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Driven inelastic Maxwell models with high energy tails.

M H Ernst1, R Brito

  • 1Instituut voor Theoretische Fysica, Universiteit Utrecht, Postbus 80 195 3508 TD Utrecht, The Netherlands. ernst@phys.uu.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2002
PubMed
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Nonlinear Boltzmann equation solutions reveal overpopulated high-energy tails in inelastic systems. These findings offer insights into the long-time behavior of both freely cooling and driven systems.

Area of Science:

  • Statistical mechanics
  • Kinetic theory
  • Nonlinear dynamics

Background:

  • The Boltzmann equation describes the statistical behavior of particles in a gas.
  • Understanding energy distribution in systems with inelastic collisions is crucial for various physical phenomena.

Purpose of the Study:

  • To analyze the high-energy tails of solutions to the nonlinear Boltzmann equation for inelastic Maxwell models.
  • To compare these solutions with those of inelastic hard spheres.
  • To present a comprehensive picture of long-time behavior in inelastic systems.

Main Methods:

  • Solving the homogeneous nonlinear Boltzmann equation for inelastic Maxwell models.
  • Utilizing different types of thermostats to drive the system.
  • Comparing results with inelastic hard sphere models.

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Main Results:

  • Solutions generally exhibit overpopulated high-energy tails, often approximated by exp(-ac).
  • Power law and Gaussian tails emerge as limiting cases.
  • Comparison with hard spheres provides a broader understanding of system dynamics.

Conclusions:

  • The study characterizes the long-time energy tail behavior in driven and freely cooling inelastic systems.
  • The findings contribute to the kinetic theory of granular materials and statistical physics.