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Energy and power fluctuations in vibrated granular gases

  • S. Aumaítre
  • J. Farago
  • S. Fauve
  • S. Mc Namara
Article

Abstract.

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 N f 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. \(\langle E \rangle /N_f\) is then an intensive variable contrary to the usually defined granular temperature \(T_{gr} = \langle E \rangle / N\). 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.

Keywords

Spectroscopy Neural Network State Physics Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  • S. Aumaítre
    • 1
  • J. Farago
    • 1
  • S. Fauve
    • 1
  • S. Mc Namara
    • 2
  1. 1.Laboratorire de Physique StatistiqueÉcole Normale Supérieure, UMR 8550ParisFrance
  2. 2.ICA 1, Universität StuttgartStuttgartGermany

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