Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
arXiv:cond-mat/0410708 · doi:10.1088/0953-8984/17/24/008
Abstract
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes transport coefficients are derived. They can be expressed in a form that generalizes the Green-Kubo relations for molecular systems, and it is shown that they can also be evaluated by means of -particle simulation methods. The form of the hydrodynamic modes to zeroth order in the gradients is used to detect the presence of inherent velocity correlations in the homogeneous cooling state, even in the low density limit. They manifest themselves in the fluctuations of the total energy of the system. The theoretical predictions are shown to be in agreement with molecular dynamics simulations. Relevant related questions deserving further attention are pointed out.
References in corpus (11)
- Mesoscopic Theory of Granular Fluids
- NMR Experiments on a Three-Dimensional Vibrofluidized Granular Medium
- Collision statistics of driven granular materials
- Violation of Molecular Chaos in dissipative gases
- A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids
- Green-Kubo Expressions for a Granular Gas
- Steady state representation of the homogeneous cooling state of a granular gas
- Temperature inversion in granular fluids under gravity
- Hydrodynamic Modes for Granular Gases
- On the validity of the Boltzmann equation to describe low density granular systems
- Linearized Boltzmann Equation and Hydrodynamics for Granular Gases
Cited by in corpus (23)
- Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas
- Theory of Transport Processes and the Method of the Nonequilibrium Statistical Operator
- Assessing a Hydrodynamic Description for Instabilities in Highly Dissipative, Freely Cooling Granular Gases
- Transport coefficients of a granular gas of inelastic rough hard spheres
- Grad's moment method for a granular fluid at moderate densities. Navier-Stokes transport coefficients
- Mass transport of impurities in a moderately dense granular gas
- What is the temperature of a granular medium?
- First-order Chapman--Enskog velocity distribution function in a granular gas
- Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases
- System of elastic hard spheres which mimics the transport properties of a granular gas
- Partitioning of energy in highly polydisperse granular gases
- Higher-order moment theories for dilute granular gases of smooth hard-spheres
- Shear-rate dependent transport coefficients for inelastic Maxwell models
- Transport coefficients for granular suspensions at moderate densities
- Long-time tails in freely cooling granular gases
- Transport coefficients of driven granular fluids at moderate volume fractions
- Optimal control of uniformly heated granular fluids in linear response
- A numerical study of the Navier-Stokes transport coefficients for 2D granular hydrodynamics
- Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid
- Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient
- Linear Response for Granular Fluids
- Navier-Stokes transport coefficients for driven inelastic Maxwell models
- Kinetic model for transport in granular mixtures