https://doi.org/10.1140/epjb/e2004-00377-4
Energy and power fluctuations in vibrated granular gases
1
Laboratorire de Physique Statistique, École Normale
Supérieure, UMR 8550,
24, rue Lhomond, 75005 Paris, France
2
ICA 1
Universität Stuttgart, 70569 Stuttgart, Germany
Corresponding author: a fauve@physique.ens.fr
Received:
15
March
2004
Revised:
3
August
2004
Published online:
14
December
2004
Using two-dimensional numerical simulations of a granular gas
excited by vibrating one of the container boundaries, we study the fluctuations
of its total kinetic energy, of the power injected into the gas by the moving boundary
and of the power dissipated by inelastic collisions. We show that an effective number
Nf of degrees of freedom that depends on the inelasticity of collisions can be
extracted from the probability density function (PDF) of the fluctuations of the total
kinetic energy E. is then an intensive variable
contrary to the usually defined granular temperature
.
We then show that an intensive temperature can also be calculated from
the probability of certain large deviations of the injected power.
Finally, we show that the fluctuations
of injected and dissipated power are related such that their ratio is inversely proportional to the square-root of the ratio of their correlation times. This allows to define a quantity homogenous
to a temperature that is intensive and conserved in the process of energy dynamics from its injection by the driving piston to its dissipation by inelastic collisions.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004