The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long-range correlations, which behave as ϳ1/r in three and ϳln(L/r) in two dimensions. We calculate the corresponding structure factors over the whole range of wave numbers, and find good agreement with two-dimensional molecular dynamics simulations. It is also shown by means of a mode coupling calculation, how the mean field values for the steady-state temperature and collision frequency, as obtained from the Enskog-Boltzmann equation, are renormalized by long wavelength hydrodynamic fluctuations.

We show, using extensive molecular dynamics simulations, that the dynamics of the electric double layer (EDL) is very much dependent on the wettability of the charged surface on which the EDL develops. For a wetting surface, the dynamics, characterized by the so-called zeta potential, is mainly controlled by the electric properties of the surface, and our work provides a clear interpretation for the traditionally introduced immobile Stern layer. In contrast, the immobile layer disappears for nonwetting surfaces, and the zeta potential deduced from electrokinetic effects is considerably amplified by the existence of a slippage at the solid substrate.

We analyze the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading (ln N/N) corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit (N→ϱ), we estimate the free energy of a defect-free crystal of particles interacting through an r Ϫ12 potential. We also estimate the free energy of perfect hard-sphere crystal near coexistence: at 3 ϭ1.0409, the excess free energy of a defect-free hard-sphere crystal is 5.918 89(4)kT per particle. This, however, is not the free energy of an equilibrium hard-sphere crystal. The presence of a finite concentration of vacancies results in a reduction of the free energy that is some two orders of magnitude larger than the present error estimate. © 2000 American Institute of Physics. ͓S0021-9606͑00͒50912-X͔The earliest numerical technique to compute the free energy of crystalline solids was introduced some 30 years ago by Hoover and Ree. 1,2 At present, the ''single-occupancycell'' method of Ree and Hoover is less widely used than the so-called ''Einstein-crystal'' method proposed by Frenkel and Ladd. 3 The latter method employs thermodynamic integration of the Helmholtz free energy along a reversible artificial pathway between the system of interest and an Einstein crystal. The Einstein crystal serves as a reference system, as its free energy can be computed analytically. Since its introduction, the Einstein-crystal method has been used extensively in studies of phase equilibria involving crystalline solids. For numerical reasons-to suppress a weak divergence of the integrand-the Einstein-crystal method calculations have to be carried out at fixed center of mass. The free energy of the reference crystal is also calculated under the center-of-mass constraint, and the final calculated free energy of the unconstrained crystal is determined by correcting for the effect of imposing the constraint in the calculations. In the original paper, the fixed center-of-mass constraint was only applied to the particle coordinates, but not to the corresponding momenta. This is irrelevant as long as one computes the free-energy difference between two structures that have either both constrained or both unconstrained centers of mass. However, when computing the absolute free energy of a crystal, one needs to transform from the constrained to the unconstrained system. In the original paper, this transformation was not performed consistently. This resulted in a small but noticeable effect on the computed absolute free energy of the crystal. Below, we describe the proper approach to calculate the free energy of arbitrary molecular crystalline solids. The derivation differs from the earlier work in two respects: first, we explicitly show the effect of momentum constraints. And second, we generalize the expression to an arbitrary crystal containing atoms or molecules with different masses.The main point of interest involves the calculation of the partition function of a crystal...