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Five Little Crystals and How They Grew

Jean E. Taylor
Rutgers University and Courant Institute of Mathematical Sciences

AWM Emmy Noether Lecture
Thursday, January 16, 2003
Baltimore, Maryland

Abstract. Five ways in which crystals can grow (or shrink, or change their shapes) are discussed: motion by weighted mean curvature motion by surface diffusion motion by surface-attachment-limited kinetics with and without external driving forces, dendritic crystal growth, and motion of crystal aggregates in which individual crystals rotate. All are part of a family of motions which can be formulated and analyzed in the same general framework. Parts of this framework include a surface energy similar to that of soap bubbles (but varying with normal direction) and inner products determining the kinetics.

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