Letter | Published:

Observing brownian motion in vibration-fluidized granular matter

Nature volume 424, pages 909912 (21 August 2003) | Download Citation

Subjects

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    & Über die Messung der rotatorischen Brownschen Bewegung mit Hilfe einer Drehwage. Naturwissenschaften 15, 15 (1927)

  2. 2.

    & A problem in Brownian motion. Phys. Rev. 34, 145–151 (1929)

  3. 3.

    & On the theory of the Brownian motion II. Rev. Mod. Phys. 17, 323–342 (1945)

  4. 4.

    , & Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer, Berlin, 1991)

  5. 5.

    , & Granular solids, liquids and gases. Rev. Mod. Phys. 68, 1259–1273 (1996)

  6. 6.

    Mehta, A. & Halsey, T. C. (eds) Proceedings of the Workshop “Challenges in Granular Physics”. Adv. Complex Syst. 4(special issue), 287–534 (2001)

  7. 7.

    , & Violation of the fluctuation-dissipation relation during the formation of a colloidal glass. Europhys. Lett. 53, 511–517 (2001)

  8. 8.

    & Observation of a fluctuation-dissipation-theorem violation in a structural glass. Phys. Rev. Lett. 83, 5038–5041 (1999)

  9. 9.

    & Speckle visibility spectroscopy and variable granular fluidization. Phys. Rev. Lett. 90, 184302 (2003)

  10. 10.

    , , , & Measurements of grain motion in dense, three-dimensional granular fluid. Phys. Rev. Lett. 88, 044301 (2002)

  11. 11.

    , & Mobility of a sphere in vibrated granular media. Europhys. Lett. 17, 315–319 (1992)

  12. 12.

    & Response properties in a model for granular matter. J. Phys. A 33, 4401–4426 (2000)

  13. 13.

    & Compaction dynamics of a granular medium under vertical tapping. Europhys. Lett. 60, 677–683 (2002)

  14. 14.

    & Vogel-Fulcher-Tammann type diffusive slowdown in weakly perturbed granular media. Phys. Rev. Lett. 87, 254–302 (2001)

  15. 15.

    , , , & Extreme events-driven glassy behaviour in granular media. Europhys. Lett. 61, 60–66 (2003)

  16. 16.

    , , , & Modeling and simulations of the behavior of glass particles in a rotating drum in heptane and water vapor atmospheres. Eur. Phys. J. B 25, 217–222 (2002)

Download references

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.

Author information

Affiliations

  1. Institut de Physique de la Matière Complexe, Faculté des Sciences de Base, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

    • G. D'Anna
    •  & P. Mayor
  2. Laboratoire de Physique Théorique, Unité Mixte de Recherche UMR 8627, Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France

    • A. Barrat
  3. Università degli Studi di Roma La Sapienza, Dipartimento di Fisica, and INFM, Center for Statistical Mechanics and Complexity, Piazzale A. Moro 5, 00185 Rome, Italy

    • V. Loreto
  4. Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan

    • Franco Nori
  5. Center for Theoretical Physics, Department of Physics, CSCS, University of Michigan, Ann Arbor, Michigan 48109-1120, USA

    • Franco Nori

Authors

  1. Search for G. D'Anna in:

  2. Search for P. Mayor in:

  3. Search for A. Barrat in:

  4. Search for V. Loreto in:

  5. Search for Franco Nori in:

Competing interests

The authors declare that they have no competing financial interests.

Corresponding author

Correspondence to G. D'Anna.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nature01867

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.