Date of Original Version

8-2013

Type

Article

Rights Management

The final publication is available at Springer via http://dx.doi.org/10.1007/s00332-014-9221-x

Abstract or Description

We study the evolution of grain boundary networks by the mean-curvature flow under the restriction that the networks are Voronoi diagrams for a set of points. For such evolution we prove a rigorous universal upper bound on the coarsening rate. The rate agrees with the rate predicted for the evolution by mean-curvature flow of the general grain boundary networks, namely that the typical grain area grows linearly in time. We perform a numerical simulation which provides evidence that the dynamics achieves the rate of coarsening that agrees with the upper bound in terms of scaling.

DOI

10.1007/s00332-014-9221-x

Included in

Mathematics Commons

Share

COinS
 

Published In

Journal of Nonlinear Science, 25, 1, 59-85.