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Analog of the Liouville Equation and BBGKY Hierarchy for a System of Hard Spheres with Inelastic Collisions

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Abstract

Dynamics of a system of hard spheres with inelastic collisions is investigated. This system is a model for granular flow. The map induced by a shift along the trajectory does not preserve the volume of the phase space, and the corresponding Jacobian is different from one. A special distribution function is defined as the product of the usual distribution function and the squared Jacobian. For this distribution function, the Liouville equation with boundary condition is derived. A sequence of correlation functions is defined for canonical and grand canonical ensemble. The generalized BBGKY hierarchy and boundary condition are deduced for correlation functions.

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REFERENCES

  1. D. Ya. Petrina, V. I. Gerasimenko, and P. V. Malyshev, Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems, Taylor and Francis, London (2002).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv, Ukraine

    D. Ya. Petrina

  2. University of Parma, Parma, Italy

    G. L. Caraffini

Authors
  1. D. Ya. Petrina
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  2. G. L. Caraffini
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 6, pp. 818–839, June, 2005.

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Petrina, D.Y., Caraffini, G.L. Analog of the Liouville Equation and BBGKY Hierarchy for a System of Hard Spheres with Inelastic Collisions. Ukr Math J 57, 967–990 (2005). https://doi.org/10.1007/s11253-005-0242-3

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  • DOI: https://doi.org/10.1007/s11253-005-0242-3

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