Issue |
Europhys. Lett.
Volume 58, Number 2, April 2002
|
|
---|---|---|
Page(s) | 182 - 187 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2002-00622-0 | |
Published online | 01 August 2002 |
High-energy tails for inelastic Maxwell models
1
Instituut voor Theoretische Fysica,
Universiteit Utrecht Postbus 80.195, 3508 TD Utrecht, The
Netherlands
2
Departamento de Física Aplicada I, Universidad Complutense -
28040 Madrid, Spain
Received:
14
November
2001
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
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