Separation and Interaction energy between domain walls in a nonlocal model.

Abstract: We analyse a nonconvex variational model from micromagnetics  with a nonlocal energy functional, depending on a small parameter epsilon > 0. The model gives rise to transition layers, called Néel walls, and we study their behaviour in the limit epsilon -> 0. The analysis has some similarity to the theory of Ginzburg-Landau vortices. In particular, it gives rise to a renormalised energy that determines the interaction (attraction or repulsion) between Néel walls to leading order.

But while Ginzburg-Landau vortices show attraction for winding numbers of the same sign and
repulsion for those of opposite signs, the pattern is reversed in this model.

First, we show that the Néel walls stay separated from each other and second, we determine the interaction energy between them.

The theory gives rise to an effective variational problem for the positions of the walls,
encapsulated in a Gamma-convergence result.

 

Date: Jun 03, 2021 at 16:15:00 h
Venue: Modalidad Vía Online.
Speaker: Radu Ignat
Affiliation: Institut de Mathématiques de Toulouse, Francia
Coordinator: Natham Aguirre
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Posted on May 31, 2021 in Differential Equations, Seminars