2007/01/31 by Alain Barrat, A Barrat, E. Trizac +3 · 20 citations
Engineering · Mathematics · Physics and Astronomy · #Boltzmann constant #Boltzmann equation #Dissipative system #Distribution (mathematics) #Exponent #Exponential function #Gas Dynamics and Kinetic Theory #Infinitesimal #Lattice Boltzmann Simulation Studies #Nonlinear system #Scaling #Thermoelastic and Magnetoelastic Phenomena #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/40/15/001
published in Journal of Physics A Mathematical and Theoretical 40(15), 4057-4073 (Institute of Physics)
openalex publication_date 2007/03/23 · arxiv created 2007/07/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 behaviour 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 = 2 b , twice as large as the standard one for the corresponding d -dimensional system at finite dissipation. For deterministic driving the behaviour 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 behaviour of such singularities.