| Abstract: |
| In this talk, I present the formation of singularities in a chiral Skyrme-type energy model, which describes magnetic solitons in two-dimensional ferromagnetic systems. In the presence of a diverging anisotropy term, which enforces a preferred background state of the magnetization, I show how to establish a weak compactness result for the topological charge density and prove that it converges to an atomic measure with quantized weights. I characterize the $\Gamma$-limit of the energies as the total variation of this measure.
Then, I consider the case of lattice-type energies and prove a corresponding compactness
and $\Gamma$-convergence result. To this end, I will first carefully define a notion of discrete topological charge for $\mathbb{S}^2$ -valued maps.
This is a joint work with Marco Cicalese and Leonard Kreutz. |
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