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The question of whether the known virial coefficients are enough to determine the packing fraction η∞ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Padé approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η∞ is equal to the maximum packing fraction corresponding to an ordered crystalline structure. [ABSTRACT FROM AUTHOR]

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus–Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients Bj are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d≥5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d≥5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2η1/d, where η is the packing fraction, is wholly consistent with the limiting value of 1 for d→∞. Finally, the values for Bj predicted by the virial and compressibility routes in the Percus–Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)]. [ABSTRACT FROM AUTHOR]

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular-dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented. [ABSTRACT FROM AUTHOR]

The direct correlation function and the (static) structure factor for a seven-dimensional hard-sphere fluid are considered. Analytical results for these quantities are derived within the Percus-Yevick [Phys. Rev.110, 1 (1958)] theory. [ABSTRACT FROM AUTHOR]

The article offers information on the equation of hard-sphere (HS) model. Among the key topics that were discussed include computer simulations, presentation of equation of state (EOS) as graph in compressibility factor, and scaling parameters of HS absolute temperatures. Other topics mentioned are the Monte Carlo (MC) method, coexistence pressure, and freezing point determination.

A correction to the article "Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular-dynamics simulations," that was published in the 2004 issue is presented.