163 research outputs found
Hydrodynamic singularities and clustering in a freely cooling inelastic gas
We employ hydrodynamic equations to follow the clustering instability of a
freely cooling dilute gas of inelastically colliding spheres into a
well-developed nonlinear regime. We simplify the problem by dealing with a
one-dimensional coarse-grained flow. We observe that at a late stage of the
instability the shear stress becomes negligibly small, and the gas flows solely
by inertia. As a result the flow formally develops a finite time singularity,
as the velocity gradient and the gas density diverge at some location. We argue
that flow by inertia represents a generic intermediate asymptotic of unstable
free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure
Inelastic Collapse of Three Particles
A system of three particles undergoing inelastic collisions in arbitrary
spatial dimensions is studied with the aim of establishing the domain of
``inelastic collapse''---an infinite number of collisions which take place in a
finite time. Analytic and simulation results show that for a sufficiently small
restitution coefficient, , collapse can
occur. In one dimension, such a collapse is stable against small perturbations
within this entire range. In higher dimensions, the collapse can be stable
against small variations of initial conditions, within a smaller range,
.Comment: 6 pages, figures on request, accepted by PR
Close-packed floating clusters: granular hydrodynamics beyond the freezing point?
Monodisperse granular flows often develop regions with hexagonal close
packing of particles. We investigate this effect in a system of inelastic hard
spheres driven from below by a "thermal" plate. Molecular dynamics simulations
show, in a wide range of parameters, a close-packed cluster supported by a
low-density region. Surprisingly, the steady-state density profile, including
the close-packed cluster part, is well described by a variant of Navier-Stokes
granular hydrodynamics (NSGH). We suggest a simple explanation for the success
of NSGH beyond the freezing point.Comment: 4 pages, 5 figures. To appear in Phys. Rev. Let
Towards granular hydrodynamics in two-dimensions
We study steady-state properties of inelastic gases in two-dimensions in the
presence of an energy source. We generalize previous hydrodynamic treatments to
situations where high and low density regions coexist. The theoretical
predictions compare well with numerical simulations in the nearly elastic
limit. It is also seen that the system can achieve a nonequilibrium
steady-state with asymmetric velocity distributions, and we discuss the
conditions under which such situations occur.Comment: 8 pages, 9 figures, revtex, references added, also available from
http://arnold.uchicago.edu/?ebn
Dynamics and stress in gravity driven granular flow
We study, using simulations, the steady-state flow of dry sand driven by
gravity in two-dimensions. An investigation of the microscopic grain dynamics
reveals that grains remain separated but with a power-law distribution of
distances and times between collisions.
While there are large random grain velocities, many of these fluctuations are
correlated across the system and local rearrangements are very slow. Stresses
in the system are almost entirely transfered by collisions and the structure of
the stress tensor comes almost entirely from a bias in the directions in which
collisions occur.Comment: 4 pages, 3 eps figures, RevTe
Granular Collapse as a Percolation Transition
Inelastic collapse is found in a two-dimensional system of inelastic hard
disks confined between two walls which act as an energy source. As the
coefficient of restitution is lowered, there is a transition between a state
containing small collapsed clusters and a state dominated by a large collapsed
cluster. The transition is analogous to that of a percolation transition. At
the transition the number of clusters n_s of size s scales as with .Comment: 10 pages revtex, 5 figures, accepted by Phys Rev E many changes and
corrections from previous submissio
On the validity of the Boltzmann equation to describe low density granular systems
The departure of a granular gas in the instable region of parameters from the
initial homogeneous cooling state is studied. Results from Molecular Dynamics
and from Direct Monte Carlo simulation of the Boltzmann equation are compared.
It is shown that the Boltzmann equation accurately predicts the low density
limit of the system. The relevant role played by the parallelization of the
velocities as time proceeds and the dependence of this effect on the density is
analyzed in detail
A nonlinear hydrodynamical approach to granular materials
We propose a nonlinear hydrodynamical model of granular materials. We show
how this model describes the formation of a sand pile from a homogeneous
distribution of material under gravity, and then discuss a simulation of a
rotating sandpile which shows, in qualitative agreement with experiment, a
static and dynamic angle of repose.Comment: 17 pages, 14 figures, RevTeX4; minor changes to wording and some
additional discussion. Accepted by Phys. Rev.
Velocity correlations in granular materials
A system of inelastic hard disks in a thin pipe capped by hot walls is
studied with the aim of investigating velocity correlations between particles.
Two effects lead to such correlations: inelastic collisions help to build
localized correlations, while momentum conservation and diffusion produce long
ranged correlations. In the quasi-elastic limit, the velocity correlation is
weak, but it is still important since it is of the same order as the deviation
from uniformity. For system with stronger inelasticity, the pipe contains a
clump of particles in highly correlated motion. A theory with empirical
parameters is developed. This theory is composed of equations similar to the
usual hydrodynamic laws of conservation of particles, energy, and momentum.
Numerical results show that the theory describes the dynamics satisfactorily in
the quasi-elastic limit, however only qualitatively for stronger inelasticity.Comment: 12 pages (REVTeX), 15 figures (Postscript). submitted to Phys. Rev.
Velocity and density profiles of granular flow in channels using lattice gas automaton
We have performed two-dimensional lattice-gas-automaton simulations of
granular flow between two parallel planes. We find that the velocity profiles
have non-parabolic distributions while simultaneously the density profiles are
non-uniform. Under non-slip boundary conditions, deviation of velocity profiles
from the parabolic form of newtonian fluids is found to be characterized solely
by ratio of maximal velocity at the center to the average velocity, though the
ratio depends on the model parameters in a complex manner. We also find that
the maximal velocity () at the center is a linear function of the
driving force (g) as with non-zero in
contrast with newtonian fluids. Regarding density profiles, we observe that
densities near the boundaries are higher than those in the center. The width of
higher densities (above the average density) relative to the channel width is a
decreasing function of a variable which scales with the driving force (g),
energy dissipation parameter () and the width of the system (L) as
with exponents and . A phenomenological theory based on a scaling argument is presented to
interpret these findings.Comment: Latex, 15 figures, to appear in PR
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