1,093 research outputs found
Power law in the angular velocity distribution of a granular needle
We show how inelastic collisions induce a power law with exponent -3 in the
decay of the angular velocity distribution of anisotropic particles with
sufficiently small moment of inertia. We investigate this question within the
Boltzmann kinetic theory for an elongated granular particle immersed in a bath.
The power law persists so long as the collisions are inelastic for a large
range of angular velocities provided the mass ratio of the anisotropic particle
and the bath particles remains small. Suggestions for observing this peculiar
feature are made.Comment: 8 pages, 4 figure
Ballistic aggregation: a solvable model of irreversible many particles dynamics
The adhesive dynamics of a one-dimensional aggregating gas of point particles
is rigorously described. The infinite hierarchy of kinetic equations for the
distributions of clusters of nearest neighbours is shown to be equivalent to a
system of two coupled equations for a large class of initial conditions. The
solution to these nonlinear equations is found by a direct construction of the
relevant probability distributions in the limit of a continuous initial mass
distribution. We show that those limiting distributions are identical to those
of the statistics of shocks in the Burgers turbulence. The analysis relies on a
mapping on a Brownian motion problem with parabolic constraints.Comment: 23 pages, 6 figures include
Angular velocity distribution of a granular planar rotator in a thermalized bath
The kinetics of a granular planar rotator with a fixed center undergoing
inelastic collisions with bath particles is analyzed both numerically and
analytically by means of the Boltzmann equation. The angular velocity
distribution evolves from quasi-gaussian in the Brownian limit to an algebraic
decay in the limit of an infinitely light particle. In addition, we compare
this model with a planar rotator with a free center. We propose experimental
tests that might confirm the predicted behaviors.Comment: 10 Pages, 9 Figure
Granular Rough Sphere in a Low-Density Thermal Bath
We study the stationary state of a rough granular sphere immersed in a
thermal bath composed of point particles. When the center of mass of the sphere
is fixed the stationary angular velocity distribution is shown to be Gaussian
with an effective temperature lower than that of the bath. For a freely moving
rough sphere coupled to the thermostat via inelastic collisions we find a
condition under which the joint distribution of the translational and
rotational velocities is a product of Gaussian distributions with the same
effective temperature. In this rather unexpected case we derive a formula for
the stationary energy flow from the thermostat to the sphere in accordance with
Fourier law
Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas
Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal
gas is studied in the framework of an exact analytic approach. For an initial
symmetric three-velocity distribution, the problem can be solved exactly and it
is shown that different regimes exist depending on the initial fraction of
particles at rest. Extension to the case of a n-velocity distribution is
discussed.Comment: 19 pages, latex, uses Revtex macro
Search for universality in one-dimensional ballistic annihilation kinetics
We study the kinetics of ballistic annihilation for a one-dimensional ideal
gas with continuous velocity distribution. A dynamical scaling theory for the
long time behavior of the system is derived. Its validity is supported by
extensive numerical simulations for several velocity distributions. This leads
us to the conjecture that all the continuous velocity distributions \phi(v)
which are symmetric, regular and such that \phi(0) does not vanish, are
attracted in the long time regime towards the same Gaussian distribution and
thus belong to the same universality class. Moreover, it is found that the
particle density decays as n(t)~t^{-\alpha}, with \alpha=0.785 +/- 0.005.Comment: 8 pages, needs multicol, epsf and revtex. 8 postscript figures
included. Submitted to Phys. Rev. E. Also avaiable at
http://mykonos.unige.ch/~rey/publi.html#Secon
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