9 research outputs found
Fluctuation-Dissipation relations in Driven Granular Gases
We study the dynamics of a 2d driven inelastic gas, by means of Direct
Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of
Molecular Chaos. Under the effect of a uniform stochastic driving in the form
of a white noise plus a friction term, the gas is kept in a non-equilibrium
Steady State characterized by fractal density correlations and non-Gaussian
distributions of velocities; the mean squared velocity, that is the so-called
{\em granular temperature}, is lower than the bath temperature. We observe that
a modified form of the Kubo relation, which relates the autocorrelation and the
linear response for the dynamics of a system {\em at equilibrium}, still holds
for the off-equilibrium, though stationary, dynamics of the systems under
investigation. Interestingly, the only needed modification to the equilibrium
Kubo relation is the replacement of the equilibrium temperature with an
effective temperature, which results equal to the global granular temperature.
We present two independent numerical experiment, i.e. two different observables
are studied: (a) the staggered density current, whose response to an impulsive
shear is proportional to its autocorrelation in the unperturbed system and (b)
the response of a tracer to a small constant force, switched on at time ,
which is proportional to the mean-square displacement in the unperturbed
system. Both measures confirm the validity of Kubo's formula, provided that the
granular temperature is used as the proportionality factor between response and
autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio
Granular fluid thermostatted by a bath of elastic hard spheres
The homogeneous steady state of a fluid of inelastic hard spheres immersed in
a bath of elastic hard spheres kept at equilibrium is analyzed by means of the
first Sonine approximation to the (spatially homogeneous) Enskog--Boltzmann
equation. The temperature of the granular fluid relative to the bath
temperature and the kurtosis of the granular distribution function are obtained
as functions of the coefficient of restitution, the mass ratio, and a
dimensionless parameter measuring the cooling rate relative to the
friction constant. Comparison with recent results obtained from an iterative
numerical solution of the Enskog--Boltzmann equation [Biben et al., Physica A
310, 308 (202)] shows an excellent agreement. Several limiting cases are also
considered. In particular, when the granular particles are much heavier than
the bath particles (but have a comparable size and number density), it is shown
that the bath acts as a white noise external driving. In the general case, the
Sonine approximation predicts the lack of a steady state if the control
parameter is larger than a certain critical value that
depends on the coefficient of restitution and the mass ratio. However, this
phenomenon appears outside the expected domain of applicability of the
approximation.Comment: 16 pages, 7 figures; minor changes; to be published in Phys. Rev.
Avalanche Dynamics in Evolution, Growth, and Depinning Models
The dynamics of complex systems in nature often occurs in terms of
punctuations, or avalanches, rather than following a smooth, gradual path. A
comprehensive theory of avalanche dynamics in models of growth, interface
depinning, and evolution is presented. Specifically, we include the Bak-Sneppen
evolution model, the Sneppen interface depinning model, the Zaitsev flux creep
model, invasion percolation, and several other depinning models into a unified
treatment encompassing a large class of far from equilibrium processes. The
formation of fractal structures, the appearance of noise, diffusion with
anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be
related to the same underlying avalanche dynamics. This dynamics can be
represented as a fractal in spatial plus one temporal dimension. We develop
a scaling theory that relates many of the critical exponents in this broad
category of extremal models, representing different universality classes, to
two basic exponents characterizing the fractal attractor. The exact equations
and the derived set of scaling relations are consistent with numerical
simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the
manuscript supplied on reques