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Robert MacPherson, Institute for Advanced StudyThe Geometry of Grains AbstractA metal or ceramic is naturally decomposed into cells called "grains", which influence the properties of the material. Some interesting mathematical problems arise in trying to understand the time evolution of these grains. Von Neumann and Mullins gave a simple formula for the growth rate of a grain in 2 dimensions, which has been used as the basis for much of the work on grain evolution. This formula will be generalized to 3 (and higher) dimensions (joint work with David Srolovitz). The generalization relies on a good notion of the linear dimension of a 3 dimensional grain called the "mean width", which should be useful in other contexts. TUESDAY, October 9, 2007 |