This Letter presents variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.

Anomolous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations

We have developed a new technique, based on the standard Monte Carlo simulation method with Markov chain sampling, in which a set of three dimensional particle configurations are generated that are consistent with the experimentally measured structure factor. A(Q), and radial distribution function, g(r), of a liquid or other disordered system. Consistency is determined by a standard χ2 test using the experimental errors. No input potential is required, we present initial results for liquid argon. Since the technique can work directly from the structure factor it promises to be useful for modelling the structures of glasses or amorphous materials. It also has other advantages in multicomponent systems and as a tool for experimental data analysis.

Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures

The ability to assemble nanoscopic components into larger structures and materials depends crucially on the ability to understand in quantitative detail and subsequently "engineer" the interparticle interactions. This Review provides a critical examination of the various interparticle forces (van der Waals, electrostatic, magnetic, molecular, and entropic) that can be used in nanoscale self-assembly. For each type of interaction, the magnitude and the length scale are discussed, as well as the scaling with particle size and interparticle distance. In all cases, the discussion emphasizes characteristics unique to the nanoscale. These theoretical considerations are accompanied by examples of recent experimental systems, in which specific interaction types were used to drive nanoscopic self-assembly. Overall, this Review aims to provide a comprehensive yet easily accessible resource of nanoscale-specific interparticle forces that can be implemented in models or simulations of self-assembly processes at this scale.

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Nanoscale Forces and Their Uses in Self‐Assembly

We review the existing simulation data and equations of state for the Lennard-Jones (LJ) fluid, and present new simulation results for both the cut and shifted and the full LJ potential. New parameters for the modified Benedict-Webb-Rubin (MBWR) equation of state used by Nicolas, Gubbins, Streett and Tildesley are presented. In contrast to previous equations, the new equation is accurate for calculations of vapour-liquid equilibria. The equation also accurately correlates pressures and internal energies from the triple point to about 4·5 times the critical temperature over the entire fluid range. An equation of state for the cut and shifted LJ fluid is presented and compared with the simulation data of this work, and previously published Gibbs ensemble data. The MBWR equation of state can be extended to mixtures via the van der Waals one-fluid theory mixing rules. Calculations for binary fluid mixtures are found to be accurate when compared with Gibbs ensemble simulations.

The Lennard-Jones equation of state revisited

As a continuation of our work on spherical associating molecules, we have derived expressions for changes in the thermodynamic properties due to association in mixtures of molecules with multiple bonding sites. The equations are written in terms of a hard-core reference whose pair distribution function is known. In practise, the hard-sphere reference mixture is the easiest to use. A reference system of homonuclear chains is examined in order to account for asymmetries in molecular shape; chains are constructed by bonding equal-sized spheres together. An equation of state for hard-sphere chains is obtained which is in good agreement with recent simulation data. Expressions for mixtures of homonuclear chains of different sizes are also presented. The approach is extended to examine associating chain molecules with multiple bonding sites. The phase equilibria of non-associating chains, and of associating chains with one or two bonding sites are determined. In this study, the separate effects of molecular ass...

Phase equilibria of associating fluids

The perturbation theory of liquids developed recently by Weeks, Chandler, and Andersen (WCA) is examined in detail: Each assumption introduced by these authors is tested by comparison with "exact" computer results. It is shown that the basic assumptions of WCA are justified. An improved expression for the radial distribution function of the hard-sphere gas enables us to correct for some further inconsistent assumptions of the WCA theory. We then succeed in giving simple analytical expressions for the thermodynamic functions of the Lennard-Jones fluid shown to be quite good at high density. We show that the remainder of the perturbation series, which converges slowly at lower density, can be evaluated with the help of the Percus-Yevick equation. We therefore possess a unified theory of liquids which is especially simple at high density. Finally we reexpress the original WCA theory in an analytical form.

Equilibrium Theory of Simple Liquids

The phase diagram of dipolar hard spheres has been determined by Monte Carlo simulation for reduced densities ${\mathrm{\ensuremath{\rho}}}^{\mathrm{*}}$ ranging from 0.02--0.3 and reduced temperatures ${\mathit{T}}^{\mathrm{*}}$ from 0.08--0.25. For ${\mathit{T}}^{\mathrm{*}}$\ensuremath{\lesssim}0.15 the particles are found to associate to form chains which at the highest density are in a polarized ferroelectric state.

Chain formation in low density dipolar hard spheres: A Monte Carlo study

We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the logarithmic Coulomb interaction are eliminated by confining the particles to the surface of a sphere. The results are compared to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions; in this case the infinite tail of the Coulomb interaction is treated as a perturbation. The “exact” simulation results are used to test various approximate theories, including a semiempirical modification of the hypernetted-chain (HNC) integral equation. The OCP freezing transition is located at a couplingγ= e2/kBT−140.

A Monte Carlo study of the classical two-dimensional one-component plasma

The perturbation theory of simple liquids has recently met with great success. In this paper we present a critical discussion of this theory. The unperturbed system is, as usual, identified with hard spheres whose diameters are determined by a self-consistency requirement. The thermodynamics of the system, including the first-order contribution, can be computed analytically. The equation of state thus obtained is used to discuss experimental results on non-polar liquids.

Perturbation theory for the thermodynamic properties of simple liquids

We show, by performing Monte Carlo simulations along a low temperature isotherm, that the structural behavior of a system of dipolar hard spheres transforms from a chainlike association at low density to a ferroelectric ordering at high density. The influence of the temperature variation and the dependence on boundary conditions are investigated.

Jean-Jacques Weis

Papers

Equilibrium Theory of Simple Liquids

Chain formation in low density dipolar hard spheres: A Monte Carlo study

A Monte Carlo study of the classical two-dimensional one-component plasma

Perturbation theory for the thermodynamic properties of simple liquids

Orientational and structural order in strongly interacting dipolar hard spheres