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• W1977553001 abstract "The effect of correlations on the viscosity of a dilute sheared inelastic fluid is analyzed using the ring-kinetic equation for the two-particle correlation function. The leading-order contribution to the stress in an expansion in $ϵ={(1ensuremath{-}e)}^{1∕2}$ is calculated, and it is shown that the leading-order viscosity is identical to that obtained from the Green-Kubo formula, provided the stress autocorrelation function in a sheared steady state is used in the Green-Kubo formula. A systemmatic extension of this to higher orders is also formulated, and the higher-order contributions to the stress from the ring-kinetic equation are determined in terms of the terms in the Chapman-Enskog solution for the Boltzmann equation. The series is resummed analytically to obtain a renormalized stress equation. The most dominant contributions to the two-particle correlation function are products of the eigenvectors of the conserved hydrodynamic modes of the two correlated particles. In Part I, it was shown that the long-time tails of the velocity autocorrelation function are not present in a sheared fluid. Using those results, we show that correlations do not cause a divergence in the transport coefficients; the viscosity is not divergent in two dimensions, and the Burnett coefficients are not divergent in three dimensions. The equations for three-particle and higher correlations are analyzed diagrammatically. It is found that the contributions due to the three-particle and higher correlation functions to the renormalized viscosity are smaller than those due to the two-particle distribution function in the limit $ϵensuremath{rightarrow}0$. This implies that the most dominant correlation effects are due to the two-particle correlations." @default.
• W1977553001 created "2016-06-24" @default.
• W1977553001 creator A5007118355 @default.
• W1977553001 date "2009-01-14" @default.
• W1977553001 modified "2023-09-27" @default.
• W1977553001 title "Dynamics of a dilute sheared inelastic fluid. II. The effect of correlations" @default.
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• W1977553001 doi "https://doi.org/10.1103/physreve.79.011302" @default.
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