434 research outputs found
Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas
The decay of a small homogeneous perturbation of the temperature of a dilute
granular gas in the steady uniform shear flow state is investigated. Using
kinetic theory based on the inelastic Boltzmann equation, a closed equation for
the decay of the perturbation is derived. The equation involves the generalized
shear viscosity of the gas in the time-dependent shear flow state, and
therefore it predicts relevant rheological effects beyond the quasi-elastic
limit. A good agreement is found when comparing the theory with molecular
dynamics simulation results. Moreover, the Onsager postulate on the regression
of fluctuations is fulfilled
Internal energy fluctuations of a granular gas under steady uniform shear flow
The stochastic properties of the total internal energy of a dilute granular
gas in the steady uniform shear flow state are investigated. A recent theory
formulated for fluctuations about the homogeneous cooling state is extended by
analogy with molecular systems. The theoretical predictions are compared with
molecular dynamics simulation results. Good agreement is found in the limit of
weak inelasticity, while systematic and relevant discrepancies are observed
when the inelasticity increases. The origin of this behavior is discussed
The Enskog equation for confined elastic hard spheres
A kinetic equation for a system of elastic hard spheres or disks confined by
a hard wall of arbitrary shape is derived. It is a generalization of the
modified Enskog equation in which the effects of the confinement are taken into
account and it is supposed to be valid up to moderate densities. From the
equation, balance equations for the hydrodynamic fields are derived,
identifying the collisional transfer contributions to the pressure tensor and
heat flux. A Lyapunov functional, , is identified. For any
solution of the kinetic equation, decays monotonically in time
until the system reaches the inhomogeneous equilibrium distribution, that is a
Maxwellian distribution with a the density field consistent with equilibrium
statistical mechanics
Homogeneous hydrodynamics of a collisional model of confined granular gases
The hydrodynamic equation governing the homogeneous time evolution of the
temperature in a model of confined granular gas is studied by means of the
Enskog equation. The existence of a normal solution of the kinetic equation is
assumed as a condition for hydrodynamics. Dimensional analysis implies a
scaling of the distribution function that is used to determine it in the first
Sonine approximation, with a coefficient that evolves in time through its
dependence on the temperature. The theoretical predictions are compared with
numerical results obtained by the direct simulation Monte Carlo method, and a
good agreement is found. The relevance of the normal homogeneous distribution
function to derive inhomogeneous hydrodynamic equations, for instance using the
Champan-Enskog algorithm, is indicated.Comment: Accepted in Phys. Rev.
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