Equations of State for Four-and Five-Dimensional Hard Hypersphere Fluids

Amorós, J.; Solana, J. R.; Villar, Eugenio

doi:10.1080/00319108908028443

Cited by 18 publications

(8 citation statements)

References 26 publications

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“…Interest in studying fluids of hard spheres in d dimensions goes back at least four decades 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28 and has recently experienced a new boom. 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,…”

Section: Introductionmentioning

confidence: 99%

Virial series for fluids of hard hyperspheres in odd dimensions

Rohrmann

Robles

Haro

et al. 2008

The Journal of Chemical Physics

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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 B(j) 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 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) 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)].

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Section: Introductionmentioning

confidence: 99%

Virial series for fluids of hard hyperspheres in odd dimensions

Rohrmann

Robles

Haro

et al. 2008

The Journal of Chemical Physics

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“…Hard-hypersphere fluids (where the interaction potential is infinite when two hyperspheres overlap and zero otherwise) are the natural extension of hard spheres to arbitrary dimensions d. Such systems have attracted an everlasting attention of many researchers [6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]. The main reason is twofold.…”

Section: Introductionmentioning

confidence: 99%

Structure of hard-hypersphere fluids in odd dimensions

Rohrmann

Santos

2007

Phys. Rev. E

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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.

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“…Although not present in nature, fluids of hard hyperspheres in high dimensions (d ≥ 4) have attracted the attention of a number of researchers over the last twenty years. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] Among these studies, one of the most important outcomes was the realization by Freasier and Isbister 1 and, independently, by Leutheusser 4 that the Percus-Yevick (PY) equation 15 admits an exact solution for a system of hard spheres in d = odd dimensions. In the special case of a five-dimensional system (d = 5), the virial series representation of the compressibility factor Z ≡ p/ρk B T (where p is the pressure, ρ is the number density, k B is the Boltzmann constant, and T is the temperature) is Z(η) = ∞ n=0 b n+1 η n , where η = (π 2 /60)ρσ 5 is the volume fraction (σ being the diameter of a sphere One of the simplest proposals is Song, Mason, and Stratt's (SMS), 7 who, by viewing the Carnahan-Starling (CS) EOS for d = 3 16 as arising from a kind of meanfield theory, arrived at a generalization for d dimensions that makes use of the first three virial coefficients.…”

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confidence: 99%