How `sticky' are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range $\lambda$ at a given packing fraction and reduced temperature can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter $\tau$. Such an equivalence cannot hold for the radial distribution function since this function has a delta singularity at contact in the SHS case, while it has a jump discontinuity at $r=\lambda$ in the SW case. Therefore, the equivalence is explored with the cavity function $y(r)$. Optimization of the agreement between y_{\sw} and y_{\shs} to first order in density suggests the choice for $\tau$. We have performed Monte Carlo (MC) simulations of the SW fluid for $\lambda=1.05$, 1.02, and 1.01 at several densities and temperatures $T^*$ such that $\tau=0.13$, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)]. Although, at given values of $\eta$ and $\tau$, some local discrepancies between y_{\sw} and y_{\shs} exist (especially for $\lambda=1.05$), the SW data converge smoothly toward the SHS values as $\lambda-1$ decreases. The approximate mapping y_{\sw}\to y_{\shs} is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y_{\shs} the solution of the Percus--Yevick equation as well as the rational-function approximation, the radial distribution function $g(r)$ of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.Comment: 14 pages, including 3 tables and 14 figures; v2: typo in Eq. (5.1) corrected, Fig. 14 redone, to be published in JC

A rotating cylinder in an asymptotically locally anti-de Sitter background

A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution for the exterior solution is found which depends both on the rotation of the interior and on its radius. For values of these parameters less than a certain limit, the exterior solution is shown to be locally isomorphic to the Linet-Tian solution. For values larger than another limit, it is shown that the exterior solution extends into a region which contains closed timelike curves. At large distances from the source, the space-time is shown to be asymptotic locally to anti-de Sitter space.Comment: To appear in Classical and Quantum Gravit

Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal

The contact values $g_{ij}(\sigma_{ij})$ of the radial distribution functions of a $d$-dimensional mixture of (additive) hard spheres are considered. A `universality' assumption is put forward, according to which $g_{ij}(\sigma_{ij})=G(\eta, z_{ij})$, where $G$ is a common function for all the mixtures of the same dimensionality, regardless of the number of components, $\eta$ is the packing fraction of the mixture, and $z_{ij}$ is a dimensionless parameter that depends on the size distribution and the diameters of spheres $i$ and $j$. For $d=3$, this universality assumption holds for the contact values of the Percus--Yevick approximation, the Scaled Particle Theory, and, consequently, the Boublik--Grundke--Henderson--Lee--Levesque approximation. Known exact consistency conditions are used to express $G(\eta,0)$, $G(\eta,1)$, and $G(\eta,2)$ in terms of the radial distribution at contact of the one-component system. Two specific proposals consistent with the above conditions (a quadratic form and a rational form) are made for the $z$-dependence of $G(\eta,z)$. For one-dimensional systems, the proposals for the contact values reduce to the exact result. Good agreement between the predictions of the proposals and available numerical results is found for $d=2$, 3, 4, and 5.Comment: 10 pages, 11 figures; Figure 1 changed; Figure 5 is new; New references added; accepted for publication in J. Chem. Phy

Fourth virial coefficients of asymmetric nonadditive hard-disc mixtures

The fourth virial coefficient of asymmetric nonadditive binary mixtures of hard disks is computed with a standard Monte Carlo method. Wide ranges of size ratio ($0.05\leq q\leq 0.95$) and nonadditivity ($-0.5\leq \Delta\leq 0.5$) are covered. A comparison is made between the numerical results and those that follow from some theoretical developments. The possible use of these data in the derivation of new equations of state for these mixtures is illustrated by considering a rescaled virial expansion truncated to fourth order. The numerical results obtained using this equation of state are compared with Monte Carlo simulation data in the case of a size ratio $q=0.7$ and two nonadditivities $\Delta=\pm 0.2$.Comment: 9 pages, 7 figures; v2: section on equation of state added; tables moved to supplementary material (http://jcp.aip.org/resource/1/jcpsa6/v136/i18/p184505_s1#artObjSF

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths $\lambda-1$ ranging from 0.1 to 1.0, in units of the diameter $\sigma$ of the particles. For each one of these widths, several densities $\rho$ and temperatures $T$ in the ranges $0.1\leq\rho\sigma^3\leq 0.8$ and $T_c(\lambda)\lesssim T\lesssim 3T_c(\lambda)$, where $T_c(\lambda)$ is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. {\bf 100}, 3079, 6665 (1994)] and the non-perturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. {\bf 101}, 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory does for long ranges and high densities.Comment: 10 pages, 10 figure