Convergence to line and surface energies in nematic liquid crystal colloids with external magnetic field

François Alouges (1) , Antonin Chambolle (2) , Dominik Stantejsky (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We use the Landau-de Gennes energy to describe a particle immersed into nematic liquid crystals with a constant applied magnetic field. We derive a limit energy in a regime where both line and point defects are present, showing quantitatively that the close-to-minimal energy is asymptotically concentrated on lines and surfaces nearby or on the particle. We also discuss regularity of minimizers and optimality conditions for the limit energy.

Mots clés: Nematic liquid crystal colloids; Landau-de Gennes model; Γ−convergence; flat chains; singular limits

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

François Alouges, Antonin Chambolle, Dominik Stantejsky. Convergence to line and surface energies in nematic liquid crystal colloids with external magnetic field. 2022. ⟨hal-03583697v2⟩