128 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.
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
The energy flux into a fluidized granular medium at a vibrating wall
We study the power input of a vibrating wall into a fluidized granular
medium, using event driven simulations of a model granular system. The system
consists of inelastic hard disks contained between a stationary and a vibrating
elastic wall, in the absence of gravity. Two scaling relations for the power
input are found, both involving the pressure. The transition between the two
occurs when waves generated at the moving wall can propagate across the system.
Choosing an appropriate waveform for the vibrating wall removes one of these
scalings and renders the second very simple.Comment: 5 pages, revtex, 7 postscript figure
Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis
The inelastic Boltzmann equation for a granular gas is applied to spatially
inhomogeneous states close to the uniform shear flow. A normal solution is
obtained via a Chapman-Enskog-like expansion around a local shear flow
distribution. The heat and momentum fluxes are determined to first order in the
deviations of the hydrodynamic field gradients from their values in the
reference state. The corresponding transport coefficients are determined from a
set of coupled linear integral equations which are approximately solved by
using a kinetic model of the Boltzmann equation. The main new ingredient in
this expansion is that the reference state (zeroth-order
approximation) retains all the hydrodynamic orders in the shear rate. In
addition, since the collisional cooling cannot be compensated locally for
viscous heating, the distribution depends on time through its
dependence on temperature. This means that in general, for a given degree of
inelasticity, the complete nonlinear dependence of the transport coefficients
on the shear rate requires the analysis of the {\em unsteady} hydrodynamic
behavior. To simplify the analysis, the steady state conditions have been
considered here in order to perform a linear stability analysis of the
hydrodynamic equations with respect to the uniform shear flow state. Conditions
for instabilities at long wavelengths are identified and discussed.Comment: 7 figures; previous stability analysis modifie
Energy flows in vibrated granular media
We study vibrated granular media, investigating each of the three components
of the energy flow: particle-particle dissipation, energy input at the
vibrating wall, and particle-wall dissipation. Energy dissipated by
interparticle collisions is well estimated by existing theories when the
granular material is dilute, and these theories are extended to include
rotational kinetic energy. When the granular material is dense, the observed
particle-particle dissipation rate decreases to as little as 2/5 of the
theoretical prediction. We observe that the rate of energy input is the weight
of the granular material times an average vibration velocity times a function
of the ratio of particle to vibration velocity. `Particle-wall' dissipation has
been neglected in all theories up to now, but can play an important role when
the granular material is dilute. The ratio between gravitational potential
energy and kinetic energy can vary by as much as a factor of 3. Previous
simulations and experiments have shown that E ~ V^delta, with delta=2 for
dilute granular material, and delta ~ 1.5 for dense granular material. We
relate this change in exponent to the departure of particle-particle
dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR
Energy non-equipartition in systems of inelastic, rough spheres
We calculate and verify with simulations the ratio between the average
translational and rotational energies of systems with rough, inelastic
particles, either forced or freely cooling. The ratio shows non-equipartition
of energy. In stationary flows, this ratio depends mainly on the particle
roughness, but in nonstationary flows, such as freely cooling granular media,
it also depends strongly on the normal dissipation. The approach presented here
unifies and simplifies different results obtained by more elaborate kinetic
theories. We observe that the boundary induced energy flux plays an important
role.Comment: 4 pages latex, 4 embedded eps figures, accepted by Phys Rev
Hydrodynamic Modes for Granular Gases
The eigenfunctions and eigenvalues of the linearized Boltzmann equation for
inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic
modes, are calculated in the long wavelength limit for a granular gas. The
transport coefficients are identified and found to agree with those from the
Chapman-Enskog solution. The dominance of hydrodynamic modes at long times and
long wavelengths is studied via an exactly solvable kinetic model. A
collisional continuum is bounded away from the hydrodynamic spectrum, assuring
a hydrodynamic description at long times. The bound is closely related to the
power law decay of the velocity distribution in the reference homogeneous
cooling state
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
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.
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
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