
agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure
The Role of Friction in Compaction and Segregation of Granular Materials
We investigate the role of friction in compaction and segregation of granular
materials by combining Edwards' thermodynamic hypothesis with a simple
mechanical model and mean-field based geometrical calculations. Systems of
single species with large friction coefficients are found to compact less.
Binary mixtures of grains differing in frictional properties are found to
segregate at high compactivities, in contrary to granular mixtures differing in
size, which segregate at low compactivities. A phase diagram for segregation
vs. friction coefficients of the two species is generated. Finally, the
characteristics of segregation are related directly to the volume fraction
without the explicit use of the yet unclear notion of compactivity.Comment: 9 pages, 6 figures, submitted to Phys. Rev.
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