In order to investigate the universal features of collective behavior due to the many-body interactions, we perform two types of computer simulations on hard-sphere systems, a Brownian-dynamics simulation on polydisperse suspensions of hard spheres, where the hydrodynamic interactions between particles are neglected, and a molecular-dynamics simulation on atomic systems of hard spheres. Thus, we show that the Iona-time self-diffusion coefficient in atomic systems has the same form as that derived theoretically by Tokuyama and Oppenheim (TO) for the monodisperse suspension by taking into account the many-body hydrodynamic interactions, except that the singular point is now replaced by a new one. We also show that the difference between two coefficients in both systems can be well explained by the short-time self-diffusion coefficient derived theoretically for a wide range of volume fractions.

We perform two kinds of computer simulations on polydisperse hard‐sphere systems; a molecular‐dynamics simulation on atomic systems and a Brownian‐dynamics simulation on colloidal suspensions. By the analyses of the mean square displacement and the radial distribution function, the simulation results suggest that the long‐time behavior of colloidal suspensions is exactly the same as that of atomic systems. It is also shown that there exist three phase regions, a liquid phase region, a metastable phase region, and a crystal phase region, where the freezing and melting points in polydisperse case are shifted to the values higher than in monodisperse case.

A mean-field nonlinear equation for the mean-square displacement, recently proposed by one of the present authors [M. Tokuyama, Phys. Rev. E 62, R5915 (2000); Physica A 289, 57 (2001)], for concentrated, equilibrium suspensions of hard spheres is extended to describe equilibrium atomic systems of hard spheres. The validity of two types of mean-field equations is investigated by two kinds of computer simulations; a Brownian-dynamics simulation on suspensions of hard spheres and a molecular-dynamics simulation on atomic systems of hard spheres. A good agreement between the mean-field equations and simulations is then shown for different volume fractions. The two types of model systems of hard spheres are thus shown to be identical to each other on the study of the liquid-solid transition. However, analyses suggest that a new interaction is indispensable to understand the mechanism for the liquid-glass transition in both systems.

We investigate how universal the collective behavior, due to the many-body interactions in polydisperse hard-sphere systems, is at higher volume fractions. We perform two types of computer simulations, a Brownian-dynamics simulation on colloidal suspensions of hard spheres, where the hydrodynamic interactions between particles are neglected, and a molecular-dynamic simulation on atomic systems of hard spheres. Thus, we show that the long-time self-diffusion coefficients DSL in both systems become singular as DSL(φ)∼(1−φ/φc)2 because of the collective interactions due to the many-body collision processes, where φ is a particle volume fraction and φc≃0.586 for 6% polydispersity. Although DSL exhibits the same singular behavior as that obtained theoretically for the monodisperse suspension with the hydrodynamic interactions, no liquid–glass transition is found because even the polydisperse hard-sphere systems crystallize without the hydrodynamic interactions for all φ above the melting volume fraction, which is lower than φc.