Harmonic maps into round cones and singularities of nematic liquid crystals

1993 ◽  
Vol 213 (1) ◽  
pp. 575-593 ◽  
Author(s):  
Robert Hardt ◽  
Fang Hua Lin
Keyword(s):  
Liquid Crystals ◽  
Harmonic Maps ◽  
Nematic Liquid Crystals

scholarly journals Sphere-valued harmonic maps with surface energy and the K13 problem

2019 ◽  
Vol 12 (4) ◽  
pp. 363-392
Author(s):  
Stuart Day ◽  
Arghir Dani Zarnescu
Keyword(s):  
Liquid Crystals ◽  
Surface Energy ◽  
Boundary Conditions ◽  
Critical Point ◽  
Partial Regularity ◽  
Harmonic Maps ◽  
Nematic Liquid Crystals ◽  
Energy Functional ◽  
Dirichlet Energy ◽  
Surface Term

AbstractWe consider an energy functional motivated by the celebrated {K_{13}} problem in the Oseen–Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an additional surface term. It is known that this energy is unbounded from below and our aim has been to study the local minimisers. We show that even having a critical point in a suitable energy space imposes severe restrictions on the boundary conditions. Having suitable boundary conditions makes the energy functional bounded and in this case we study the partial regularity of the global minimisers.

The electrohydrodynamic instability in twisted nematic liquid crystals

1994 ◽  
Vol 4 (2) ◽  
pp. 239-252 ◽  
Author(s):  
A. Hertrich ◽  
A. P. Krekhov ◽  
O. A. Scaldin
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Electrohydrodynamic Instability ◽  
Twisted Nematic

Surface disclinations in nematic liquid crystals

1975 ◽  
Vol 36 (1) ◽  
pp. 59-67 ◽  
Author(s):  
V. Vitek ◽  
M. Kléman
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals

Field-induced transient periodic structures in nematic liquid crystals : the splay Frederiks transition

1985 ◽  
Vol 46 (6) ◽  
pp. 905-917 ◽  
Author(s):  
A.J. Hurd ◽  
S. Fraden ◽  
F. Lonberg ◽  
R.B. Meyer
Keyword(s):  
Liquid Crystals ◽  
Periodic Structures ◽  
Nematic Liquid Crystals
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