Calculus of Variations and Geometric Measure Theory

G. Scilla

Motion of discrete interfaces in low-contrast periodic media

created by scilla on 21 Jun 2013
modified on 11 Apr 2014


Published Paper

Inserted: 21 jun 2013
Last Updated: 11 apr 2014

Journal: Netw. Heterog. Media
Volume: 9
Number: 1
Pages: 169-189
Year: 2014
Doi: 10.3934/nhm.2014.9.169


We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional low-contrast periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuum analysis. As in a recent paper by Braides and Scilla dealing with high-contrast periodic media, we give an example showing that in general the effective motion does not depend only on the $\Gamma$-limit, but also on geometrical features that are not detected in the static description. We show that there exists a critical value $\widetilde{\delta}$ of the contrast parameter $\delta$ above which the discrete motion is constrained and coincides with the high-contrast case. If $\delta<\widetilde{\delta}$ we have a new pinning threshold and a new effective velocity both depending on $\delta$. We also consider the case of non-uniform inclusions distributed into periodic uniform layers.

Keywords: discrete systems, minimizing movements, motion by curvature, crystalline curvature, Geometric motion, low-contrast media