A New Approach based on Langevin type Equation for Driven Granular Gas under Gravity

Details A New Approach based on Langevin type Equation for Driven Granular Gas under Gravity A New Approach based on Langevin type Equation for Driven Granular Gas under Gravity

2010-02-06

arxiv.org/abs/1002.1388v2

AIP Conference Proceedings 1227, 135 (2010)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 11 figures; corrected typos, to be published in the AIP Conference Proceedings of the IUTAM-ISIMM Symposium "Mathema

Scientific paper

We propose a novel approach based on a Langevin equation for fluctuating motion of the center of mass of granular media fluidized by energy injection from a bottom plate. In this framework, the analytical solution of the Langevin equation is used to derive analytic expressions for several macroscopic quantities and the power spectrum for the center of mass. In order to test our theory, we performed event-driven molecular dynamics simulations for one- and two-dimensional systems. Energy is injected from a vibrating bottom plate in the one-dimensional case and from a thermal wall at the bottom in the two-dimensional case. We found that the theoretical predictions are in good agreement with the results of those simulations under the assumption that the fluctuation-dissipation relation holds in the case of nearly elastic collisions between particles. However, as the inelasticity of the interparticle collisions increases, the power spectrum for the center of mass obtained by the simulations gradually deviates from the prediction of theoretical curve. Connection between this deviation and violation of the fluctuation-dissipation relation is discussed.

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