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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.
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.
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.
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