On first-order corrections to the LSW-theory

Andreas Hönig, Barbara Niethammer, and Felix Otto

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Submission date: 05. Mar. 2002
MSC-Numbers: 35B27, 74N20, 82C26
Keywords and phrases: ostwald ripening, monopole approximation, stochastic homogenization

Abstract:
The classical LSW-model describes the evolution of the radii of particles of one phase immersed in the other phase during the last stage of a phase transformation. Despite its simplicity, the LSW-model captures self-similar coarsening of the radii distribution. It is derived under the assumption of vanishing volume fraction of the particles. Unfortunately, quantitative predictions of this model do not well agree with experiments. Hence there is a large interest in deriving first-order corrections of the LSW-model in . In the first part of this paper, we present a new heuristic method to efficiently identify the first-order correction for a statistically homogeneous (and thus infinite) system. As was previously known, the first-order correction is of order . In the second part of this paper we consider finite systems (cluster). Numerical simulations have shown a cross-over in the scaling of the correction term from to when the cluster becomes larger than the screening length. We rigorously derive this cross-over for the time derivative of the energy. Our starting point for both parts is the monopole approximation.