237 research outputs found
Granular clustering in a hydrodynamic simulation
We present a numerical simulation of a granular material using hydrodynamic
equations. We show that, in the absence of external forces, such a system
phase-separates into high density and low density regions. We show that this
separation is dependent on the inelasticity of collisions, and comment on the
mechanism for this clustering behavior. Our results are compatible with the
granular clustering seen in experiments and molecular dynamic simulations of
inelastic hard disks.Comment: 4 pages, 5 figure
Scaling and universality of critical fluctuations in granular gases
The global energy fluctuations of a low density gas granular gas in the
homogeneous cooling state near its clustering instability are studied by means
of molecular dynamics simulations. The relative dispersion of the fluctuations
is shown to exhibit a power-law divergent behavior. Moreover, the probability
distribution of the fluctuations presents data collapse as the system
approaches the instability, for different values of the inelasticity. The
function describing the collapse turns out to be the same as the one found in
several molecular equilibrium and non-equilibrium systems, except for the
change in the sign of the fluctuations
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
Dynamics of Freely Cooling Granular Gases
We study dynamics of freely cooling granular gases in two-dimensions using
large-scale molecular dynamics simulations. We find that for dilute systems the
typical kinetic energy decays algebraically with time, E(t) ~ t^{-1}, in the
long time limit. Asymptotically, velocity statistics are characterized by a
universal Gaussian distribution, in contrast with the exponential high-energy
tails characterizing the early homogeneous regime. We show that in the late
clustering regime particles move coherently as typical local velocity
fluctuations, Delta v, are small compared with the typical velocity, Delta v/v
~ t^{-1/4}. Furthermore, locally averaged shear modes dominate over acoustic
modes. The small thermal velocity fluctuations suggest that the system can be
heuristically described by Burgers-like equations.Comment: 4 pages, 5 figure
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
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
The Granular Phase Diagram
The kinetic energy distribution function satisfying the Boltzmann equation is
studied analytically and numerically for a system of inelastic hard spheres in
the case of binary collisions. Analytically, this function is shown to have a
similarity form in the simple cases of uniform or steady-state flows. This
determines the region of validity of hydrodynamic description. The latter is
used to construct the phase diagram of granular systems, and discriminate
between clustering instability and inelastic collapse. The molecular dynamics
results support analytical results, but also exhibit a novel fluctuational
breakdown of mean-field descriptions.Comment: 15 pages, 4 figure
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
- …