Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails



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Ernst, M. H. and Brito, Ricardo (2002) Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails. Journal of Statistical Physics, 109 (03-abr). pp. 407-432. ISSN 0022-4715

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This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to these limits. We demonstrate how the velocity distribution approaches in the scaling limit to a similarity solution with a power law tail for general classes of initial conditions and derive a transcendental equation from which the exponents in the tails can be calculated. Moreover on the basis of the available analytic and numerical results for inelastic hard spheres and inelastic Maxwell models we formulate a conjecture on the approach of the velocity distribution function to a scaling form.

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© 2002 Plenum Publishing Corporation. The authors want to thank A. Baldassarri et al. for making their simulation results available to them, and C. Cercignani, A. Bobylev, and A. Santos for helpful correspondence. M.E. wants to thank E. Ben-Naim for having stimulated his interest in dissipative one-dimensional Maxwell models during his stay at CNLS, Los Alamos National Laboratories in August 2000. This work is supported by DGES (Spain), Grant No BFM-2001-0291. Moreover R.B. acknowledges support of the foundation "Fundamenteel Onderzoek der Materie (FOM)," which is financially supported by the Dutch National Science Foundation (NWO).

Uncontrolled Keywords:Granular fluids; Dynamics; State; Flow; Similarity solutions; Power law tails; Granular Maxwell model; Characteristic functions
Subjects:Sciences > Physics > Thermodynamics
ID Code:21364
Deposited On:10 Jun 2013 10:56
Last Modified:24 Jul 2018 11:11

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