Editor's Summary

26 April 2007

Added dimensions

Cellular structures or tessellations are ubiquitous in nature: examples include foams and crystalline grains in metals and ceramics. In many situations, the cell/grain/bubble walls move under the influence of surface tension (capillarity), with a velocity proportional to their mean curvature. As a result, the cells evolve and the structure coarsens. Over 50 years ago, the Hungarian-born mathematician John von Neumann derived an exact formula for the growth rate of a cell in a two-dimensional cellular structure. Now the much-sought extension of this result into three (or more) dimensions has been found. The formula should lead to predictive models for various industrial and commercial processes, from the heat treatment of metals to controlling the head on a glass of beer.

News and Views: Mathematical physics: Added dimensions to grain growth

A long-standing mathematical model for the growth of grains in two dimensions has been generalized to three and higher dimensions. This will aid our practical understanding of certain crucial properties of materials.

David Kinderlehrer

doi:10.1038/446995a

Full Text | PDF (200K)

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

Robert D. MacPherson & David J. Srolovitz

doi:10.1038/nature05745

Abstract | Full Text | PDF (188K) | Supplementary information