5 research outputs found
Linear Response for Granular Fluids
The linear response of an isolated, homogeneous granular fluid to small
spatial perturbations is studied by methods of non-equilibrium statistical
mechanics. The long wavelength linear hydrodynamic equations are obtained, with
formally exact expressions for the susceptibilities and transport coefficients.
The latter are given in equivalent Einstein-Helfand and Green-Kubo forms. The
context of these results and their contrast with corresponding results for
normal fluids are discussed.Comment: Submitted to PR
Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid
The response functions for small spatial perturbations of a homogeneous
granular fluid have been described recently. In appropriate dimensionless
variables, they have the form of stationary state time correlation functions.
Here, these functions are expressed in terms of reduced single particle
functions that are expected to obey a linear kinetic equation. The functional
assumption required for such a kinetic equation, and a Markov approximation for
its implementation are discussed. If, in addition, static velocity correlations
are neglected, a granular fluid version of the linearized Enskog kinetic theory
is obtained. The derivation makes no a priori limitation on the density, space
and time scale, nor degree of inelasticity. As an illustration, recently
derived Helfand and Green-Kubo expressions for the Navier-Stokes order
transport coefficients are evaluated with this kinetic theory. The results are
in agreement with those obtained from the Chapman-Enskog solution to the
nonlinear Enskog kinetic equation.Comment: Submitted to J. Stat. Mec
Gaussian Kinetic Model for Granular Gases
A kinetic model for the Boltzmann equation is proposed and explored as a
practical means to investigate the properties of a dilute granular gas. It is
shown that all spatially homogeneous initial distributions approach a universal
"homogeneous cooling solution" after a few collisions. The homogeneous cooling
solution (HCS) is studied in some detail and the exact solution is compared
with known results for the hard sphere Boltzmann equation. It is shown that all
qualitative features of the HCS, including the nature of over population at
large velocities, are reproduced semi-quantitatively by the kinetic model. It
is also shown that all the transport coefficients are in excellent agreement
with those from the Boltzmann equation. Also, the model is specialized to one
having a velocity independent collision frequency and the resulting HCS and
transport coefficients are compared to known results for the Maxwell Model. The
potential of the model for the study of more complex spatially inhomogeneous
states is discussed.Comment: to be submitted to Phys. Rev.
Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles
The presence of the aging phenomenon in the homogeneous cooling state (HCS)
of a granular fluid composed of inelastic hard spheres or disks is
investigated. As a consequence of the scaling property of the -particle
distribution function, it is obtained that the decay of the normalized two-time
correlation functions slows down as the time elapsed since the beginning of the
measurement increases. This result is confirmed by molecular dynamics
simulations for the particular case of the total energy of the system. The
agreement is also quantitative in the low density limit, for which an explicit
analytical form of the time correlation function has been derived. The reported
results also provide support for the existence of the HCS as a solution of the
N-particle Liouville equation.Comment: 17 pages, 3 figures; v3 revised version (minor changes, corrected
typos, v2=v1 due to a submission error)accepted for publication in J. Phys.
A: Math. Theo