caa a22 4500 467891400 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-006-9062-6 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9062-6 The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres [Elektronische Daten] [M. Ernst, E. Trizac, A. Barrat] We study a generic class of inelastic soft sphere models with a binary collision rate g^ν that depends on the relative velocity g. This includes previously studied inelastic hard spheres (ν = 1) and inelastic Maxwell molecules (ν = 0). We develop a new asymptotic method for analyzing large deviations from Gaussian behavior for the velocity distribution function f(c). The framework is that of the spatially uniform nonlinear Boltzmann equation and special emphasis is put on the situation where the system is driven by white noise. Depending on the value of exponent ν, three different situations are reported. For ν < −2, the non-equilibrium steady state is a repelling fixed point of the dynamics. For ν > −2, it becomes an attractive fixed point, with velocity distributions f(c) having stretched exponential behavior at large c. The corresponding dominant behavior of f(c) is computed together with sub-leading corrections. In the marginally stable case ν = −2, the high energy tail of f(c) is of power law type and the associated exponents are calculated. Our analytical predictions are confronted with Monte Carlo simulations, with a remarkably good agreement. Springer Science+Business Media, Inc., 2006 Ernst M. Instituut voor Theoretische Fysica, Universiteit Utrecht, Postbus 80.195, 3508, Utrecht, TD, The Netherlands aut Trizac E. Laboratoire de Physique Théorique et Modéles Statistiques (UMR du CNRS 8626), Bâtiment 100, Université de Paris-Sud, 91405, Orsay Cedex, France aut Barrat A. Laboratoire de Physique Théorique (UMR du CNRS 8627), Bâtiment 210, Université de Paris-Sud, 91405, Orsay Cedex, France aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 549-586 0022-4715 124:2-4<549 2006 124 10955 https://doi.org/10.1007/s10955-006-9062-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9062-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ernst M. Instituut voor Theoretische Fysica, Universiteit Utrecht, Postbus 80.195, 3508, Utrecht, TD, The Netherlands aut NATIONALLICENCE 700 1- Trizac E. Laboratoire de Physique Théorique et Modéles Statistiques (UMR du CNRS 8626), Bâtiment 100, Université de Paris-Sud, 91405, Orsay Cedex, France aut NATIONALLICENCE 700 1- Barrat A. Laboratoire de Physique Théorique (UMR du CNRS 8627), Bâtiment 210, Université de Paris-Sud, 91405, Orsay Cedex, France aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 549-586 0022-4715 124:2-4<549 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer