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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 ͑2000͒; Physica A 289, 57 ͑2001͔͒, 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 adoi:10.1103/physreve.67.062403 pmid:16241280 fatcat:owgeitnsdjbftjstoorfbx6muu