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Observing brownian motion in vibration-fluidized granular matter

Abstract

Observation of the rotational brownian motion1,2 of a very fine wire immersed in a gas led to one of the most important ideas of equilibrium statistical mechanics. Namely, the many-particle problem of a large number of molecules colliding with the wire can be represented by just two macroscopic parameters: viscosity and temperature. Interest has arisen in the question of whether this idea (mathematically developed in the Langevin model and the fluctuation-dissipation theorem3,4) can also be used to describe systems that are far from equilibrium. Here we report an experimental investigation of an archetypal non-equilibrium system, involving a sensitive torsion oscillator immersed in a granular system5,6 of millimetre-size grains that are fluidized by strong external vibrations. The vibro-fluidized granular medium is a driven environment, with continuous injection and dissipation of energy, and the immersed oscillator can be seen as analogous to an elastically bound brownian particle. By measuring the noise and the susceptibility, we show that the experiment can be treated (to a first approximation) with the equilibrium formalism. This gives experimental access to a granular viscosity and an effective temperature; however, these quantities are anisotropic and inhomogeneous. Surprisingly, the vibro-fluidized granular matter behaves as a ‘thermal’ bath satisfying a fluctuation-dissipation relation.

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Figure 1: Sketch of the torsion oscillator immersed in a ‘viscous liquid’.
Figure 2: Noise and susceptibility for different vibration intensities.
Figure 3: FD ratio and the effective temperature.

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Acknowledgements

We thank Z. Racz and A. Vespignani for discussions and comments. A.B. and V.L. wish to thank the Ecole Polytechnique Fédérale de Lausanne for its hospitality during the realization of this work. F.B. thanks the National Science Foundation for support.

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Correspondence to G. D'Anna.

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D'Anna, G., Mayor, P., Barrat, A. et al. Observing brownian motion in vibration-fluidized granular matter. Nature 424, 909–912 (2003). https://doi.org/10.1038/nature01867

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