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Linear response and hydrodynamics for granular fluids.

James Dufty1, Aparna Baskaran, J Javier Brey

  • 1Department of Physics, University of Florida, Gainesville, Florida 32611, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
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This study derives linear hydrodynamics for granular fluids, defining transport coefficients analogous to normal fluids. Key differences and a scaling limit for inelastic hard spheres are identified.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Fluid Dynamics

Background:

  • Granular fluids exhibit complex behaviors distinct from normal fluids.
  • Understanding their hydrodynamic properties is crucial for various applications.

Purpose of the Study:

  • To formally derive linear hydrodynamics for granular fluids.
  • To define and analyze transport coefficients using nonequilibrium statistical mechanics.
  • To identify differences from normal fluid hydrodynamics.

Main Methods:

  • Linear response theory applied to spatial perturbations.
  • Nonequilibrium statistical mechanics.
  • Wave vector expansion to second order.
  • Definition of a transport matrix and time correlation functions.

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Main Results:

  • Formal derivation of linear hydrodynamics for granular fluids.
  • Identification of phenomenological susceptibilities and transport coefficients.
  • Generalization of Helfand and Green-Kubo relations for granular systems.
  • Discussion of differences from normal fluid behavior.

Conclusions:

  • The derived framework provides a rigorous approach to granular fluid hydrodynamics.
  • The study highlights unique aspects of granular fluid transport phenomena.
  • A scaling limit relevant to inelastic hard sphere models is described.