Kinetic theory of self-diffusion in a hard-sphere fluid

A classical long-time tail in a driven granular fluid

“…In a fluid in thermal equilibrium, long-time tails are a result of the coupling to the transverse current modes, j T k , labelled by the wave vector k. A number of approaches (see [3] and references therein, and [13,14,15,16,17]) confirmed the result ψ(t → ∞) ∝ t −3/2 . In a Lorentz gas, momentum is not conserved and it was argued [18] that this leads to a faster decay, ψ(t → ∞) ∝ t −5/2 .…”

“…Actually, the memory kernel should vanish for t → 0. For elastic hard spheres, a number of proposals to that end have been made [12,13,15]. As I am only interested in the asymptotic behaviour, I will not further discuss this divergence.…”

Br diffusion in molten NaBr explored by coherent quasielastic neutron scattering

“…The neglect of more complex correlated collisions is the reason for deviations of the macroscopic self-diffusion constant at high and low densities. A kinetic theory with inclusion of correlated collisions has been given first by Cukier and Mehaffey [49] for a hard sphere liquid and later by Wahnstrom and Sjogren [50] for continuous potentials. At high densities coupling to density fluctuations with wave numbers near the structure factor maximum hinder the diffusion process and hence reduce the diffusion constant [10].…”

Dense Granular Fluids and the Granular Glass Transition

“…Apart form the mode coupling approach, the velocity autocorrelation function has also been calculated with the help of other kinetic theories, see e.g., Refs. [270][271][272][273].…”

“…The results obtained in this section are a variant of those found in Refs. [261,272]. Technically, I closely follow the formalism of Bosse et al [269].…”