Theory of nucleation and growth during phase separation

We present a new model for the entire process of phase-separation that comb ines steady-state homogeneous nucleation theory with the classical Lifshitz -Slyozov mechanism of ripening, modified to account for the substantial cor relations among the droplets. A set of self-consistent interface equations describes the decay of metastable states, incorporating naturally the cross over from early-stage nucleation to the late-stage scaling regime without a d hoc assumptions. We present simulation results for both two and three dim ensions. We also present a mean-field, Thomas-Fermi approximation that prov ides an approximate solution to the many-body problem.