On the first Sonine correction for granular gases

Abstract

We consider the velocity distribution for a granular gas of inelastic hard spheres described by the Boltzmann equation. We investigate both the free of forcing case and a system heated by a stochastic force. We propose a new method to compute the first correction to Gaussian behavior in a Sonine polynomial expansion quantified by the fourth cumulant $a_2$. Our expressions are compared to previous results and to those obtained through the numerical solution of the Boltzmann equation. It is numerically shown that our method yields very accurate results for small velocities of the rescaled distribution. We finally discuss the ambiguities inherent to a linear approximation method in $a_2$.

9 pages, 8 eps figures included

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• Probabilistic ballistic annihilation with continuous velocity distributions
• Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description
• Energy fluctuations in a randomly driven granular fluid
• Stationary state of a heated granular gas: fate of the usual H-functional
• Kullback--Leibler Divergence of a Freely Cooling Granular Gas
• Tuning the distance to the equipartition by controlling the collision rate in a driven granular gas experiment
• Fluctuations in granular gases
• Kinetic model for transport in granular mixtures
• Kinetic theory of polydisperse granular mixtures: influence of the partial temperatures on transport properties. A review