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The ability to predict transport properties (e.g., diffusivity, viscosity, and conductivity) is one of the primary benefits of molecular simulation. Although most studies focus on the accuracy of the simulation output compared to experimental data, such a comparison primarily tests the adequacy of the force field (i.e., the model). By contrast, the reliability of different simulation methodologies for predicting transport properties is the focus of this manuscript. Unfortunately, obtaining reproducible estimates of transport properties from molecular simulation is not as straightforward as static properties. Therefore, this manuscript discusses the best practices that should be followed to ensure that the simulation output is reliable, i.e., is a valid representation of the force field implemented. We also discuss procedures to use so that the results are reproducible (i.e., can be obtained by other researchers following the same methods and procedures). There are two classes by which transport properties are predicted: equilibrium molecular dynamics (EMD) and non-equilibrium molecular dynamics (NEMD). This manuscript presents the best practices for EMD, leaving NEMD for a future publication. As self-diffusivity and shear viscosity are the most prevalent transport properties found in the literature, the discussion will also be limited to these properties with the expectation that future publications will discuss best practices for thermal conductivity, ionic conductivity, and multicomponent diffusivity.

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Global Oscillation Network Group data reveal that the internal structure of the sun can be well represented by a calibrated standard model. However, immediately beneath the convection zone and at the edge of the energy-generating core, the sound-speed variation is somewhat smoother in the sun than it is in the model. This could be a consequence of chemical inhomogeneity that is too severe in the model, perhaps owing to inaccurate modeling of gravitational settling or to neglected macroscopic motion that may be present in the sun. Accurate knowledge of the sun's structure enables inferences to be made about the physics that controls the sun; for example, through the opacity, the equation of state, or wave motion. Those inferences can then be used elsewhere in astrophysics.

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The dynamics of the vigorous convection in the outer envelope of the Sun must determine the transport of energy, angular momentum, and magnetic Ðelds and must therefore be responsible for the observed surface activity and the angular velocity proÐle inferred helioseismically from SOI-MDI p-mode frequency splittings. Many di †erent theoretical treatments have been applied to the problem, ranging from simple physical models such as mixing-length theory to sophisticated numerical simulations. Although mixing-length models provide a good Ðrst approximation to the structure of the convection zone, recent progress has mainly come from numerical simulations. Computational constraints have until now limited simulations in full spheres to essentially laminar convection. The angular velocity proÐles have shown constancy on cylinders, in striking contrast to the approximately constant angular velocity on radial lines inferred for the Sun. In an e †ort to further our understanding of the dynamics of the solar convection zone, we have developed a new computer code that, by exploiting massively parallel architectures, enables us to study fully turbulent spherical shell convection. Here we present Ðve fully evolved solutions. Motivated by the fact that a constant entropy upper boundary condition produces a latitudinal modulation of the emergent energy Ñux (of about 10%, i.e., far larger than is observed for the Sun), three of these solutions have a constant energy Ñux upper boundary condition. This leads to a latitudinal modulation of the speciÐc entropy that breaks the constancy of the angular velocity on cylinders, making it more nearly constant on radial lines at midlatitudes. The e †ect of lowering the Prandtl number is also consideredÈhighly time-dependent, vortical convective motions are revealed, and the Reynolds stresses are altered, leading to a reduced di †erential rotation. The di †erential rotation in all of our simulations shows a balance between driving by Reynolds stresses and damping by viscosity. This contrasts with the situation in the Sun, where the e †ect of viscosity on the mean di †erential rotation is almost negligible.

Results of molecular dynamics (MD) simulations on square-well fluids with λ=1.25, 1.375, 1.5, 1.75, and 2.0 are presented. The calculation of vapor-liquid equilibrium was performed by isochoric integration of the liquid NVE data to obtain the free energy of the liquid and equating this to the vapor free energy from a modified virial equation. The saturation pressure was investigated and compared with that from Monte Carlo simulation and second-order analytical perturbation theory. The vapor pressures from the isochoric integration technique are shown to be smoother than previous results, permitting accurate estimation of the effect of the square-well width on acentric factor. With the saturated properties from molecular dynamics, the f value used in Kofke’s Gibbs-Duhem integration was calculated and was found to be nearly constant. The related integration of the Clapeyron equation was implemented as a check on thermodynamic consistency. Vapor pressures presented here are consistent to within 2%.