2025/05/12 by Giacomo Canevari, Canevari, Giacomo, Federico Luigi Dipasquale +3 · 1 citation
Materials Science · Mathematics · #26B30 #35Q56 #49Q15 #76A15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Liquid Crystal Research Advancements #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2505.07506
openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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, the largest part of which is carried by the \Q-component, includes a singular coupling term favouring alignment between~\Q and~\M. In this article and in the companion paper~\citeCDS2, we analyse the asymptotic behaviour of (not necessarily minimizing) critical points as a small parameter~\eps tends to zero. In this paper, we prove that the (rescaled) energy density for the \Q-component, concentrates, to leading order, on a finite number of singular points. Moreover, we prove energy estimates and compactness results that will be crucially used in~\citeCDS2 to determine the structure of the energy concentration set for the \M-component as well as the relationship between the two singular sets.