Journal of Nonlinear Science

, Volume 28, Issue 4, pp 1443–1465 | Cite as

Spherical Particle in Nematic Liquid Crystal Under an External Field: The Saturn Ring Regime

  • Stan Alama
  • Lia Bronsard
  • Xavier Lamy


We consider a nematic liquid crystal occupying the exterior region in \({\mathbb {R}}^3\) outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes theory, we study minimizers subject to an external field, modeled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough, we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn ring defect around the particle, rather than a dipolar director field typical of a point defect.


Partial differential equations Calculus of variations Liquid crystals Line defects 

Mathematics Subject Classification

35J50 35Q56 



We thank E. C. Gartland for useful discussions on nondimensionalization. SA and LB were supported by NSERC (Canada) Discovery Grants.


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Institut de Mathématiques de Toulouse, UMR5219, CNRS, UPS IMTUniversité de ToulouseToulouse Cedex 9France

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