Exponential growth in Lennard-Jones ballistic aggregation

Determine whether exponential cluster-mass growth is possible in the single-component Lennard-Jones systems undergoing ballistic aggregation, particularly given the distinct particle interactions, temperature-dependent competition between relaxation times, and restricted ballistic-aggregation regime.

Background

The paper develops a ballistic-aggregation theory for phase-transition kinetics in low-density two- and three-dimensional Lennard-Jones fluids. Clusters move ballistically and coalesce, with their growth exponent determined by the cluster fractal dimension and the mass dependence of cluster velocity.

The theory predicts that the usual algebraic growth can become exponential when the parameters satisfy a specific relation between fractal dimension and velocity exponent. The authors identify physically plausible examples in dipolar systems, but emphasize that the corresponding phenomenon has not been established for the Lennard-Jones model studied here. They note that varying both temperature and density could provide a way to investigate it, although such simulations would be computationally demanding.