Statistics of nucleation in small and large systems

Statistics of single- and multiple nucleation events in systems of variable sizes is considered in the context of large scale simulations. The earlier obtained singular perturbation solution of the time-dependent Becker-D\"oring equation is used to predict the probability distribution of the waiting times to detect the first nucleus in a small system and to establish connection with the number of nuclei when the system is large. Examples include dynamic Monte Carlo simulations of condensation of a supersaturated lattice gas \footnote{V.A. Shneidman \textbf{ J. Chem. Phys.} 141 (2014) 051101.}, where exact results for the nucleation rates obtained from low-temperature cluster expansions \footnote{V.A. Shneidman and G.M. Nita, \textbf{ Phys. Rev. Lett.} 97 (2006) 065703.} provide a rigorous independent test. Stochastic (Langevin) simulations \footnote{V.A. Shneidman \textbf{ J. Chem. Phys.} 147 (2017) 061101.} of the evolution of a bubble in viscous and inertial fluid, discussed in the context of the cavitation problem \footnote{V.A. Shneidman \textbf{Phys. Rev. E} 94 (2016) 062101. } also are considered.