1202.2224 (Jun'ichi Wakou et al.)

Fluctuation-Dissipation Relations for Motions of Center of Mass in
Driven Granular Fluids under Gravity    [PDF]

Jun'ichi Wakou, Masaharu Isobe

We investigate a validity of fluctuation-dissipation relations in a
nonequilibrium stationary state of fluidized granular media under gravity. A
phenomenological Langevin-type theory describing the fluctuation of center of
mass height, which was originally constructed for one-dimensional granular gas
on a vibrating bottom plate, is generalized to any dimensions even for the case
that the vibrating bottom plate is replaced by a thermal wall. The theory gives
analytical expressions for the power spectrum and response function of the
center of mass height; furthermore, it predicts a fluctuationdissipation
relation between them, which is known to be satisfied at equilibrium, with a
modification that equilibrium temperature is replaced by an effective
temperature defined by a kinetic energy of the center of mass. To check these
explicit theoretical predictions, we performed extensive and accurate
event-driven molecular dynamics simulations for the model system with a thermal
wall at the bottom. We found that the power spectrum and response function of
the center of mass height show good agreement with theoretical predictions
within a range of time scales in which our theory is valid. As the most
remarkable result, it is shown that a fluctuation-dissipation relation for the
granular system is well satisfied especially at a large frequency (short time)
region in a wide range of system parameter. We finally remark that the relation
between systematic deviations at a small frequency (long time) region and time
scales of the driven granular system.

View original: http://arxiv.org/abs/1202.2224