Geodesic
Numeric modeling of static electric field effect on nematic liquid crystal director orientation
Matematičeskoe modelirovanie, Tome 30 (2018) no. 4, pp. 97-107

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Two-dimensional model of Frederiks effect has been used for the investigation of the static electric field effect on nematic liquid crystal director orientation in the side–electrode cell. The solutions have been obtained by the standard finite–difference methods. The programmes for numerical solution of two-dimensional parabolic partial differential equation have been developed both in FORTRAN and C/C++. Frederiks transition threshold for the central part of the cell, as well as dependencies of the distribution of the director orientation on the high electric field have been obtained. The results of the calculation have been compared to the experiment.
Keywords: nematic liquid crystal, two-dimensional model of the Fredericks effect, director, electric field, numerical solution, finite-difference methods. 
@article{MM_2018_30_4_a6,
     author = {A. S. Ayriyan and E. A. Ayrjan and A. A. Egorov and I. A. Maslyanitsyn and V. D. Shigorin},
     title = {Numeric modeling of static electric field effect on nematic liquid crystal director orientation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {97--107},
     publisher = {mathdoc},
     volume = {30},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_4_a6/}
}
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A. S. Ayriyan; E. A. Ayrjan; A. A. Egorov; I. A. Maslyanitsyn; V. D. Shigorin. Numeric modeling of static electric field effect on nematic liquid crystal director orientation. Matematičeskoe modelirovanie, Tome 30 (2018) no. 4, pp. 97-107. http://geodesic.mathdoc.fr/item/MM_2018_30_4_a6/