Related papers: Virial series for fluids of hard hyperspheres in o…
We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integro-differential equations. This work generalizes an approach we developed previously for hard discs. We numerically obtain both the pair…
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…
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…
Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial…
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…
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…
The fourth virial coefficient is calculated exactly for a fluid of hard spheres in odd dimensions up to 11.
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 theory
Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical…
Virial coefficients for the two-dimensional hard-disk fluid, when expressed in powers of density relative to maximum close packing, lead to an accurate closed equation-of-state for the equilibrium fluid, analogous to that recently found for…
We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory…
An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically…
As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus--Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the…
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 \textbf{83}, 011201…
A new closed virial equation of state of hard-sphere fluids is proposed which reproduces the calculated or estimated values of the first sixteen virial coefficients at the same time as giving very good accuracy when compared with computer…
The equation of state for five-dimensional hard hyperspheres arising as a weighted average of the Percus-Yevick compressibility (3/5) and virial (2/5) equations of state is considered. This Carnahan-Starling-like equation turns out to be…
The fourth virial coefficient of additive hard-sphere mixtures, as predicted by the Percus-Yevick (PY) and hypernetted-chain (HNC) theories, is derived via the compressibility, virial, and chemical-potential routes, the outcomes being…
The demixing transition of a binary fluid mixture of additive hard spheres is analyzed for different size asymmetries by starting from the exact low-density expansion of the pressure. Already within the second virial approximation the fluid…
Based on the survey of the literatures on the new improvements on the equation of state (EOS) for the hard sphere fluids, we here compare lots of different EOSs and present a very accurate equation of state for this kind of fluids. The new…
The question of whether the known virial coefficients are enough to determine the packing fraction $\eta_\infty$ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived…