Erratum: “Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular-dynamics simulations” [J. Chem. Phys. 120, 9113 (2004)]

Robles, Miguel; Haro, M. López de; Santos, Andrés

doi:10.1063/1.2390712

Cited by 16 publications

(32 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

Self Cite

View full text Add to dashboard Cite

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)].

show abstract

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…We have shown that this approach gives the exact solution of the OZ equation with the PY closure. From that perspective, our work extends, on one hand, the Lebowitz solution for 3D-sphere mixtures [80] to higher dimensions and, on the other hand, the PY solution for one-component hyperspheres [3,7,45,62] to the case of mixtures.…”

Section: Discussionmentioning

confidence: 60%

Multicomponent fluids of hard hyperspheres in odd dimensions

Rohrmann

Santos

2011

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

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)] 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.

show abstract

“…Again η f is unknown but we may once more recur to the one-component case. For this system, Colot and Baus [19] have conjectured that (η f /η cp ) 1/d becomes independent of d for high d. Further, from the analysis of the results in d = 3, 4, 5 [16,20], and d = 7 [23] one finds that η f ≈ 1.3. Since at freezing or melting the Helmholtz free energies of the fluid and the solid should be of the same order of magnitude, by considering the former given by the second virial approximation and the latter as obtained from free volume theory with the estimate (η f /η cp ) 1/d ≈ 0.8, we obtain the rough estimate η f ≈ 2.3.…”

mentioning

confidence: 88%

“…Although there had been a few earlier papers [15,16] dealing with hard spheres in dimensions greater than three, it was after the pioneer work of Frisch et al [17] in which they showed that the classical hard-sphere fluid in infinitely many dimensions was amenable to full analytical solution, that studies of high dimensional hard-sphere systems became common over the years [4,18,19,20,21,22,23]. The fact that features such as the freezing transition are present in all dimensionalities (except for d = 1) and the parallel between high spatial dimensions and limiting high density situations that seems to exist in fluids (with the added bonus of greater mathematical simplicity as one increases the number of dimensions) suggest that one can gain insight into the thermodynamic behavior of say three-dimensional systems by looking at a similar problem in higher dimensions.…”

mentioning

confidence: 99%

Demixing can occur in binary hard-sphere mixtures with negative nonadditivity

Santos

Haro

2005

Phys. Rev. E

View full text Add to dashboard Cite

A binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma = sigma(2)/sigma(1) < 1 and a nonadditivity parameter Delta = 2 sigma(12)/(sigma(1) + sigma(2)) - 1 is considered in infinitely many dimensions. From the equation of state in the second virial approximation (which is exact in the limit d--> infinity) a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2(-d) is found, even for slightly negative nonadditivity, if Delta >-1/8 (ln gamma)(2). Arguments concerning the stability of the demixing with respect to freezing are provided.

show abstract

Erratum: “Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular-dynamics simulations” [J. Chem. Phys. 120, 9113 (2004)]

Cited by 16 publications

References 1 publication

Virial series for fluids of hard hyperspheres in odd dimensions

Virial series for fluids of hard hyperspheres in odd dimensions

Multicomponent fluids of hard hyperspheres in odd dimensions

Demixing can occur in binary hard-sphere mixtures with negative nonadditivity

Contact Info

Product

Resources

About