Seminar in the framework of the PDE Afternoon
|Time||15:00 - 15:45|
|Place||University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz, 1, Vienna (map)|
|Room||From 15:00 to 15:45: Hörsaal 2 (ground floor) - from 16:00 to 17:00: WPI Seminarraum (8th floor)|
|Speaker||Lucia De Luca (SISSA, Italy)|
|Title||Variational analysis for dipoles of topological singularities in two dimensions|
We present two continuous models for the study of topological singularities in 2D: the core-radius approach and the Ginzburg-Landau theory.
It is well known that - at zero temperature and under suitable regimes - the energies associated to these models tend to concentrate, as the length scale parameter $\varepsilon$ goes to zero, around a finite number of points, the so-called vortices.
We focus on low energy regimes that prevent the formation of vortices in the limit as $\varepsilon$ tends to zero, but that are compatible (for positive $\varepsilon$) with configurations of short (in terms of $\varepsilon$) dipoles, and more in general with short clusters of vortices having zero average.
By using a $\Gamma$-convergence approach, we provide a quantitative analysis of the energy induced by such configurations on a continuous range of length scales.
Joint work with M. Ponsiglione (Rome).