279 research outputs found

### Chains of Viscoelastic Spheres

Given a chain of viscoelastic spheres with fixed masses of the first and last
particles. We raise the question: How to chose the masses of the other
particles of the chain to assure maximal energy transfer? The results are
compared with a chain of particles for which a constant coefficient of
restitution is assumed. Our simple example shows that the assumption of
viscoelastic particle properties has not only important consequences for very
large systems (see [1]) but leads also to qualitative changes in small systems
as compared with particles interacting via a constant restitution coefficient.Comment: 11 pages, 6 figure

### Impact of high-energy tails on granular gas properties

The velocity distribution function of granular gases in the homogeneous
cooling state as well as some heated granular gases decays for large velocities
as $f\propto\exp(- {\rm const.} v)$. That is, its high-energy tail is
overpopulated as compared with the Maxwell distribution. At the present time,
there is no theory to describe the influence of the tail on the kinetic
characteristics of granular gases. We develop an approach to quantify the
overpopulated tail and analyze its impact on granular gas properties, in
particular on the cooling coefficient. We observe and explain anomalously slow
relaxation of the velocity distribution function to its steady state.Comment: 5 pages, 5 figure

### Third and fourth degree collisional moments for inelastic Maxwell models

The third and fourth degree collisional moments for $d$-dimensional inelastic
Maxwell models are exactly evaluated in terms of the velocity moments, with
explicit expressions for the associated eigenvalues and cross coefficients as
functions of the coefficient of normal restitution. The results are applied to
the analysis of the time evolution of the moments (scaled with the thermal
speed) in the free cooling problem. It is observed that the characteristic
relaxation time toward the homogeneous cooling state decreases as the
anisotropy of the corresponding moment increases. In particular, in contrast to
what happens in the one-dimensional case, all the anisotropic moments of degree
equal to or less than four vanish in the homogeneous cooling state for $d\geq
2$.Comment: 15 pages, 3 figures; v2: addition of two new reference

### Collision of Viscoelastic Spheres: Compact Expressions for the Coefficient of Normal Restitution

The coefficient of restitution of colliding viscoelastic spheres is
analytically known as a complete series expansion in terms of the impact
velocity where all (infinitely many) coefficients are known. While beeing
analytically exact, this result is not suitable for applications in efficient
event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on
the analytic result, here we derive expressions for the coefficient of
restitution which allow for an application in efficient eMD and MC simulations
of granular Systems.Comment: 4 pages, 4 figure

### The second and third Sonine coefficients of a freely cooling granular gas revisited

In its simplest statistical-mechanical description, a granular fluid can be
modeled as composed of smooth inelastic hard spheres (with a constant
coefficient of normal restitution $\alpha$) whose velocity distribution
function obeys the Enskog-Boltzmann equation. The basic state of a granular
fluid is the homogeneous cooling state, characterized by a homogeneous,
isotropic, and stationary distribution of scaled velocities, $F(\mathbf{c})$.
The behavior of $F(\mathbf{c})$ in the domain of thermal velocities ($c\sim 1$)
can be characterized by the two first non-trivial coefficients ($a_2$ and
$a_3$) of an expansion in Sonine polynomials. The main goals of this paper are
to review some of the previous efforts made to estimate (and measure in
computer simulations) the $\alpha$-dependence of $a_2$ and $a_3$, to report new
computer simulations results of $a_2$ and $a_3$ for two-dimensional systems,
and to investigate the possibility of proposing theoretical estimates of $a_2$
and $a_3$ with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change

### Rolling friction of a hard cylinder on a viscous plane

The resistance against rolling of a rigid cylinder on a flat viscous surface
is investigated. We found that the rolling-friction coefficient reveals
strongly non-linear dependence on the cylinder's velocity. For low velocity the
rolling-friction coefficient rises with velocity due to increasing deformation
rate of the surface. For larger velocity, however, it decreases with velocity
according to decreasing contact area and deformation of the surface.Comment: 7 pages, 3 figure

### 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

### Granular mixtures modeled as elastic hard spheres subject to a drag force

Granular gaseous mixtures under rapid flow conditions are usually modeled by
a multicomponent system of smooth inelastic hard spheres with constant
coefficients of normal restitution. In the low density regime an adequate
framework is provided by the set of coupled inelastic Boltzmann equations. Due
to the intricacy of the inelastic Boltzmann collision operator, in this paper
we propose a simpler model of elastic hard spheres subject to the action of an
effective drag force, which mimics the effect of dissipation present in the
original granular gas. The Navier--Stokes transport coefficients for a binary
mixture are obtained from the model by application of the Chapman--Enskog
method. The three coefficients associated with the mass flux are the same as
those obtained from the inelastic Boltzmann equation, while the remaining four
transport coefficients show a general good agreement, especially in the case of
the thermal conductivity. Finally, the approximate decomposition of the
inelastic Boltzmann collision operator is exploited to construct a model
kinetic equation for granular mixtures as a direct extension of a known kinetic
model for elastic collisions.Comment: The title has been changed, 4 figures, and to be published in Phys.
Rev.

### Long-time tails and cage effect in driven granular fluids

We study the velocity autocorrelation function (VACF) of a driven granular
fluid in the stationary state in 3 dimensions. As the critical volume fraction
of the glass transition in the corresponding elastic system is approached, we
observe pronounced cage effects in the VACF as well as a strong decrease of the
diffusion constant. At moderate densities the VACF is shown to decay
algebraically in time (t^{-3/2}) like in a molecular fluid, as long as the
driving conserves momentum locally.Comment: 4 pages, 4 figure

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