Simulation-based equation of state of the hard disk fluid and prediction of higher-order virial coefficients

We present new molecular dynamics results for the pressure of the pure hard disk fluid up to the hexatic transition (about reduced density 0.9). The data combined with the known virial coefficients (up to $B_{10}$) are used to build an equation of state, to estimate higher-order virial coefficients, and also to obtain a better value of $B_{10}$. Finite size effects are discussed in detail. The ``van der Waals-like'' loop reported in literature in the vicinity of the fluid/hexatic transition is explained by suppressed density fluctuations in the canonical ensemble. The inflection point on the pressure-density dependence is predicted by the equation of state even if the hexatic phase simulation data are not considered.Comment: 9 pages, 3 figures, presented at The Seventh Liblice Conference on the Statistical Mechanics of Liquids (Lednice, Czech Republic, June 11--16, 2006

Nonanalytical equation of state of the hard sphere fluid

An equation of state of the hard sphere fluid which is not analytical at the freezing density is proposed and tested. The nonanalytical term is based on the the classical nucleation theory and is able to capture the observed ``anomalous increase'' of pressure at high densities. It is combined with the virial expansion at low densities.Comment: 5 pages, 3 figure

Optimized Periodic Coulomb Potential in Two Dimension

The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us efficient calculations of any periodic (long-ranged) potential up to high precision. We discuss the parameter space of the optimized potential for the periodic Coulomb potential. Compared to the analytic Ewald potential, the optimized potentials can reach higher precisions by up to several orders of magnitude. We explicitly give simple expressions for fast calculations of the periodic Coulomb potential where the summation in reciprocal space is reduced to a few terms

Glassiness in Simple Liquids

In previous work the parameter of glassiness was introduced to distinguish between a liquid and a glass, using a formal analogy with the quantum Bose system. The glassiness is defined in such a way that it is unity in a frozen system and less than one in a liquid. In the present letter we revise first the results obtained for the glassiness in a hard sphere liquid as a function of the density. Then we investigate the influence of an attractive potential by obtaining the glassiness as a function of the density, temperature and the attractive tail when a square well potential is added to the hard core.Comment: 8 pages, 4 figure

Polarization effects at the surface of aqueous alkali halide solutions

The polarizability of ions, with its strong influence on their surface affinity, is one of the crucial pieces of the complex puzzle that determines the surface properties of electrolyte solutions. Here, we investigate the electrical and structural properties of alkali halide solutions at a concentration of about 1.3 M using molecular dynamics simulations of polarizable water and ions models. We show that capillary fluctuations have a dramatic impact on the sampled quantities and that without removing their smearing effect, it would be impossible to resolve the local structure of the interfacial region. This procedure allows us to investigate in detail the dependence of the permanent and induced dipoles on the distance from the interface. The enhanced resolution gives us access to the surface charges, estimated using the Gouy-Chapman theory, despite the Debye length being shorter than the amplitude of capillary fluctuations

On extrapolation of virial coefficients of hard spheres

Several methods of extrapolating the virial coefficients, including those proposed in this work, are discussed. The methods are demonstrated on predicting higher virial coefficients of one-component hard spheres. Estimated values of the eleventh to fifteenth virial coefficients are suggested. It has been speculated that the virial coefficients, B_n, beyond B_{14} may decrease with increasing n, and may reach negative values at large n. The extrapolation techniques may be utilized in other fields of science where the art of extrapolation plays a role.Comment: 8 pages, 1 figur

"The numerical accuracy of truncated Ewald sums for periodic systems with long-range Coulomb interactions"

Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in the Ewald formulation. We derive an optimal choice for the Fourier-space cutoff given a screening parameter $\eta$. We find that the number of vectors in Fourier space required to achieve a given accuracy scales with $\eta^3$. The proposed method can be used to determine computationally efficient parameters for Ewald sums, to assess the quality of Ewald-sum implementations, and to compare different implementations.Comment: 6 pages, 3 figures (Encapsulated PostScript), LaTe

Optimum Monte Carlo Simulations: Some Exact Results

We obtain exact results for the acceptance ratio and mean squared displacement in Monte Carlo simulations of the simple harmonic oscillator in $D$ dimensions. When the trial displacement is made uniformly in the radius, we demonstrate that the results are independent of the dimensionality of the space. We also study the dynamics of the process via a spectral analysis and we obtain an accurate description for the relaxation time.Comment: 17 pages, 8 figures. submitted to J. Phys.

Chemical potential of quadrupolar two-centre Lennard-Jones fluids by gradual insertion

The gradual insertion method for direct calculation of the chemical potential by molecular simulation is applied in the NpT ensemble to different quadrupolar two-centre Lennard-Jones fluids at high density state points. The results agree well with Widom's test particle insertion but show at very high densities significantly smaller statistical uncertainties. The gradual insertion method, which is coupled here with preferential sampling, extends the density range where reliable information on the chemical potential can be obtained. Application details are reported

Logarithmic corrections in the aging of the fully-frustrated Ising model

We study the dynamics of the critical two-dimensional fully-frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be compatible with the value $z_c=2$. In a second step, the system is prepared in the paramagnetic phase and then quenched at its critical temperature $T_c=0$. Numerical evidences for the existence of logarithmic corrections in the aging regime are presented. These corrections may be related to the topological defects observed in other fully-frustrated models. The autocorrelation exponent is estimated to be $\lambda=d$ as for the Ising chain quenched at $T_c=0$.Comment: 12 pages, 9 figure