51 research outputs found
Thermalization of an anisotropic granular particle
We investigate the dynamics of a needle in a two-dimensional bath composed of
thermalized point particles. Collisions between the needle and points are
inelastic and characterized by a normal restitution coefficient . By
using the Enskog-Boltzmann equation, we obtain analytical expressions for the
translational and rotational granular temperatures of the needle and show that
these are, in general, different from the bath temperature. The translational
temperature always exceeds the rotational one, though the difference decreases
with increasing moment of inertia. The predictions of the theory are in very
good agreement with numerical simulations of the model.Comment: 7 pages, 6 Figures, submitted to PRE. Revised version (Fig1, Fig5 and
Fig6 corrected + minor typos
Granular cooling of hard needles
We have developed a kinetic theory of hard needles undergoing binary
collisions with loss of energy due to normal and tangential restitution. In
addition, we have simulated many particle systems of granular hard needles. The
theory, based on the assumption of a homogeneous cooling state, predicts that
granular cooling of the needles proceeds in two stages: An exponential decay of
the initial configuration to a state where translational and rotational
energies take on a time independent ratio (not necessarily unity), followed by
an algebraic decay of the total kinetic energy . The simulations
support the theory very well for low and moderate densities. For higher
densities, we have observed the onset of the formation of clusters and shear
bands.Comment: 7 pages, 8 figures; major changes, extended versio
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 non-equipartition in systems of inelastic, rough spheres
We calculate and verify with simulations the ratio between the average
translational and rotational energies of systems with rough, inelastic
particles, either forced or freely cooling. The ratio shows non-equipartition
of energy. In stationary flows, this ratio depends mainly on the particle
roughness, but in nonstationary flows, such as freely cooling granular media,
it also depends strongly on the normal dissipation. The approach presented here
unifies and simplifies different results obtained by more elaborate kinetic
theories. We observe that the boundary induced energy flux plays an important
role.Comment: 4 pages latex, 4 embedded eps figures, accepted by Phys Rev
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
Two-dimensional Granular Gas of Inelastic Spheres with Multiplicative Driving
We study a two-dimensional granular gas of inelastic spheres subject to
multiplicative driving proportional to a power of the
local particle velocity . The steady state properties of the model
are examined for different values of , and compared with the
homogeneous case . A driving linearly proportional to
seems to reproduce some experimental observations which could not be reproduced
by a homogeneous driving. Furthermore, we obtain that the system can be
homogenized even for strong dissipation, if a driving inversely proportional toComment: 4 pages, 5 figures (accepted as Phys. Rev. Lett.
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 ) 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, .
The behavior of in the domain of thermal velocities ()
can be characterized by the two first non-trivial coefficients ( and
) 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 -dependence of and , to report new
computer simulations results of and for two-dimensional systems,
and to investigate the possibility of proposing theoretical estimates of
and with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change
Universality and its Origins at the Amorphous Solidification Transition
Systems undergoing an equilibrium phase transition from a liquid state to an
amorphous solid state exhibit certain universal characteristics. Chief among
these are the fraction of particles that are randomly localized and the scaling
functions that describe the order parameter and (equivalently) the statistical
distribution of localization lengths for these localized particles. The purpose
of this Paper is to discuss the origins and consequences of this universality,
and in doing so, three themes are explored. First, a replica-Landau-type
approach is formulated for the universality class of systems that are composed
of extended objects connected by permanent random constraints and undergo
amorphous solidification at a critical density of constraints. This formulation
generalizes the cases of randomly cross-linked and end-linked macromolecular
systems, discussed previously. The universal replica free energy is
constructed, in terms of the replica order parameter appropriate to amorphous
solidification, the value of the order parameter is obtained in the liquid and
amorphous solid states, and the chief universal characteristics are determined.
Second, the theory is reformulated in terms of the distribution of local static
density fluctuations rather than the replica order parameter. It is shown that
a suitable free energy can be constructed, depending on the distribution of
static density fluctuations, and that this formulation yields precisely the
same conclusions as the replica approach. Third, the universal predictions of
the theory are compared with the results of extensive numerical simulations of
randomly cross-linked macromolecular systems, due to Barsky and Plischke, and
excellent agreement is found.Comment: 10 pages, including 3 figures (REVTEX
Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a
macromolecular liquid is transformed into a solid when a sufficient density of
permanent crosslinks is introduced at random. At this continuous equi- librium
phase transition, the liquid state, in which all macromolecules are
delocalised, is transformed into a solid state, in which a nonzero fraction of
macromolecules have spontaneously become localised. This solid state is a most
unusual one: localisation occurs about mean positions that are distributed
homogeneously and randomly, and to an extent that varies randomly from monomer
to monomer. Thus, the solid state emerging at the vulcanisation transition is
an equilibrium amorphous solid state: it is properly viewed as a solid state
that bears the same relationship to the liquid and crystalline states as the
spin glass state of certain magnetic systems bears to the paramagnetic and
ferromagnetic states, in the sense that, like the spin glass state, it is
diagnosed by a subtle order parameter.
In this review we give a detailed exposition of a theoretical approach to the
physical properties of systems of randomly, permanently crosslinked
macromolecules. Our primary focus is on the equilibrium properties of such
systems, especially in the regime of Goodyear's vulcanisation transition.Comment: Review Article, REVTEX, 58 pages, 3 PostScript figure
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