Molecular dynamics computations for the hard sphere system

Abstract

Fast electronic computers were employed to solve exactiy the simultaneous classical equations of motion of several hundred rigid elastic spheres. The equation of state for 32 particles shows a first-order transition with a loop of the van der Waals type at a density corresponding to about 50% expansion from close packing. The dependence of thc equation of state and in particular the transition on the number of particles used is discussed. The relatively slow rate of the configurational distribution to rcach equilibrium is contrasted with the quite fast establishment of the Maxwellian velocity distribution. The approach of the Boltzmann H-function to equilibrium is monotonic even at high density. The equilibrium collision rate can be accurately evaluated at all densities by means of the Enskog theory, while this theory gives good results for the self-diffusion coefficient only up to the transition point. Above that density the Enskog theory correctly predicts the initial decay of the fractional relaxation but fails to take into account the non- Markoffian character in the further time evolution of the relaxation. (auth)