References
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- de Gennes , P. G. Such torques and forces are closely related to the forces in pre-smectic fluids discussed by, in a recent preprint
- Sheng , P. 1976 . Phys. Rev. Leu. , 37 : 1059 For examples o f closely related work see
- 1982 . Phys. Rev. , A26 : 1610
- Horn , R. G. , Israelachvili , J. N. and Perez , E. 1981 . J. Phys. (Paris) , 42 : 39
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- Goldbart , P. M. and Tarlie , M. B. July 1990 . July , manuscript in preparation, Whilst we have not found a discussion of this nematic Josephson-type effect in the literature, we suspect that similar results have been previously reported, and we would be grateful if our attention were drawn to relevant articles
- Frank , F. C. 1958 . Discuss. Faraday. Soc. , 25 : 19
- Mermin , N. D. 1979 . Rev. Mod. Phys. , 51 : 591 The technical statement is that the director lives in the coset space SO(3)/Dz, i. e., the projective plane P2. whose first hornotopy group T, (SO(3)/Dz.) is Z2, the additive group of integers, modulo 2. For a genuinely readable introduction to these matters
- Charles , Fox . 1950 . An Inrroduction to the Calculus of Variations , Oxford University Press . In fact we shall simply assume that the barrier-top states we find do indeed have the appropriate character. One scheme for checking this would be to extend the Jacobi test for extrema of functionals; see e. g.
- That there are two degrees of freedom results from subjecting the three components of the director to the single non-linear constraint that it has unit magnitude
- As the Frank free energy involves only gradient terms, the lagrangean does not contain a potential energy term; equivalently, there is no non-trivial rotationally invariant potential that can be built from a unit vector
- de Gennes , P. G. 1975 . The Physics of Liquid Crystals , Oxford : Clarendun Press .
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