Structural precursor to freezing: An integral equation study

Recent simulation studies have drawn attention to the shoulder which forms in the second peak of the radial distribution function of hard-spheres at densities close to freezing and which is associated with local crystalline ordering in the dense fluid. We address this structural precursor to freezing using an inhomogeneous integral equation theory capable of describing local packing constraints to a high level of accuracy. The addition of a short-range attractive interaction leads to a well known broadening of the fluid-solid coexistence region as a function of attraction strength. The appearence of a shoulder in our calculated radial distribution functions is found to be consistent with the broadened coexistence region for a simple model potential, thus demonstrating that the shoulder is not exclusively a high density packing effect

A globally accurate theory for a class of binary mixture models

Using the self-consistent Ornstein-Zernike approximation (SCOZA) results for the 3D Ising model, we obtain phase diagrams for binary mixtures described by decorated models. We obtain the plait point, binodals, and closed-loop coexistence curves for the models proposed by Widom, Clark, Neece, and Wheeler. The results are in good agreement with series expansions and experiments.Comment: 16 pages, 10 figure

Federated authentication and authorisation for e-science

The Grid and Web service community are defining a range of standards for a complete solution for security. The National e-Science Centre (NeSC) at the University of Glasgow is investigating how the various pre-integration components work together in a variety of e-Science projects. The EPSRC-funded nanoCMOS project aims to allow electronics designers and manufacturers to use e-Science technologies and expertise to solve problems of device variability and its impact on system design. To support the security requirements of nanoCMOS, two NeSC projects (VPMan and OMII-SP) are providing tools to allow easy configuration of security infrastructures, exploiting previous successful projects using Shibboleth and PERMIS. This paper presents the model in which these tools interoperate to provide secure and simple access to Grid resources for non-technical users

Mesoscopic theory for size- and charge- asymmetric ionic systems. I. Case of extreme asymmetry

A mesoscopic theory for the primitive model of ionic systems is developed for arbitrary size, $\lambda=\sigma_+/\sigma_-$, and charge, $Z=e_+/|e_-|$, asymmetry. Our theory is an extension of the theory we developed earlier for the restricted primitive model. The case of extreme asymmetries $\lambda\to\infty$ and $Z \to\infty$ is studied in some detail in a mean-field approximation. The phase diagram and correlation functions are obtained in the asymptotic regime $\lambda\to\infty$ and $Z \to\infty$, and for infinite dilution of the larger ions (volume fraction $n_p\sim 1/Z$ or less). We find a coexistence between a very dilute 'gas' phase and a crystalline phase in which the macroions form a bcc structure with the lattice constant $\approx 3.6\sigma_+$. Such coexistence was observed experimentally in deionized aqueous solutions of highly charged colloidal particles

The density functional theory of classical fluids revisited

We reconsider the density functional theory of nonuniform classical fluids from the point of view of convex analysis. From the observation that the logarithm of the grand-partition function $\log \Xi [\phi]$ is a convex functional of the external potential $\phi$ it is shown that the Kohn-Sham free energy ${\cal A}[\rho]$ is a convex functional of the density $\rho$. $\log \Xi [\phi]$ and ${\cal A}[\rho]$ constitute a pair of Legendre transforms and each of these functionals can therefore be obtained as the solution of a variational principle. The convexity ensures the unicity of the solution in both cases. The variational principle which gives $\log \Xi [\phi]$ as the maximum of a functional of $\rho$ is precisely that considered in the density functional theory while the dual principle, which gives ${\cal A}[\rho]$ as the maximum of a functional of $\phi$ seems to be a new result.Comment: 10 page

Long wavelength structural anomalies in jammed systems

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wavenumber $k$, we argue that the anomalous behavior in the static structure factor, $S(k) \sim k$, is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that $S(0) \to 0$ at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that jamming transitions of frictional spheres lie at lower packing fractions that that for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.Comment: 8 pages, 6 figure captions. Completely revised version to appear in Phys. Rev.

Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach

Using a liquid-state approach based on Ornstein-Zernike equations, we study the behavior of a fluid inside a porous disordered matrix near the liquid-gas critical point.The results obtained within various standard approximation schemes such as lowest-order $\gamma$-ordering and the mean-spherical approximation suggest that the critical behavior is closely related to that of the random-field Ising model (RFIM).Comment: 10 pages, revtex, to appear in Physical Review Letter

Thermo-statistical description of gas mixtures from space partitions

The new mathematical framework based on the free energy of pure classical fluids presented in [R. D. Rohrmann, Physica A 347, 221 (2005)] is extended to multi-component systems to determine thermodynamic and structural properties of chemically complex fluids. Presently, the theory focuses on $D$-dimensional mixtures in the low-density limit (packing factor $\eta < 0.01$). The formalism combines the free-energy minimization technique with space partitions that assign an available volume $v$ to each particle. $v$ is related to the closeness of the nearest neighbor and provides an useful tool to evaluate the perturbations experimented by particles in a fluid. The theory shows a close relationship between statistical geometry and statistical mechanics. New, unconventional thermodynamic variables and mathematical identities are derived as a result of the space division. Thermodynamic potentials $\mu_{il}$, conjugate variable of the populations $N_{il}$ of particles class $i$ with the nearest neighbors of class $l$ are defined and their relationships with the usual chemical potentials $\mu_i$ are established. Systems of hard spheres are treated as illustrative examples and their thermodynamics functions are derived analytically. The low-density expressions obtained agree nicely with those of scaled-particle theory and Percus-Yevick approximation. Several pair distribution functions are introduced and evaluated. Analytical expressions are also presented for hard spheres with attractive forces due to K\^ac-tails and square-well potentials. Finally, we derive general chemical equilibrium conditions.Comment: 14 pages, 8 figures. Accepted for publication in Physical Review

Gas-liquid critical point in ionic fluids

Based on the method of collective variables we develop the statistical field theory for the study of a simple charge-asymmetric $1:z$ primitive model (SPM). It is shown that the well-known approximations for the free energy, in particular DHLL and ORPA, can be obtained within the framework of this theory. In order to study the gas-liquid critical point of SPM we propose the method for the calculation of chemical potential conjugate to the total number density which allows us to take into account the higher order fluctuation effects. As a result, the gas-liquid phase diagrams are calculated for $z=2-4$. The results demonstrate the qualitative agreement with MC simulation data: critical temperature decreases when $z$ increases and critical density increases rapidly with $z$.Comment: 18 pages, 1 figur

Exact factorization of correlation functions in 2-D critical percolation

By use of conformal field theory, we discover several exact factorizations of higher-order density correlation functions in critical two-dimensional percolation. Our formulas are valid in the upper half-plane, or any conformally equivalent region. We find excellent agreement of our results with high-precision computer simulations. There are indications that our formulas hold more generally.Comment: 6 pages, 3 figures. Oral presentation given at STATPHYS 23. V2: Minor additions and corrections, figures improve