High-energy tails for inelastic Maxwell models
Instituut voor Theoretische Fysica,
Universiteit Utrecht Postbus 80.195, 3508 TD Utrecht, The
2 Departamento de Física Aplicada I, Universidad Complutense - 28040 Madrid, Spain
Accepted: 25 January 2002
Monte Carlo simulations of the spatially homogeneous Boltzmann equation for inelastic Maxwell molecules, performed by Baldassarri et al. (cond-mat/0111066), have shown that general classes of initial distributions evolve for large times into a singular nonlinear scaling solution with a power law tail. By applying an asymptotic analysis we derive these results from the nonlinear Boltzmann equation, and obtain a transcendental equation from which the exponents, appearing in the power law tails, can be calculated. The dynamics of this model describes a dissipative flow in v-space, which drives the system to an attractor, the nonlinear scaling solution, with a constant negative rate of irreversible entropy production, given by , where is the coefficient of restitution.
PACS: 05.20.Dd – Kinetic theory / 45.70.Mg – Granular flow: mixing, segregation and stratification / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems
© EDP Sciences, 2002