Federico Dipasquale (SSM Napoli) – Seminario di Analisi

Martedì 16 settembre⋅ Sala Professori I livello ore 15:00 – 16:00

“The formation of gradient-driven singular structures of codimension one and two in two-dimensions: The case study of ferronematics”

We study a two-dimensional 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 analyse the asymptotic behaviour of general critical points as a small parameter~$varepsilon$ 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. We also illustrate the relationship between these two singular sets. Joint work with Giacomo Canevari (UniVR) and Bianca Stroffolini (UniNA)