105 research outputs found
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.
Nontrivial Velocity Distributions in Inelastic Gases
We study freely evolving and forced inelastic gases using the Boltzmann
equation. We consider uniform collision rates and obtain analytical results
valid for arbitrary spatial dimension d and arbitrary dissipation coefficient
epsilon. In the freely evolving case, we find that the velocity distribution
decays algebraically, P(v,t) ~ v^{-sigma} for sufficiently large velocities. We
derive the exponent sigma(d,epsilon), which exhibits nontrivial dependence on
both d and epsilon, exactly. In the forced case, the velocity distribution
approaches a steady-state with a Gaussian large velocity tail.Comment: 4 pages, 1 figur
Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy
We study the exchange of kinetic energy between translational and rotational
degrees of freedom for inelastic collisions of rough spheres. Even if
equipartition holds in the initial state it is immediately destroyed by
collisions. The simplest generalisation of the homogeneous cooling state allows
for two temperatures, characterizing translational and rotational degrees of
freedom separately. For times larger than a crossover frequency, which is
determined by the Enskog frequency and the initial temperature, both energies
decay algebraically like with a fixed ratio of amplitudes, different
from one.Comment: 5 pages, RevTeX, 2 eps figures, slightly expanded discussion, new
figures with dimensionless units, added references, accepted for publication
in PRE as a Rapid Com
Gaussian Kinetic Model for Granular Gases
A kinetic model for the Boltzmann equation is proposed and explored as a
practical means to investigate the properties of a dilute granular gas. It is
shown that all spatially homogeneous initial distributions approach a universal
"homogeneous cooling solution" after a few collisions. The homogeneous cooling
solution (HCS) is studied in some detail and the exact solution is compared
with known results for the hard sphere Boltzmann equation. It is shown that all
qualitative features of the HCS, including the nature of over population at
large velocities, are reproduced semi-quantitatively by the kinetic model. It
is also shown that all the transport coefficients are in excellent agreement
with those from the Boltzmann equation. Also, the model is specialized to one
having a velocity independent collision frequency and the resulting HCS and
transport coefficients are compared to known results for the Maxwell Model. The
potential of the model for the study of more complex spatially inhomogeneous
states is discussed.Comment: to be submitted to Phys. Rev.
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
Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic
hard spheres can be identified, and calculated in the long wavelength limit.
Assuming they dominate at long times, formal expressions for the Navier-Stokes
transport coefficients are derived. They can be expressed in a form that
generalizes the Green-Kubo relations for molecular systems, and it is shown
that they can also be evaluated by means of -particle simulation methods.
The form of the hydrodynamic modes to zeroth order in the gradients is used to
detect the presence of inherent velocity correlations in the homogeneous
cooling state, even in the low density limit. They manifest themselves in the
fluctuations of the total energy of the system. The theoretical predictions are
shown to be in agreement with molecular dynamics simulations. Relevant related
questions deserving further attention are pointed out
Homogeneous cooling of rough, dissipative particles: Theory and simulations
We investigate freely cooling systems of rough spheres in two and three
dimensions. Simulations using an event driven algorithm are compared with
results of an approximate kinetic theory, based on the assumption of a
generalized homogeneous cooling state. For short times , translational and
rotational energy are found to change linearly with . For large times both
energies decay like with a ratio independent of time, but not
corresponding to equipartition. Good agreement is found between theory and
simulations, as long as no clustering instability is observed. System
parameters, i.e. density, particle size, and particle mass can be absorbed in a
rescaled time, so that the decay of translational and rotational energy is
solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure
Granular cooling of hard needles
We have developed a kinetic theory of hard needles undergoing binary
collisions with loss of energy due to normal and tangential restitution. In
addition, we have simulated many particle systems of granular hard needles. The
theory, based on the assumption of a homogeneous cooling state, predicts that
granular cooling of the needles proceeds in two stages: An exponential decay of
the initial configuration to a state where translational and rotational
energies take on a time independent ratio (not necessarily unity), followed by
an algebraic decay of the total kinetic energy . The simulations
support the theory very well for low and moderate densities. For higher
densities, we have observed the onset of the formation of clusters and shear
bands.Comment: 7 pages, 8 figures; major changes, extended versio
Shocks in supersonic sand
We measure time-averaged velocity, density, and temperature fields for steady
granular flow past a wedge and calculate a speed of granular pressure
disturbances (sound speed) equal to 10% of the flow speed. The flow is
supersonic, forming shocks nearly identical to those in a supersonic gas.
Molecular dynamics simulations of Newton's laws and Monte Carlo simulations of
the Boltzmann equation yield fields in quantitative agreement with experiment.
A numerical solution of Navier-Stokes-like equations agrees with a molecular
dynamics simulation for experimental conditions excluding wall friction.Comment: 4 pages, 5 figure
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