Kinetic approach to granular gases

A. Puglisi, V. Loreto, U. Marini Bettolo Marconi, A. Vulpiani

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We address the problem of the so-called “granular gases,” i.e., gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the result of the balance between the dissipation and the random forces which inject energies. These models exhibit a genuine thermodynamic limit, i.e., at fixed density the mean values of kinetic energy and dissipated energy per particle are independent of the number N of particles, for large values of N. One has two regimes: when the typical relaxation time [Formula Presented] of the driving Brownian process is small compared with the mean collision time [Formula Presented] the spatial density is nearly homogeneous and the velocity probability distribution is Gaussian. In the opposite limit [Formula Presented] one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the Gaussian one. Simulations performed in one and two dimensions under the Stosszahlansatz Boltzmann approximation confirm the scenario. Furthermore, we analyze the instabilities bringing to the spatial and the velocity clusterization. Firstly, in the framework of a mean-field model, we explain how the existence of the inelasticity can lead to a spatial clusterization; on the other hand, we discuss, in the framework of a Langevin dynamics treating the collisions in a mean-field way, how a non-Gaussian distribution of velocity can arise. The comparison between the numerical and the analytical results exhibits an excellent agreement. © 1999 The American Physical Society.
Original languageEnglish
Pages (from-to)5582 - 5595
Number of pages14
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - 1999
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Puglisi, A., Loreto, V., Marini Bettolo Marconi, U., & Vulpiani, A. (1999). Kinetic approach to granular gases. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 59(5), 5582 - 5595.