Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.Comment: 3 pages, 1 figur

Communication: Inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities

A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The proposal is illustrated by using recent Monte Carlo simulation data for the pressure of a binary mixture. It is further shown to exhibit high internal consistency.Comment: 4 pages, 2 figures; v2: Simulation data for one-component hard spheres included in Fig.

Depletion potential in the infinite dilution limit

The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the Rational Function Approximation method for the structural properties of hard-sphere mixtures [S. B. Yuste, A. Santos, and M. L\'opez de Haro, J. Chem. Phys. {\bf 108}, 3683 (1998)]. The cases of equal solute particles and of one big particle and a hard planar wall in a background monodisperse hard-sphere fluid are explicitly analyzed. An improvement over the performance of the Percus-Yevick theory and good agreement with available simulation results are foundComment: 10 pages, 5 figures; v2: few minor additions and reduction in the number of figures; v3: Fig. 2 corrected (see http://dx.doi.org/10.1063/1.4874639

Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid

The contact values $g(\sigma,\sigma')$ of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution $f(\sigma)$ are considered. A ``universality'' assumption is introduced, according to which, at a given packing fraction $\eta$, $g(\sigma,\sigma')=G(z(\sigma,\sigma'))$, where $G$ is a common function independent of the number of components (either finite or infinite) and $z(\sigma,\sigma')=[2 \sigma \sigma'/(\sigma+\sigma')]\mu_2/\mu_3$ is a dimensionless parameter, $\mu_n$ being the $n$-th moment of the diameter distribution. A cubic form proposal for the $z$-dependence of $G$ is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express $G(z)$ in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations.Comment: 9 pages, 7 figure

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

A simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction $\phi_\text{J}$ of the polydisperse system as a simple function of $M_1M_3/M_2^2$, where $M_k$ is the $k$th moment of the size distribution. An analysis of experimental and simulation data of $\phi_\text{J}$ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures.Comment: 5 pages, 3 figures; v2: slight changes plus new reference

Las cargazones del galeón de la Carrera de Poniente: primera mitad del siglo XVII

Editada en la Fundación Empresa PúblicaEl objetivo de este trabajo es discutir cómo la visión tradicional del comercio Acapulco-Manila, centrado en el envío, casi exclusivo, de plata con dirección a Filipinas, restringe el estudio del comercio exterior Nueva España-Asia y desdeña al grupo de mercancías remitidas desde México a las islas de Poniente para subvenir las necesidades de la administración española. En ese sentido el origen de las mercancías, la entrada y salida de barcos del puerto de Acapulco y los valores de los productos alistados para la gobernación insular permiten establecer una tipología de las cargazones del galeón.The aim of this work is to discuss the traditional view of the Acapulco-Manila business, which so far has been exclusively centred on the silver trade. The significant merchandise trade has been neglected. In the paper we examine de volume and value of ships arriving and departing from Acapulco, which allows us to have a better knowledge of the «galleon cargo».Publicad