Smooth-particle methods have a 20-year history of solving complex problems in fluid and solid mechanics. Here we first discuss the method, pointing out an interesting and fruitful parallel linking smooth-particle methods to atomistic molecular dynamics. We then assess the accuracy and applicabili ty of the method by comparing a set of smooth-particle Rayleigh-Benard problems, all in the laminar re gime, to corresponding highly accurate grid-based numerical solutions of the continuum equations. Both transient and stationary smooth-particle solutions reproduce the grid-based data with velocity er rors on the order of a few percent.
We simulate both microscopic and macroscopic shear flows in two space dimensions using nonequiIi brium molecular dynamics and smooth-particle applied mechanics. The time-reversible microscopic equations of motion are isomorphic to the smooth-particle description of inviscid macroscopic continu um mechanics. The corresponding microscopic particle interactions are relatively weak and long ranged. Though conventional Green-Kubo theory suggests instability or divergence in two-dimensional flows, we successfully define and measure a finite shear viscosity coefficient by simulating stationary plane Couette flow. The special nature of the weak long-ranged smooth-particle functions corresponds to an unusual kind of microscopic transport. This microscopic analog is mainly kinetic, even at high density. For the soft Lucy potential which we use in the present work, nearly all the system energy is po tential, but the reSUlting shear viscosity is nearly all kinetic. We show that the measured shear viscosi ties can be understood, in terms of a simple weak-scattering model, and that this understanding is useful in assessing the usefulness of continuum simulations using the smooth-particle method. We apply that method to the Rayleigh-Benard problem of thermally driven convection in a gravitational field.
Parallel replica dynamics simulation methods appropriate for the simulation of chemical reactions in molecular systems with many conformational degrees of freedom have been developed and applied to study the microsecond-scale pyrolysis of n-hexadecane in the temperature range of 2100-2500 K. The algorithm uses a transition detection scheme that is based on molecular topology, rather than energetic basins. This algorithm allows efficient parallelization of small systems even when using more processors than particles (in contrast to more traditional parallelization algorithms), and even when there are frequent conformational transitions (in contrast to previous implementations of the parallel replica algorithm). The parallel efficiency for pyrolysis initiation reactions was over 90% on 61 processors for this 50-atom system. The parallel replica dynamics technique results in reaction probabilities that are statistically indistinguishable from those obtained from direct molecular dynamics, under conditions where both are feasible, but allows simulations at temperatures as much as 1000 K lower than direct molecular dynamics simulations. The rate of initiation displayed Arrhenius behavior over the entire temperature range, with an activation energy and frequency factor of E(a) = 79.7 kcal/mol and log A/s(-1) = 14.8, respectively, in reasonable agreement with experiment and empirical kinetic models. Several interesting unimolecular reaction mechanisms were observed in simulations of the chain propagation reactions above 2000 K, which are not included in most coarse-grained kinetic models. More studies are needed in order to determine whether these mechanisms are experimentally relevant, or specific to the potential energy surface used.
We use molecular dynamics to study the structure of moderately strong shock waves in dense twodimensional fluids, using Lucy's pair potential. The stationary profiles show relatively broad temperature maxima, for both the longitudinal and the average kinetic temperatures, just as does Mott-Smith's model for strong shock waves in dilute three-dimensional gases. ͓S1063-651X͑97͒01507-9͔
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