100 research outputs found
Propagation of an Acoustic Pulse of Finite Amplitude in a Granular Medium
A study of propagation of a wide-band acoustic signal in a granular medium is reported. Experimental data on the propagation of pulses with an amplitude up to 3 MPa and characteristic length about 1 µs through a sample of cobalt-manganese nodules are compared with a computer model of the process. An anomalous sig'rfal absorption in the high-frequency range observed with relatively weak sounding pulses is explained under the assumption of a fractal sample structure on a certain scale. When the signal amplitude increases, the ahsorption assumes a normal power form which is evidence of substance structural changes
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
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
On the velocity distributions of the one-dimensional inelastic gas
We consider the single-particle velocity distribution of a one-dimensional
fluid of inelastic particles. Both the freely evolving (cooling) system and the
non-equilibrium stationary state obtained in the presence of random forcing are
investigated, and special emphasis is paid to the small inelasticity limit. The
results are obtained from analytical arguments applied to the Boltzmann
equation along with three complementary numerical techniques (Molecular
Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of
integro-differential kinetic equations). For the freely cooling fluid, we
investigate in detail the scaling properties of the bimodal velocity
distribution emerging close to elasticity and calculate the scaling function
associated with the distribution function. In the heated steady state, we find
that, depending on the inelasticity, the distribution function may display two
different stretched exponential tails at large velocities. The inelasticity
dependence of the crossover velocity is determined and it is found that the
extremely high velocity tail may not be observable at ``experimentally
relevant'' inelasticities.Comment: Latex, 14 pages, 12 eps figure
Symmetry-breaking instability in a prototypical driven granular gas
Symmetry-breaking instability of a laterally uniform granular cluster (strip
state) in a prototypical driven granular gas is investigated. The system
consists of smooth hard disks in a two-dimensional box, colliding inelastically
with each other and driven, at zero gravity, by a "thermal" wall. The limit of
nearly elastic particle collisions is considered, and granular hydrodynamics
with the Jenkins-Richman constitutive relations is employed. The hydrodynamic
problem is completely described by two scaled parameters and the aspect ratio
of the box. Marginal stability analysis predicts a spontaneous symmetry
breaking instability of the strip state, similar to that predicted recently for
a different set of constitutive relations. If the system is big enough, the
marginal stability curve becomes independent of the details of the boundary
condition at the driving wall. In this regime, the density perturbation is
exponentially localized at the elastic wall opposite to the thermal wall. The
short- and long-wavelength asymptotics of the marginal stability curves are
obtained analytically in the dilute limit. The physics of the symmetry-breaking
instability is discussed.Comment: 11 pages, 14 figure
Stable Distributions in Stochastic Fragmentation
We investigate a class of stochastic fragmentation processes involving stable
and unstable fragments. We solve analytically for the fragment length density
and find that a generic algebraic divergence characterizes its small-size tail.
Furthermore, the entire range of acceptable values of decay exponent consistent
with the length conservation can be realized. We show that the stochastic
fragmentation process is non-self-averaging as moments exhibit significant
sample-to-sample fluctuations. Additionally, we find that the distributions of
the moments and of extremal characteristics possess an infinite set of
progressively weaker singularities.Comment: 11 pages, 5 figure
Clustering, Order, and Collapse in a Driven Granular Monolayer
Steady state dynamics of clustering, long range order, and inelastic collapse
are experimentally observed in vertically shaken granular monolayers. At large
vibration amplitudes, particle correlations show only short range order like
equilibrium 2D hard sphere gases. Lowering the amplitude "cools" the system,
resulting in a dramatic increase in correlations leading either to clustering
or an ordered state. Further cooling forms a collapse: a condensate of
motionless balls co-existing with a less dense gas. Measured velocity
distributions are non-Gaussian, showing nearly exponential tails.Comment: 9 pages of text in Revtex, 5 figures; references added, minor
modifications Paper accepted to Phys Rev Letters. Tentatively scheduled for
Nov. 9, 199
Self-diffusion in granular gases
The coefficient of self-diffusion for a homogeneously cooling granular gas
changes significantly if the impact-velocity dependence of the restitution
coefficient is taken into account. For the case of a constant
the particles spread logarithmically slow with time, whereas the
velocity dependent coefficient yields a power law time-dependence. The impact
of the difference in these time dependences on the properties of a freely
cooling granular gas is discussed.Comment: 6 pages, no figure
Scaling, Multiscaling, and Nontrivial Exponents in Inelastic Collision Processes
We investigate velocity statistics of homogeneous inelastic gases using the
Boltzmann equation. Employing an approximate uniform collision rate, we obtain
analytic results valid in arbitrary dimension. In the freely evolving case, the
velocity distribution is characterized by an algebraic large velocity tail,
P(v,t) ~ v^{-sigma}. The exponent sigma(d,epsilon), a nontrivial root of an
integral equation, varies continuously with the spatial dimension, d, and the
dissipation coefficient, epsilon. Although the velocity distribution follows a
scaling form, its moments exhibit multiscaling asymptotic behavior.
Furthermore, the velocity autocorrelation function decays algebraically with
time, A(t)= ~ t^{-alpha}, with a non-universal dissipation-dependent
exponent alpha=1/epsilon. In the forced case, the steady state Fourier
transform is obtained via a cumulant expansion. Even in this case, velocity
correlations develop and the velocity distribution is non-Maxwellian.Comment: 10 pages, 3 figure
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