Defects of liquid crystals with variable degree of orientation

2016/10/31 by Onur Alper, Robert Hardt, Fanghua Lin +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Condensed matter physics #Degree (music) #Energy (signal processing) #Geometry #Liquid crystal #Mathematical analysis #Mathematics #Mathematics and Applications #Orientation (vector space) #Physics #Point processes and geometric inequalities #Set (abstract data type) #Statistics #Variable (mathematics) #math-ph #math.AP #math.MP #msc:49Q20 #msc:58E15 #msc:58E20 #msc:76A15

paper · pdf · doi:10.1007/s00526-017-1218-5

32 pages; minor revisions; typographical errors corrected; new references added

arxiv created 2017/08/21 · openalex publication_date 2017/08/23 · arxiv updated 2017/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that the zero set of a minimizer of the modified Ericksen energy for nematic liquid crystals with variable degree of orientation consists locally of isolated points and a finite union of Hölder continuous curves with only finitely many crossings.

Citations

• A regularity theory for harmonic maps
• Multiple Integrals in the Calculus of Variations
• Mappings minimizing the L p norm of the gradient
• Liquid crystals with variable degree of orientation
• The Physics of Liquid Crystals
• Solution of the Plateau problem for m-dimensional surfaces of varying topological type