Granular gas of viscoelastic particles in a homogeneous cooling state

A. S. Bodrova, N. V. Brilliantov

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6 Citations (Scopus)


Kinetic properties of a granular gas of viscoelastic particles in a homogeneous cooling state are studied analytically and numerically. We employ the most recent expression for the velocity-dependent restitution coefficient for colliding viscoelastic particles, which allows us to describe systems with large inelasticity. In contrast to previous studies, the third coefficient a3 of the Sonine polynomials expansion of the velocity distribution function is taken into account. We observe a complicated evolution of this coefficient. Moreover, we find that a3 is always of the same order of magnitude as the leading second Sonine coefficient a2; this contradicts the existing hypothesis that the subsequent Sonine coefficients a2, a3 ..., are of an ascending order of a small parameter, characterizing particles inelasticity. We analyze evolution of the high-energy tail of the velocity distribution function. In particular, we study the time dependence of the tail amplitude and of the threshold velocity, which demarcates the main part of the velocity distribution and the high-energy part. We also study evolution of the self-diffusion coefficient D and explore the impact of the third Sonine coefficient on the self-diffusion. Our analytical predictions for the third Sonine coefficient, threshold velocity and the self-diffusion coefficient are in a good agreement with the numerical finding.

Original languageEnglish
Pages (from-to)3315-3324
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Issue number17
Publication statusPublished - 1 Sep 2009
Externally publishedYes


  • Granular gas
  • Self-diffusion
  • Velocity dependent coefficient of restitution
  • Velocity distribution function
  • Viscoelastic particles


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