We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The case of a homogeneous environment has been recently treated by Braides, Gelli and Novaga, showing that the effective continuous motion is a flat motion related to the crystalline perimeter obtained by Γ-convergence from the ferromagnetic energies, with an additional discontinuous dependence on the curvature, giving in particular a pinning threshold. In this paper we give an example showing that in general the motion does not depend only on the Γ-limit, but also on geometrical features that are not detected in the static description. In particular we show how the pinning threshold is influenced by the microstructure and that the effective motion is described by a new homogenized velocity.
1
Università di Roma Tor Vergata, Italy
2
Università di Roma La Sapienza, Italy
Andrea Braides; Giovanni Scilla. Motion of discrete interfaces in periodic media. Interfaces and free boundaries, Tome 15 (2013) no. 4, pp. 451-476. doi: 10.4171/ifb/310
@article{10_4171_ifb_310,
author = {Andrea Braides and Giovanni Scilla},
title = {Motion of discrete interfaces in periodic media},
journal = {Interfaces and free boundaries},
pages = {451--476},
year = {2013},
volume = {15},
number = {4},
doi = {10.4171/ifb/310},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/310/}
}
TY - JOUR
AU - Andrea Braides
AU - Giovanni Scilla
TI - Motion of discrete interfaces in periodic media
JO - Interfaces and free boundaries
PY - 2013
SP - 451
EP - 476
VL - 15
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/310/
DO - 10.4171/ifb/310
ID - 10_4171_ifb_310
ER -
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%A Giovanni Scilla
%T Motion of discrete interfaces in periodic media
%J Interfaces and free boundaries
%D 2013
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%V 15
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/310/
%R 10.4171/ifb/310
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