8,078 research outputs found
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
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
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
Semi-classical geometry of charged black holes
At the classical level, two-dimensional dilaton gravity coupled to an abelian
gauge field has charged black hole solutions, which have much in common with
four-dimensional Reissner-Nordstrom black holes, including multiple asymptotic
regions, timelike curvature singularities, and Cauchy horizons. The black hole
spacetime is, however, significantly modified by quantum effects, which can be
systematically studied in this two-dimensional context. In particular, the
back-reaction on the geometry due to pair-creation of charged fermions
destabilizes the inner horizon and replaces it with a spacelike curvature
singularity. The semi-classical geometry has the same global topology as an
electrically neutral black hole.Comment: REVTeX, 4 pages, 2 figures; references adde
Instability of the symmetric Couette-flow in a granular gas: hydrodynamic field profiles and transport
We investigate the inelastic hard disk gas sheared by two parallel bumpy
walls (Couette-flow). In our molecular dynamic simulations we found a
sensitivity to the asymmetries of the initial condition of the particle places
and velocities and an asymmetric stationary state, where the deviation from
(anti)symmetric hydrodynamic fields is stronger as the normal restitution
coefficient decreases. For the better understanding of this sensitivity we
carried out a linear stability analysis of the former kinetic theoretical
solution [Jenkins and Richman: J. Fluid. Mech. {\bf 171} (1986)] and found it
to be unstable. The effect of this asymmetry on the self-diffusion coefficient
is also discussed.Comment: 9 pages RevTeX, 14 postscript figures, sent to Phys. Rev.
Coefficient of restitution for elastic disks
We calculate the coefficient of restitution, , starting from a
microscopic model of elastic disks. The theory is shown to agree with the
approach of Hertz in the quasistatic limit, but predicts inelastic collisions
for finite relative velocities of two approaching disks. The velocity
dependence of is calculated numerically for a wide range of
velocities. The coefficient of restitution furthermore depends on the elastic
constants of the material via Poisson's number. The elastic vibrations absorb
kinetic energy more effectively for materials with low values of the shear
modulus.Comment: 25 pages, 12 Postscript figures, LaTex2
Velocity distributions in dissipative granular gases
Motivated by recent experiments reporting non-Gaussian velocity distributions
in driven dilute granular materials, we study by numerical simulation the
properties of 2D inelastic gases. We find theoretically that the form of the
observed velocity distribution is governed primarily by the coefficient of
restitution and , the ratio between the average number of
heatings and the average number of collisions in the gas. The differences in
distributions we find between uniform and boundary heating can then be
understood as different limits of , for and
respectively.Comment: 5 figure
Velocity Correlations in Driven Two-Dimensional Granular Media
Simulations of volumetrically forced granular media in two dimensions produce
s tates with nearly homogeneous density. In these states, long-range velocity
correlations with a characteristic vortex structure develop; given sufficient
time, the correlations fill the entire simulated area. These velocity
correlations reduce the rate and violence of collisions, so that pressure is
smaller for driven inelastic particles than for undriven elastic particles in
the same thermodynamic state. As the simulation box size increases, the effects
of veloc ity correlations on the pressure are enhanced rather than reduced.Comment: 12 pages, 6 figures, 21 reference
Shock-Like Dynamics of Inelastic Gases
We provide a simple physical picture which suggests that the asymptotic
dynamics of inelastic gases in one dimension is independent of the degree of
inelasticity. Statistical characteristics, including velocity fluctuations and
the velocity distribution are identical to those of a perfectly inelastic
sticky gas, which in turn is described by the inviscid Burgers equation.
Asymptotic predictions of this continuum theory, including the t^{-2/3}
temperature decay and the development of discontinuities in the velocity
profile, are verified numerically for inelastic gases.Comment: 4 pages, 5 figures, revte
Inelastic collapse of a randomly forced particle
We consider a randomly forced particle moving in a finite region, which
rebounds inelastically with coefficient of restitution r on collision with the
boundaries. We show that there is a transition at a critical value of r,
r_c\equiv e^{-\pi/\sqrt{3}}, above which the dynamics is ergodic but beneath
which the particle undergoes inelastic collapse, coming to rest after an
infinite number of collisions in a finite time. The value of r_c is argued to
be independent of the size of the region or the presence of a viscous damping
term in the equation of motion.Comment: 4 pages, REVTEX, 2 EPS figures, uses multicol.sty and epsf.st
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