Skip to main content
SpringerLink
Log in

Moment Equations for a Granular Material in a Thermal Bath

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We compute the moment equations for a granular material under the simplifying assumption of pseudo-Maxwellian particles approximating dissipative hard spheres. We obtain the general moment equations of second and third order and the isotropic moment equations of any order. Our equations describe, in the space homogeneous case, the granular system described by a Boltzmann-like collision term and subject to a Brownian motion due to the interaction with a bath, described by a Fokker–Planck term. The trend to equilibrium is studied in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. C. Bizon, J. B. Shattuck, M. D. Swift, W. D. McCormick, and H. L. Swinney, Patterns in 3D vertically oscillated granular layers:Simulation and experiment, Phys. Rev. Lett. 80:57-60 (1998).

    Google Scholar 

  2. A. V. Bobylev, Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a maxwellian gas, Teoret. Mat. Fiz. 60:280-310 (1984).

    Google Scholar 

  3. A. V. Bobylev, J. A. Carrillo, and I. A. Gamba, On some kinetic properties and hydrodynamics equations for inelastic interaction, J. Statist. Phys. 98:743-773 (2000).

    Google Scholar 

  4. C. Cercignani, J. A. Carrillo, and I. A. Gamba, Steady states of a Boltzmann equation for driven granular media, Phys. Rev. E 62:7700-7707 (2000).

    Google Scholar 

  5. W. Feller An Introduction to Probability Theory and Its Applications, Vol. 2 (Wiley, New York, 1966).

    Google Scholar 

  6. D. Goldman, M. D. Shattuck, C. Bizon, W. D. McCormick, J. B. Swift, and H. L. Swinney, Absence of inelastic collapse in a realistic three ball model, Phys. Rev. E 57:4831-4833 (1998).

    Google Scholar 

  7. D. R. M. Williams and F. C. MacKintosh, Driven granular media in one dimension: Correlations and equation of state, Phys. Rev. E 54:9-12 (1996).

    Google Scholar 

  8. M. R. Swift, M. Boamfa, J. S. Cornell, and A. Maritan, Scale invariant correlations in a driven dissipative gas, Phys. Rev. Lett. 80:4410-4413 (1998).

    Google Scholar 

  9. C. Cercignani, Shear flow of a granular material, J. Statist. Phys. 102:1407-1415 (2001).

    Google Scholar 

  10. A. V. Bobylev, The theory on the nonlinear spatially uniform Boltzmann equation for Maxwell molecules, Sov. Sci. Rev. C Math. Phys. 7:11-233 (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Engineering Sciences, Physics and Mathematics, Karlstad University, Karlstad, Sweden

    A. V. Bobylev

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    C. Cercignani

Authors
  1. A. V. Bobylev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Cercignani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bobylev, A.V., Cercignani, C. Moment Equations for a Granular Material in a Thermal Bath. Journal of Statistical Physics 106, 547–567 (2002). https://doi.org/10.1023/A:1013754205008

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013754205008

Search

Navigation