Supplementary information

From the following article:

The von Neumann relation generalized to coarsening of three-dimensional microstructures

Robert D. MacPherson & David J. Srolovitz

Nature 446, 1053-1055(26 April 2007)

doi:10.1038/nature05745

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Supplementary Information

This file contains Supplementary Notes with the derivation of the main result in the Article, Supplementary Equation illustrating the generalization of the von Neumann-Mullins relation to three dimensions and Supplementary Discussion of practical approaches to calculating the mean width of a domain – including exact methods for polyhedra and a few special shapes plus a numerical method for determining the mean width of arbitrary three-dimensional domains.

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