Weak selection and stability of localized distributions in Ostwald ripening

TL;DR

This paper develops an asymptotic perturbation theory to support and extend a weak selection rule in Ostwald ripening, predicting convergence to a self-similar distribution and validated by numerical simulations.

Contribution

It introduces a generalized weak selection rule and an asymptotic perturbation approach for Ostwald ripening, enhancing understanding of distribution stability.

Findings

Supports the weak selection rule for self-similar distributions.

Predicts power-law convergence towards the selected distribution.

Numerical simulations confirm theoretical predictions.

Abstract

We support and generalize a weak selection rule predicted recently for the self-similar asymptotics of the distribution function (DF) in the zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation theory is developed that, when combined with an exact invariance property of the system, yields the selection rule, predicts a power-law convergence towards the selected self-similar DF and agrees well with our numerical simulations for the interface- and diffusion-controlled OR.