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High-energy tails for inelastic Maxwell models

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Ernst, M. H. and Brito, Ricardo (2002) High-energy tails for inelastic Maxwell models. Europhysics Letters, 58 (2). pp. 182-187. ISSN 0295-5075

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Official URL: http://iopscience.iop.org/0295-5075/58/2/182/pdf/0295-5075_58_2_182.pdf




Abstract

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 -1/4 (1- alpha(2)), where alpha is the coefficient of restitution.


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© EDP Sciences. The authors want to thank A. Baldassarri et al. for useful correspondence and J. R. Dorfman for informing them about the negative rate of irreversible entropy production on an attractor in Chaos Theory. ME 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. Moreover, ME acknowledges support of the Office for International Relations of the Universidad Complutense de Madrid for a visit to UCM during September and October 2001, where part of this work was done. RB acknowledges financial support from DGES (Spain), grant BFM2001-0291.

Uncontrolled Keywords:Dynamics; Flow
Subjects:Sciences > Physics > Thermodynamics
ID Code:21392
Deposited On:17 May 2013 10:27
Last Modified:24 Jul 2018 11:03

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