English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider a nematic liquid crystal occupying the three-dimensional domainin the exterior of a spherical colloid particle. The nematic is subject toDirichlet boundary conditions that enforce orthogonal attachment of nematicmolecules to the surface of the particle. Our main interest is to understandthe behavior of energy-critical configurations of the Landau-de Gennes$Q$-tensor model in the limit of vanishing correlation length. We demonstrateexistence of configurations with a single Saturn-ring defect approaching theequator of the particle and no other line or point defects. We show this byanalyzing asymptotics of energy minimizers under two symmetry constraints:rotational equivariance around the vertical axis and reflection across thehorizontal plane. Energy blow-up at the ring defect is a significant obstacleto constructing well-behaved comparison maps needed to eliminate thepossibility of point defects. The boundary estimates we develop to address thisissue are new and should be applicable to a wider class of problems.

Saturn ring defect around a spherical particle immersed in nematic liquid crystal