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Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials

M. K. Müller, S. Luding (2011)

Mathematical Modelling of Natural Phenomena

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, ...

Homogenization and diffusion asymptotics of the linear Boltzmann equation

Thierry Goudon, Antoine Mellet (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation

Thierry Goudon, Antoine Mellet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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.

Hydrodynamics of Inelastic Maxwell Models

V. Garzó, A. Santos (2011)

Mathematical Modelling of Natural Phenomena

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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