Inserted: 20 may 2004
Last Updated: 17 apr 2016
Journal: Math. Mod. Meth. Appl. Sc.
In this paper we analyze the stability properties of the Wulff-shape in the crystalline flow. It is well known that the Wulff-shape evolves self-similarly, and eventually shrinks to a point. We consider the flow restricted to the set of convex polyhedra, we show that the crystalline evolutions may be viewed, after a proper rescaling, as an integral curve in the space of polyhedra with fixed volume, and we compute the Jacobian matrix of this field. If the eigenvalues of such a matrix have real part different from zero, we can determine if the Wulff-shape is stable or unstable, i.e., if all the evolutions starting close enough to the Wulff-shape converge or not, after rescaling, to the Wulff-shape itself.
Keywords: stability, crystal, evolution, wulff