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Molecular dynamics of two- and three-dimensional liquids undergoing a homogeneous adiabatic expansion provides a direct numerical simulation of the atomization process. The Lennard-Jones potential is used with different force cutoff distances; the cluster distributions do not depend strongly on the cutoff parameter. Expansion rates, scaled by the natural molecular time unit (about a picosecond), are investigated from unity down to 0.01; over this range the mean droplet size follows the scaling behavior of an energy balance model which minimizes the sum of kinetic plus surface energy. A second model which equates the elastic stored energy to the surface energy gives better agreement with the simulation results. The simulation results indicate that both the mean and the maximum droplet size have a power-law dependence upon the expansion rate; the exponents are {minus}2d/3 (mean) and {minus}d/2 (maximum), where {ital d} is the dimensionality. The mean does not show a dependence upon the system size, whereas the maximum does increase with system size, and furthermore, its exponent increases with an increase in the force cutoff distance. A mean droplet size of 2.8/{eta}{sup 2}, where {eta} is the expansion rate, describes our high-density three-dimensional simulation results, and this relation is also close to experimentalmore » results from the free-jet expansion of liquid helium. Thus, one relation spans a cluster size range from one atom to over 40 million atoms. The structure and temperature of the atomic clusters are described. {copyright} {ital 1999} {ital The American Physical Society}« less

The mean passage rate of a propagating interface, subject to random advection or random variation of the local propagation speed, is investigated analytically and computationally. A model representing the longitudinal propagation of two points of the interface separated by a fixed transverse distance is formulated and analyzed. In the limit of weak random perturbations, the model predicts several parameter dependences of the mean passage rate. These predictions are evaluated by performing two-dimensional and three-dimensional numerical simulations of interface propagation. The analysis addresses broadband (i.e., multiscale, as in turbulent flow) as well as narrow-band perturbations. In the broadband case, scaling laws governing transient as well as statistically steady propagation are derived. The numerical simulations span a sufficient range of perturbation amplitudes to exhibit the complete amplitude dependence of the mean passage rate, including scaling behaviors governing the weak and strong perturbation limits.