The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or C-v(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, phi(r) = epsilon(sigma/r)". The C-v(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of C-v(t) to order O(t(4)) for n large are derived for this fluid. We propose novel expressions for C-v(t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, tau(E).