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We use the Percus-Yevick approach in the chemical-potential route to evaluate the equation of state of hard hyperspheres in five dimensions. The evaluation requires the derivation of an analytical expression for the contact value of the pair distribution function between particles of the bulk fluid and a solute particle with arbitrary size. The equation of state is compared with those obtained from the conventional virial and compressibility thermodynamic routes and the associated virial coefficients are computed. The pressure calculated from all routes is exact up to third density order, but it deviates with respect to simulation data as density increases, the compressibility and the chemical-potential routes exhibiting smaller deviations than the virial route. Accurate linear interpolations between the compressibility route and either the chemical-potential route or the virial one are constructed. [ABSTRACT FROM AUTHOR]

The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route (p route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxter's model) are derived within the Perçus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the p route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the p route yields a general better description than the virial, energy, compressibility, and zero-separation routes. [ABSTRACT FROM AUTHOR]

The chemical potentials of multicomponent fluids are derived in terms of the pair correlation functions for arbitrary number of components, interaction potentials, and dimensionality. The formally exact result is particularized to hard-sphere mixtures with zero or positive nonadditivity. As a simple application, the chemical potentials of three-dimensional additive hard-sphere mixtures are derived from the Perçus-Yevick theory and the associated equation of state is obtained. This Perçus-Yevick chemical-route equation of state is shown to be more accurate than the virial equation of state. An interpolation between the chemical-potential and compressibility routes exhibits a better performance than the well-known Boublik-Mansoori-Carnahan-Starling-Leland equation of state. [ABSTRACT FROM AUTHOR]

We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to within a certain distance of each other, with each of these two having a nearest neighbor to a fixed but otherwise arbitrary distance. This function describes special four-body configurations, but also contains contributions due to the so-called mutual nearest neighbor (two-body) and shared neighbor (three-body) configurations. The CPDF is introduced to improve a Helmholtz free energy method based on space partitions. We derive exact expressions of the CPDF and various associated quantities for randomly distributed, noninteracting points at Euclidean spaces of one, two, and three dimensions. Results may be of interest in many diverse scientific fields, from fluid physics to social and biological sciences. [ABSTRACT FROM AUTHOR]

Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E 83, 011201 (2011)]. It is demonstrated here that the RFA technique yields the exact solution of the Percus-Yevick (PY) closure to the Ornstein-Zernike (OZ) equation for binary mixtures at arbitrary odd dimensions. The proof relies mainly on the Fourier transforms ĉij(k) of the direct correlation functions defined by the OZ relation. From the analysis of the poles of ĉij(k) we show that the direct correlation functions evaluated by the RFA method vanish outside the hard core, as required by the PY theory. [ABSTRACT FROM AUTHOR]

Mixtures of hard hyperspheres in odd-space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called rational function approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlation functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein-Zernike equation coupled with the Percus-Yevick closure, thus, extending the solution for hard-sphere mixtures [J. L. Lebowitz, Phys. Rev. 133, A895 (1964)1 to arbitrary odd dimensions. Explicit evaluations for binary mixtures in five dimensions are performed. The results are compared with computer simulations, and a good agreement is found. [ABSTRACT FROM AUTHOR]

The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities d are studied with an analytical approximation method that generalizes the rational function approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimensions. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at d=5 and d=7 is obtained.