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

TL;DR

This paper analyzes the asymptotic behavior of nematic liquid crystal colloids under magnetic fields, showing energy concentration on defects and deriving a limit energy with implications for defect structures.

Contribution

It introduces a new limit energy model capturing line and surface defects in nematic colloids with magnetic fields, extending previous theories.

Findings

Energy concentrates on lines and surfaces near the particle

Derived a limit energy describing defect structures

Discussed regularity and optimality of minimizers

Abstract

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.