Shocks preempt continuous curvature divergence in interface motion - art. no. 205701

The dichotomy between two approaches to interface motion is illustrated in the context of two-dimensional crystal growth. Analyzing singularity format ion based on the curvature of the interface predicts a continuous divergenc e of curvature in contrast to the discrete loss of orientations predicted w hen the evolution is described by an equation for the two-vector of the int erface. We prove that the formation of a shock in the latter approach preem pts continuous curvature divergence predicted in the former approach. The r esults are broadly applicable to kinematic interface motion problems, and w e connect them with experiments reported by Maruyama et al. [Phys. Rev. Let t. 85, 2545 (2000)].