1,511 research outputs found
Free cooling and inelastic collapse of granular gases in high dimensions
The connection between granular gases and sticky gases has recently been
considered, leading to the conjecture that inelastic collapse is avoided for
space dimensions higher than 4. We report Molecular Dynamics simulations of
hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular
medium is monitored throughout the cooling process. The behaviour is found to
be very similar to that of a two-dimensional system, with a shearing-like
instability of the velocity field and inelastic collapse when collisions are
inelastic enough, showing that the connection with sticky gases needs to be
revised.Comment: 6 pages, 6 figures (7 postscript files), submitted to EPJ
The rich behavior of the Boltzmann equation for dissipative gases
Within the framework of the homogeneous non-linear Boltzmann equation, we
present a new analytic method, without the intrinsic limitations of existing
methods, for obtaining asymptotic solutions. This method permits extension of
existing results for Maxwell molecules and hard spheres to large classes of
particle interactions, from very hard spheres to softer than Maxwell molecules,
as well as to more general forcing mechanisms, beyond free cooling and white
noise driving. By combining this method with numerical solutions, obtained from
the Direct Simulation Monte Carlo (DSMC) method, we study a broad class of
models relevant for the dynamics of dissipative fluids, including granular
gases. We establish a criterion connecting the stability of the non-equilibrium
steady state to an exponentially bound form for the velocity distribution ,
which varies depending on the forcing mechanism. Power laws arise in marginal
stability cases, of which several new cases are reported. Our results provide a
minimal framework for interpreting large classes of experiments on driven
granular gases
Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
Combining analytical and numerical methods, we study within the framework of
the homogeneous non-linear Boltzmann equation, a broad class of models relevant
for the dynamics of dissipative fluids, including granular gases. We use the
new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and
extend our results to a different heating mechanism, namely a deterministic
non-linear friction force. We derive analytically the high energy tail of the
velocity distribution and compare the theoretical predictions with high
precision numerical simulations. Stretched exponential forms are obtained when
the non-equilibrium steady state is stable. We derive sub-leading corrections
and emphasize their relevance. In marginal stability cases, power-law behaviors
arise, with exponents obtained as the roots of transcendental equations. We
also consider some simple BGK (Bhatnagar, Gross, Krook) models, driven by
similar heating devices, to test the robustness of our predictions
Relaxation in yield stress systems through elastically interacting activated events
We study consequences of long-range elasticity in thermally assisted dynamics
of yield stress materials. Within a two-dimensinal mesoscopic model we
calculate the mean-square displacement and the dynamical structure factor for
tracer particle trajectories. The ballistic regime at short time scales is
associated with a compressed exponential decay in the dynamical structure
factor, followed by a subdiffusive crossover prior to the onset of diffusion.
We relate this crossover to spatiotemporal correlations and thus go beyond
established mean field predictions.Comment: 5 pages, 2 figures, to appear in PR
On the definition of temperature in dense granular media
In this Letter we report the measurement of a pseudo-temperature for
compacting granular media on the basis of the Fluctuation-Dissipation relations
in the aging dynamics of a model system. From the violation of the
Fluctuation-Dissipation Theorem an effective temperature emerges (a dynamical
temperature T_{dyn}) whose ratio with the equilibrium temperature T_d^{eq}
depends on the particle density. We compare the results for the
Fluctuation-Dissipation Ratio (FDR) T_{dyn}/T_d^{eq} at several densities with
the outcomes of Edwards' approach at the corresponding densities. It turns out
that the FDR and the so-called Edwards' ratio coincide at several densities
(very different ages of the system), opening in this way the door to
experimental checks as well as theoretical constructions.Comment: RevTex4 4 pages, 4 eps figure
Power injected in a granular gas
A granular gas may be modeled as a set of hard-spheres undergoing inelastic
collisions; its microscopic dynamics is thus strongly irreversible. As pointed
out in several experimental works bearing on turbulent flows or granular
materials, the power injected in a dissipative system to sustain a steady-state
over an asymptotically large time window is a central observable. We describe
an analytic approach allowing us to determine the full distribution of the
power injected in a granular gas within a steady-state resulting from
subjecting each particle independently either to a random force (stochastic
thermostat) or to a deterministic force proportional to its velocity (Gaussian
thermostat). We provide an analysis of our results in the light of the
relevance, for other types of systems, of the injected power to fluctuation
relations.Comment: 9 pages, 4 figures. Contribution to Proceedings of "Work,
Dissipation, and Fluctuations in Nonequilibrium Physics", Brussels, 200
Injected power and entropy flow in a heated granular gas
Our interest goes to the power injected in a heated granular gas and to the
possibility to interpret it in terms of entropy flow. We numerically determine
the distribution of the injected power by means of Monte-Carlo simulations.
Then, we provide a kinetic theory approach to the computation of such a
distribution function. Finally, after showing why the injected power does not
satisfy a Fluctuation Relation a la Gallavotti-Cohen, we put forward a new
quantity which does fulfill such a relation, and is not only applicable in a
variety of frameworks outside the granular world, but also experimentally
accessible.Comment: accepted in Europhys. Let
Fluctuations of power injection in randomly driven granular gases
We investigate the large deviation function pi(w) for the fluctuations of the
power W(t)=w t, integrated over a time t, injected by a homogeneous random
driving into a granular gas, in the infinite time limit. Starting from a
generalized Liouville equation we obtain an equation for the generating
function of the cumulants mu(lambda) which appears as a generalization of the
inelastic Boltzmann equation and has a clear physical interpretation.
Reasonable assumptions are used to obtain mu(lambda) in a closed analytical
form. A Legendre transform is sufficient to get the large deviation function
pi(w). Our main result, apart from an estimate of all the cumulants of W(t) at
large times t, is that pi(w) has no negative branch. This immediately results
in the failure of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in
previous studies had been suggested to be valid for injected power in driven
granular gases. We also present numerical results, in order to discuss the
finite time behavior of the fluctuations of W(t). We discover that their
probability density function converges extremely slowly to its asymptotic
scaling form: the third cumulant saturates after a characteristic time larger
than 50 mean free times and the higher order cumulants evolve even slower. The
asymptotic value is in good agreement with our theory. Remarkably, a numerical
check of the GCFR is feasible only at small times, since negative events
disappear at larger times. At such small times this check leads to the
misleading conclusion that GCFR is satisfied for pi(w). We offer an explanation
for this remarkable apparent verification. In the inelastic Maxwell model,
where a better statistics can be achieved, we are able to numerically observe
the failure of GCFR.Comment: 23 pages, 15 figure
Memory in aged granular media
Stimulated by recent experimental results, we simulate
``temperature''-cycling experiments in a model for the compaction of granular
media. We report on the existence of two types of memory effects: short-term
dependence on the history of the sample, and long-term memory for highly
compact (aged) systems. A natural interpretation of these results is provided
by the analysis of the density heterogeneities.Comment: 5 eps figures, uses euromacr.tex and europhys.sty (included
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