Motion by curvature in discrete media

I describe the motion of interfaces in a discrete environment, obtained by coupling the minimizing movements approach of Almgren, Taylor and Wang and a discrete-to-continuous analysis. I show that, below a critical ratio of the time and space scalings there is no motion of interfaces (pinning), while above that ratio the discrete motion is approximately described by the crystalline motion by curvature on the continuum. The critical regime is quite richer, exhibiting a pinning threshold, partial pinning, quantization of the interface velocity, and non-uniqueness effects.

This is a joint work with A. Braides (Rome) and M.S. Gelli (Pisa).