Orateur
Description
We consider a variational model for ferronematics --- composite materials formed by dispersing magnetic nanoparticles into a liquid crystal matrix. The model features two coupled order parameters: a Landau-de Gennes $Q$-tensor for the liquid crystal component and a magnetisation vector field $M$, both of them governed by a Ginzburg-Landau-type energy. The energy includes a singular coupling term favouring alignment between $Q$ and $M$. We report on some recent results on the asymptotic behaviour of (not necessarily minimizing) critical points as a small parameter $eps$ tends to zero. Our main results show that the energy concentrates along distinct singular sets: the (rescaled) energy density for the $Q$-component concentrates, to leading order, on a finite number of singular points, while the energy density for the $M$-component concentrates along a one-dimensional rectifiable set. Moreover, we will see that the curvature of the singular set for the $M$-component (technically, the first variation of the associated varifold) is concentrated on a finite number of points, i.e. the singular set for the $Q$-component.
Joint work with G.Canevari (University of Verona) and B. Stroffolini (University of Naples ``Federico II'').
