A new Hamiltonian method for deformation simulations is related to the Green-Kubo fluctuation theory through perturbation theory and linear-response theory. Numerical results for the bulk and shear viscosity coefficients are compared to corresponding Green-Kubo calculations. Both viscosity coefficients depend similarly on frequency, in a way consistent with enhanced "long-time tails."

Nonequilibrium molecular dynamic results of shear viscosity near the freezing density have a strain rate dependence that is best described by the Ree-Eyring hyperbolic arcsine relation. A square root dependence is not consistent with low gradient results or theoretical predictions. We conclude that symmetry, experiment, calculation, and theory all favor the Ree-Eyring form.

In order to understand the static and dynamic bases of macroscopic fracture mechanics, we study flawed microscopic crystals obeying Newton's equations of motion. The particles in these crystals interact with truncated Hooke's-law forces. The static results for energy, entropy, stress concentration, and crack structure are all consistent with expectations from macroscopic elasticity theory. Dynamic theory is less well developed. Our dynamic results illustrate the importance of surface energy and nonlinear terms in the interparticle forces in influencing crack morphology and propagation velocity. The propagating cracks, except in crystals preloaded nearly to the theoretical tensile strength, travel at speeds somewhat less than the long-wavelength Rayleigh surface-wave speed.

A novel fluid-transport calculation by computer simulation, via nonequilibrium molecular dynamics, of laboratory methods of transport measurement is described. Shear viscosity of soft-sphere (${r}^{\ensuremath{-}12}$ potential) and Lennard-Jones particles (${r}^{\ensuremath{-}12}\ensuremath{-}{r}^{\ensuremath{-}6}$ potential) has been obtained from molecular dynamic modeling of Couette flow. Soft-sphere deviations from Enskog theory are similar to those found for hard spheres by Alder, Gass, and Wainwright, using time-correlations of equilibrium molecular dynamic system fluctuations. For the Lennard-Jones shear viscosity near the triple-point region, there is agreement between the equilibrium calculation of Levesque, Verlet, and Kurkijarvi and the nonequilibrium results using 108 atoms in a cube. However, systems two and three cubes wide give lower results, which, when extrapolated with inverse width, yield close agreement with the experimental argon shear viscosity. Comparison of the Lennard-Jones shear viscosity with experimental argon data along the saturated vapor-pressure line of argon confirms our successful simulation of macroscopic viscous flow with few-particle nonequilibrium molecular dynamic systems. A new result of the nonequilibrium molecular dynamics is the characterization of nonequilibrium distribution functions, which might provide the basis for a perturbation theory of transport. Since momentum transport is primarily accomplished by the repulsive potential core for high temperatures, the Lennard-Jones shear viscosity must behave like the soft-sphere system for high temperatures [viscosity divided by ${(\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e})}^{\frac{2}{3}}$ is a function of density divided by ${(\mathrm{temperature})}^{\mathrm{\textonequarter{}}}$]. In fact, the calculated excess shear viscosity (that part above the zero-density temperature dependence) has been successfully correlated in terms of the 12th-power scaling variables for temperatures as low as the critical value (along the freezing line). The utilization of soft-sphere scaling variables yields relatively simple functions for describing both the excess shear viscosity and the thermal-conductivity behavior throughout the fluid phase. The introduction of these scaling variables also clearly reveals two features: (i) weak temperature dependence, and (ii) the sign of the temperature derivative at constant density (negative for shear viscosity and positive for thermal conductivity). While both of these features have been experimentally observed in simple fluid experimental data, their cause has not been previously traced to the dominance of the core potential. Thus, the soft-sphere scaling variables should be useful for correlating experimental data.

The mathematical analogy between the elastic stress due to particle displacements in Hooke's law solids and the viscous stress due to velocity gradients in incompressible fluids correlates two interesting phenomena. In a two-dimensional crystal the elastic restoring force opposing particle displacements approaches zero with increasing crystal size, leading to a logarithmically diverging rms displacement in the large-system limit. The vanishing of the solid-phase force is mathematically analogous to the lack of viscous damping for a particle moving slowly through a two-dimensional incompressible fluid. These two continuum results are compared with discrete-particle computer simulations of two-dimensional solids and fluids. The divergence predicted by macroscopic elasticity theory agrees quantitatively with computer results for two-dimensional harmonic crystals. These same results can also be correlated with White's experimental study of the viscous resistance to a cylinder (a falling wire) moving slowly through a viscous fluid. The agreement is good. Finally, we carried out a computer study of a two-dimensional fluid confined between two moving walls (plane Couette flow). Despite theoretical predictions that transport coefficients in two-dimensional systems diverge, no viscosity anomalies were observed under the conditions of the computer simulation.

Nonequilibrium molecular dynamic simulation of liquid argon yields the strain-rate dependence of shear viscosity. Near the triple point the apparent viscosity decreases with increasing strain rate; the extrapolated zero-gradient viscosity is consistent with the equilibrium Green-Kubo viscosity calculated by Levesque, Verlet, and Kurkijarvi. At higher temperatures along the saturated vapor pressure line, our results are insensitive to the strain rate and agree well with experimental data for liquid argon.

Cell-like models for many-body thermodynamic properties can be derived by considering the motion of a single very light particle in a classical system. Because the configuration probabilities are mass independent, the pressure and the energy calculated for such a light particle are identical with thermodynamic values. In the special case of hard spheres it is shown that the pressure from collisions is proportional to the surface-to-volume ratio of the hard sphere free volume.

In theoretical equation-of-state investigations an important goal is to obtain the Helmholtz free energy, from which other thennod)lnamic properties can be obtained. The Helmholtz free energy is hard to cal­ culate directly. A less ambitious goal is to relate the free energy for the system of interest to the properties of a simpler, well-understood system. The simplest example of such a calculation considers the effect on the free energy when attractive forces are added to a purely repulsive hard-sphere system. This idea that attractive forces can be treated as a perturbation, with the distribution of particles being determined by short-range repulsive forces goes back to van der Waals and Boltzmann. Zwanzig1 formulated the corresponding perturbation theory precisely, show­ ing that the change in Helmholtz free energy caused by adding an attractive potential to a repulsive hard-core interaction could be expressed as a high-temperature series in liT, where T is the temperature. Until recently it had been relatively unnoticed that the first tenn in Zwanzig's series provides a rigorous upper bound on the Helmholtz free energy: