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The interplay between dissipation and long-range repulsive/attractive forces in
homogeneous, dilute, mono-disperse particle systems is studied. The
pseudo-Liouville operator formalism, originally
introduced for hard-sphere interactions, is modified such that it provides very good
predictions for systems with weak long-range forces at low densities, with the ratio of
potential to fluctuation kinetic energy as control parameter. By numerical simulations,
...
We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.
We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients.
Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow
and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation.
We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.
An overview of recent results pertaining to the hydrodynamic description (both Newtonian
and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic
Maxwell models is presented. The use of this mathematical model allows us to get exact
results for different problems. First, the Navier–Stokes constitutive equations with
explicit expressions for the corresponding transport coefficients are derived by applying
the Chapman–Enskog...
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