306 research outputs found
Application of the Gillespie algorithm to a granular intruder particle
We show how the Gillespie algorithm, originally developed to describe coupled
chemical reactions, can be used to perform numerical simulations of a granular
intruder particle colliding with thermalized bath particles. The algorithm
generates a sequence of collision ``events'' separated by variable time
intervals. As input, it requires the position-dependent flux of bath particles
at each point on the surface of the intruder particle. We validate the method
by applying it to a one-dimensional system for which the exact solution of the
homogeneous Boltzmann equation is known and investigate the case where the bath
particle velocity distribution has algebraic tails. We also present an
application to a granular needle in bath of point particles where we
demonstrate the presence of correlations between the translational and
rotational degrees of freedom of the intruder particle. The relationship
between the Gillespie algorithm and the commonly used Direct Simulation Monte
Carlo (DSMC) method is also discussed.Comment: 13 pages, 8 figures, to be published in J. Phys. A Math. Ge
Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery
The coefficient of normal restitution of colliding viscoelastic spheres is
computed as a function of the material properties and the impact velocity. From
simple arguments it becomes clear that in a collision of purely repulsively
interacting particles, the particles loose contact slightly before the distance
of the centers of the spheres reaches the sum of the radii, that is, the
particles recover their shape only after they lose contact with their collision
partner. This effect was neglected in earlier calculations which leads
erroneously to attractive forces and, thus, to an underestimation of the
coefficient of restitution. As a result we find a novel dependence of the
coefficient of restitution on the impact rate.Comment: 11 pages, 2 figure
Coefficient of tangential restitution for the linear dashpot model
The linear dashpot model for the inelastic normal force between colliding
spheres leads to a constant coefficient of normal restitution,
const., which makes this model very popular for the investigation
of dilute and moderately dense granular systems. For two frequently used models
for the tangential interaction force we determine the coefficient of tangential
restitution , both analytically and by numerical integration of
Newton's equation. Although const. for the linear-dashpot model,
we obtain pronounced and characteristic dependencies of the tangential
coefficient on the impact velocity . The
results may be used for event-driven simulations of granular systems of
frictional particles.Comment: 12 pages, 12 figure
Oscillatory instability in a driven granular gas
We discovered an oscillatory instability in a system of inelastically
colliding hard spheres, driven by two opposite "thermal" walls at zero gravity.
The instability, predicted by a linear stability analysis of the equations of
granular hydrodynamics, occurs when the inelasticity of particle collisions
exceeds a critical value. Molecular dynamic simulations support the theory and
show a stripe-shaped cluster moving back and forth in the middle of the box
away from the driving walls. The oscillations are irregular but have a single
dominating frequency that is close to the frequency at the instability onset,
predicted from hydrodynamics.Comment: 7 pages, 4 figures, to appear in Europhysics Letter
Movers and shakers: Granular damping in microgravity
The response of an oscillating granular damper to an initial perturbation is
studied using experiments performed in microgravity and granular dynamics
mulations. High-speed video and image processing techniques are used to extract
experimental data. An inelastic hard sphere model is developed to perform
simulations and the results are in excellent agreement with the experiments.
The granular damper behaves like a frictional damper and a linear decay of the
amplitude is bserved. This is true even for the simulation model, where
friction forces are absent. A simple expression is developed which predicts the
optimal damping conditions for a given amplitude and is independent of the
oscillation frequency and particle inelasticities.Comment: 9 pages, 9 figure
Towards a continuum theory of clustering in a freely cooling inelastic gas
We performed molecular dynamics simulations to investigate the clustering
instability of a freely cooling dilute gas of inelastically colliding disks in
a quasi-one-dimensional setting. We observe that, as the gas cools, the shear
stress becomes negligibly small, and the gas flows by inertia only. Finite-time
singularities, intrinsic in such a flow, are arrested only when close-packed
clusters are formed. We observe that the late-time dynamics of this system are
describable by the Burgers equation with vanishing viscosity, and predict the
long-time coarsening behavior.Comment: 7 pages, 5 eps figures, to appear in Europhys. Let
Fractal Substructure of a Nanopowder
The structural evolution of a nano-powder by repeated dispersion and settling
can lead to characteristic fractal substructures. This is shown by numerical
simulations of a two-dimensional model agglomerate of adhesive rigid particles.
The agglomerate is cut into fragments of a characteristic size l, which then
are settling under gravity. Repeating this procedure converges to a loosely
packed structure, the properties of which are investigated: a) The final
packing density is independent of the initialization, b) the short-range
correlation function is independent of the fragment size, c) the structure is
fractal up to the fragmentation scale l with a fractal dimension close to 1.7,
and d) the relaxation time increases linearly with l.Comment: 4 pages, 8 figure
Finite-sample frequency distributions originating from an equiprobability distribution
Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the
expected corresponding rank ordered frequency distribution f(i), i=1..N, if an
ensemble of M events is drawn?Comment: 4 pages, 4 figure
Linear Response for Granular Fluids
The linear response of an isolated, homogeneous granular fluid to small
spatial perturbations is studied by methods of non-equilibrium statistical
mechanics. The long wavelength linear hydrodynamic equations are obtained, with
formally exact expressions for the susceptibilities and transport coefficients.
The latter are given in equivalent Einstein-Helfand and Green-Kubo forms. The
context of these results and their contrast with corresponding results for
normal fluids are discussed.Comment: Submitted to PR
Phase separation of a driven granular gas in annular geometry
This work investigates phase separation of a monodisperse gas of
inelastically colliding hard disks confined in a two-dimensional annulus, the
inner circle of which represents a "thermal wall". When described by granular
hydrodynamic equations, the basic steady state of this system is an azimuthally
symmetric state of increased particle density at the exterior circle of the
annulus. When the inelastic energy loss is sufficiently large, hydrodynamics
predicts spontaneous symmetry breaking of the annular state, analogous to the
van der Waals-like phase separation phenomenon previously found in a driven
granular gas in rectangular geometry. At a fixed aspect ratio of the annulus,
the phase separation involves a "spinodal interval" of particle area fractions,
where the gas has negative compressibility in the azimuthal direction. The heat
conduction in the azimuthal direction tends to suppress the instability, as
corroborated by a marginal stability analysis of the basic steady state with
respect to small perturbations. To test and complement our theoretical
predictions we performed event-driven molecular dynamics (MD) simulations of
this system. We clearly identify the transition to phase separated states in
the MD simulations, despite large fluctuations present, by measuring the
probability distribution of the amplitude of the fundamental Fourier mode of
the azimuthal spectrum of the particle density. We find that the instability
region, predicted from hydrodynamics, is always located within the phase
separation region observed in the MD simulations. This implies the presence of
a binodal (coexistence) region, where the annular state is metastable. The
phase separation persists when the driving and elastic walls are interchanged,
and also when the elastic wall is replaced by weakly inelastic one.Comment: 9 pages, 10 figures, to be published in PR
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