The general expressions, valid for any potential, for the calculation of elastic constants through computer simulation are given. At zero temperature, the elastic constants are found to be the sum of a generalization of the Born term and a term accounting for internal relaxations that arise when a system with more than one atom in the primitive unit cell is strained. The fluctuation formulae used in finite temperature simulations are found to be straightforward generalizations of those used for pair potentials. The connection between the finite-temperature and zero-temperature methods is also made.

The local stress tensor commonly used in statistical mechanics is cast in a form useful for molecular dynamics (MD) simulations. It is then used to derive fluctuation formulas for the local elastic constants of a system. The formulas are used in an MD measurement of the local elastic constants of an ideal crystal which are found to be in good agreement with the bulk elastic constants of the same system.

We present classical density functional theory calculations of the free energy landscape for fluids below their triple point as a function of density and crystallinity. We find that for both a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.PACS numbers: 82.60. Nh,87.15.Nn,05.20.Jj Crystallization is an intricate process of fundamental importance in many areas of physics, chemistry and engineering. The classical picture of crystallization from supersaturated solutions goes back to Gibbs and consists of the spontaneous formation of crystalline clusters which then either grow or shrink depending on the relative importance of the free energy gain due to the lower bulk free energy of the crystal cluster and the free energy penalty due to the surface tension between the two phases. In this picture, the local density is the only order parameter: the crystalline cluster is (in general) denser than the fluid. In recent years, this picture has been called into question by simulation, theory and experiment for the particular and important case of the crystallization of globular proteins. ten Wolde and Frenkel (hereafter tWF) showed by means of simulation that the free energy landscape of protein crystal clusters as a function of the number of atoms in the cluster and the "crystallinity " favored paths leading from no clusters to clusters with low order to ordered clusters over paths moving from no clusters directly to ordered clusters [1]. This picture was confirmed by Talanquer and Oxtoby [2] and Shiryayev and Gunton[3] who showed using a parameterized van der Waals-type model of globular proteins that surface wetting did indeed lower the free energy of crystal clusters. More recently, the simple picture has also been challenged by novel experimental investigations. Vekilov and co-workers have shown that, prior to crystallization, protein solutions harbor metastable droplets of dense fluid and they have suggested that these droplets are necessary precursors of crystallization [4,5,6,7]. The picture that emerges is one of the formation of metastable droplets of dense fluid which then subsequently crystallize. In this paper, we show by means of classical density functional theory calculations that there is an intrinsic free-energy advantage in first densifying into a metastable densefluid state and then crystallizing rather than following the classical path which goes directly from gas to crystal. Furthermore, our calculations suggest that a similar advantage exists for fluids of small molecules, modeled here via the Lennard-Jones (LJ) interaction, thus indicating that this mechanism may underlie most crystallization processes.The starting point for our analysis is classical density functional theory (DFT) which is based...

The revised Enskog approximation for a fluid of hard spheres which lose energy upon collision is discussed for the case that the energy is lost from the normal component of the velocity at collision but is otherwise arbitrary. Granular fluids with a velocity-dependent coefficient of restitution are an important special case covered by this model. A normal solution to the Enskog equation is developed using the Chapman-Enskog expansion. The lowest order solution describes the general homogeneous cooling state and a generating function formalism is introduced for the determination of the distribution function. The first order solution, evaluated in the lowest Sonine approximation, provides estimates for the transport coefficients for the Navier-Stokes hydrodynamic description. All calculations are performed in an arbitrary number of dimensions.

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