41 research outputs found
Hydrodynamics and transport coefficients for Granular Gases
The hydrodynamics of granular gases of viscoelastic particles, whose
collision is described by an impact-velocity dependent coefficient of
restitution, is developed using a modified Chapman-Enskog approach. We derive
the hydrodynamic equations and the according transport coefficients with the
assumption that the shape of the velocity distribution function follows
adiabatically the decaying temperature. We show numerically that this
approximation is justified up to intermediate dissipation. The transport
coefficients and the coefficient of cooling are expressed in terms of the
elastic and dissipative parameters of the particle material and by the gas
parameters. The dependence of these coefficients on temperature differs
qualitatively from that obtained with the simplifying assumption of a constant
coefficient of restitution which was used in previous studies. The approach
formulated for gases of viscoelastic particles may be applied also for other
impact-velocity dependencies of the restitution coefficient.Comment: 16 pages, 4 figure
Hydrodynamics of driven granular gases
Hydrodynamic equations for granular gases driven by the Fokker-Planck
operator are derived. Transport coefficients appeared in Navier-Stokes order
change from the values of a free cooling state to those of a steady state.Comment: 5 pages, 3 figure
Long time behaviour and self-similarity in an addition model with slow Input of monomers
We consider a coagulation equation with constant coefficients and a time dependent
power law input of monomers. We discuss the asymptotic behaviour of solutions as , and we prove solutions converge to a similarity profile along the non-characteristic
direction
Integral representation of the linear Boltzmann operator for granular gas dynamics with applications
We investigate the properties of the collision operator associated to the
linear Boltzmann equation for dissipative hard-spheres arising in granular gas
dynamics. We establish that, as in the case of non-dissipative interactions,
the gain collision operator is an integral operator whose kernel is made
explicit. One deduces from this result a complete picture of the spectrum of
the collision operator in an Hilbert space setting, generalizing results from
T. Carleman to granular gases. In the same way, we obtain from this integral
representation of the gain operator that the semigroup in L^1(\R \times \R,\d
\x \otimes \d\v) associated to the linear Boltzmann equation for dissipative
hard spheres is honest generalizing known results from the first author.Comment: 19 pages, to appear in Journal of Statistical Physic
Attractive Interactions Between Rod-like Polyelectrolytes: Polarization, Crystallization, and Packing
We study the attractive interactions between rod-like charged polymers in
solution that appear in the presence of multi-valence counterions. The
counterions condensed to the rods exhibit both a strong transversal
polarization and a longitudinal crystalline arrangement. At short distances
between the rods, the fraction of condensed counterions increases, and the
majority of these occupy the region between the rods, where they minimize their
repulsive interactions by arranging themselves into packing structures. The
attractive interaction is strongest for multivalent counterions. Our model
takes into account the hard-core volume of the condensed counterions and their
angular distribution around the rods. The hard core constraint strongly
suppresses longitudinal charge fluctuations.Comment: 4 figures, uses revtex, psfig and epsf. The new version contains a
different introduction, and the bibliography has been expande
Studies of Mass and Size Effects in Three-Dimensional Vibrofluidized Granular Mixtures
We examine the steady state properties of binary systems of driven inelastic
hard spheres. The spheres, which move under the influence of gravity, are
contained in a vertical cylinder with a vibrating base. We computed the
trajectories of the spheres using an event-driven molecular dynamics algorithm.
In the first part of the study, we chose simulation parameters that match those
of experiments performed by Wildman and Parker. Various properties computed
from the simulation including the density profile, granular temperature and
circulation pattern are in good qualitative agreement with the experiments. We
then studied the effect of varying the mass ratio and the size ratio
independently while holding the other parameters constant. The mass and size
ratio are shown to affect the distribution of the energy. The changes in the
energy distributions affect the packing fraction and temperature of each
component. The temperature of the heavier component has a non-linear dependence
on the mass of the lighter component, while the temperature of the lighter
component is approximately proportional to its mass. The temperature of both
components is inversely dependent on the size of the smaller component.Comment: 14 Pages, 12 Figures, RevTeX
Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state
The collisional rates associated with the isotropic velocity moments
and
are exactly derived in the case of the
inelastic Maxwell model as functions of the exponent , the coefficient of
restitution , and the dimensionality . The results are applied to
the evolution of the moments in the homogeneous free cooling state. It is found
that, at a given value of , not only the isotropic moments of a degree
higher than a certain value diverge but also the anisotropic moments do. This
implies that, while the scaled distribution function has been proven in the
literature to converge to the isotropic self-similar solution in well-defined
mathematical terms, nonzero initial anisotropic moments do not decay with time.
On the other hand, our results show that the ratio between an anisotropic
moment and the isotropic moment of the same degree tends to zero.Comment: 7 pages, 2 figures; v2: clarification of some mathematical statements
and addition of 7 new references; v3: Published in "Special Issue: Isaac
Goldhirsch - A Pioneer of Granular Matter Theory
Jamming coverage in competitive random sequential adsorption of binary mixture
We propose a generalized car parking problem where cars of two different
sizes are sequentially parked on a line with a given probability . The free
parameter interpolates between the classical car parking problem of only
one car size and the competitive random sequential adsorption (CRSA) of a
binary mixture. We give an exact solution to the CRSA rate equations and find
that the final coverage, the jamming limit, of the line is always larger for a
binary mixture than for the uni-sized case. The analytical results are in good
agreement with our direct numerical simulations of the problem.Comment: 4 pages 2-column RevTeX, Four figures, (there was an error in the
previous version. We replaced it (including figures) with corrected and
improved version that lead to new results and conclusions
Self-Similarity for Ballistic Aggregation Equation
We consider ballistic aggregation equation for gases in which each particle
is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For
the constant aggregation rate we prove existence of self-similar solutions as
well as convergence to the self-similarity for generic solutions. For some
classes of mass and/or impulsion dependent rates we are also able to estimate
the large time decay of some moments of generic solutions or to build some new
classes of self-similar solutions