Quasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases

Abstract

The solutions of the one-dimensional homogeneous nonlinear Boltzmann equation are studied in the QE-limit (Quasi-Elastic; infinitesimal dissipation) by a combination of analytical and numerical techniques. Their behavior at large velocities differs qualitatively from that for higher dimensional systems. In our generic model, a dissipative fluid is maintained in a non-equilibrium steady state by a stochastic or deterministic driving force. The velocity distribution for stochastic driving is regular and for infinitesimal dissipation, has a stretched exponential tail, with an unusual stretching exponent $b_{QE}=2b$, twice as large as the standard one for the corresponding $d$-dimensional system at finite dissipation. For deterministic driving the behavior is more subtle and displays singularities, such as multi-peaked velocity distribution functions. We classify the corresponding velocity distributions according to the nature and scaling behavior of such singularities.

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Cited by in corpus (13)

• Simple shear flow in inelastic Maxwell models
• Shear-rate dependent transport coefficients for inelastic Maxwell models
• Hydrodynamics of inelastic Maxwell models
• High-Energy Tail of the Velocity Distribution of Driven Inelastic Maxwell Gases
• Energy fluctuations in a randomly driven granular fluid
• Driven inelastic Maxwell gases
• Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
• Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
• Asymptotic behavior of the velocity distribution of driven inelastic gas with scalar velocities: analytical results
• Velocity distribution of driven granular gases
• Navier-Stokes transport coefficients for driven inelastic Maxwell models
• Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
• Inelastic Maxwell models for monodisperse gas-solid flows