On first order corrections to classical coarsening models

The classical theory by Lifshitz, Slyozov and Wagner describes diffusion limited coarsening of particles in the limit of vanishing volume fraction $\phi$. Recently there has been a large interest in identifying higher order correction terms due to some shortcomings of the LSW theory. We first present a rigorous mathematical analysis in a stochastic setting which identifies the scaling of the first order correction to the LSW theory. The order of the relative deviation of the coarsening rate from the LSW theory shows a cross--over between $\phi^{1/3}$ and $\phi^{1/2}$ when screening effects become important. Second, we discuss a self-consistent derivation of the expected growth rate of a particle under certain assumptions on the statistics of the system. In particular we study the the influence of correlations.