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The full canonical ensemble of a granular system

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  • Edwards, S.F.

Abstract

There is now ample experimental and computational evidence that a well-defined and reproducible state can be achieved in a granular system under a repeated disturbance; e.g., if subjected to disturbance of amplitude A and frequency ω, a volume V(A,ω) is found which will be returned to if the system is subjected to A′, ω′ and then returned to A, ω. A microcanonical ensemble defines the entropy from volume V, equally the volume function W, just as E equals H in conventional statistical physics. A canonical version exists via a compactivity ∂V/∂S. Granular systems also have a distribution of intergranular forces generated by external forces or gravity. This paper shows that the idea that the configurations are determined by the Gibbsian formula exp(-W(∂S/∂V)) can be extended to the distribution of forces with a microcanonical condition P(external)=(stressesingrains). The canonical ensemble immediately gives the exponential distribution of intergranular forces, found experimentally.

Suggested Citation

  • Edwards, S.F., 2005. "The full canonical ensemble of a granular system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 114-118.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:114-118
    DOI: 10.1016/j.physa.2005.01.045
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    Cited by:

    1. Tejada, Ignacio G., 2011. "A new statistical mechanics approach to dense granular media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2664-2677.

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