In the density functional theory formulation of molecular solvents, the solvation free energy of a solute can be obtained directly by minimization of a functional, instead of the thermodynamic integration scheme necessary when using atomistic simulations. In the homogeneous reference fluid approximation, the expression of the free-energy functional relies on the direct correlation function of the pure solvent. To obtain that function as exactly as possible for a given atomistic solvent model, we propose the following approach: first to perform molecular simulations of the homogeneous solvent and compute the position and angle-dependent two-body distribution functions, and then to invert the Ornstein-Zernike relation using a finite rotational invariant basis set to get the corresponding direct correlation function. This rather natural scheme is proved, for the first time to our knowledge, to be valuable for a dipolar solvent involving long range interactions. The resulting solvent free-energy functional can then be minimized on a three-dimensional grid around a solute to get the solvent particle and polarization density profiles and solvation free energies. The viability of this approach is proven in a comparison with "exact" molecular dynamics calculations for the simple test case of spherical ions in a dipolar solvent.

Recent studies of the Lyapunov spectrum of the hard sphere fluid reveal that there are "hydrodynamic" Lyapunov exponents corresponding to collective perturbations in phase space. We show that these collective perturbations are due to the conservation of certain quantities during collisions. These new conservation laws generate new hydrodynamic fields, just as the conservation of mass, momentum, and energy generate the density, velocity, and temperature fields. We then construct a detailed theory of the new hydrodynamic fields using a kinetic theory approach. This theory predicts several properties of the modes, but not all of them. This suggests that the underlying idea is correct, but a detailed theory must be elaborated in another way. The hydrodynamic exponents are not related in a simple way to the transport coefficients.

Molecular dynamics simulations of the inelastic hard sphere model for granular media have been done to study the heat conduction between two parallel plates. The results show that Fourier's law is not valid and a new term proportional to the density gradient must be added to compute the heat flux. The new transport coefficient associated with the density gradient dependence has been measured vanishing in the case of elastic collisions.

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Results of Monte Carlo and molecular-dynamics simulations of Lennard-Jones systems are presented in order to compare various methods of computing interfacial properties of liquid-vapour systems. For the computation of the surface tension gamma a new method is developed, which makes use of the Bennett procedure for calculating free-energy differences. The method is compared with the conventional route to the surface tension via the virial expression. For the temperature derivative of the surface tension, gamma /dT, both a fluctuation equation and the Gibbs adsorption equation are employed. It is found that d gamma /dT is determined more accurately by the absorption equation (through the surface entropy). Results of simulations of binary Lennard-Jones mixtures are also presented. For the argon-krypton system, values of the adsorption of argon at the interface are determined from density profiles, and are compared with values predicted by the adsorption equation. Positive adsorption of argon manifests itself in krypton-rich mixtures as a significant 'bump' in the argon density profile near the interface.