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BIRS Workshop Lecture Videos

Some Ginzburg-Landau problems for vector fields on manifolds. Jerrard, Bob


Motivated in part by problems arising in micromagnetics, we study several variational models of Ginzburg-Landau type, depending on a small parameter $\epsilon >0$, for (tangent) vector fields on a 2-dimensional compact Riemannian surface. As $\epsilon\to 0$, the vector fields tend to be of unit length and develop singular points of a (non-zero) index, called vortices. Our main result determines the interaction energy between these vortices as $\epsilon\to 0$, allowing us to characterize the asymptotic behaviour of minimizing sequence. This is joint work with Radu Ignat.

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