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Bifurcations analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions: the asymmetric case

Published online by Cambridge University Press:  16 June 2016

FERNANDO P. DA COSTA ,
MARIA ISABEL MÉNDEZ  and
JOÃO T. PINTO
FERNANDO P. DA COSTA
Affiliation:
Departamento de Ciências e Tecnologia, Universidade Aberta, Rua da Escola Politécnica 141–147, 1269-001 Lisboa, Portugal Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal email: [email protected]
MARIA ISABEL MÉNDEZ
Affiliation:
Departamento de Matemáticas, IES Antonio López García, Calle Arquitectos 39, 28903 Getafe, Madrid, Spain email: [email protected]
JOÃO T. PINTO
Affiliation:
Department of Mathematics and Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal email: [email protected]
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Abstract

In the paper, Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions (2009 Eur. J. Appl. Math.20, 269–287) by da Costa et al. the twist-Fréedericksz transition in a nematic liquid-crystal one-dimensional cell of lenght L was studied, imposing an antisymmetric net twist Dirichlet condition at the cell boundaries. In the present paper, we extend that study to the more general case of net twist Dirichlet conditions without any kind of symmetry restrictions. We use phase-plane analysis tools and appropriately defined time maps to obtain the bifurcation diagrams of the model when L is the bifurcation parameter, and related these diagrams with the one in the antisymmetric situation. The stability of the bifurcating solutions is investigated by applying the method of Maginu (1978 J. Math. Anal. Appl.63, 224–243).

Keywords

Twist-Fréedericksz transitionLiquid-crystal cellsNon-homogeneous Dirichlet two-point boundary value problemsBifurcation of equilibria
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 2 , April 2017 , pp. 243 - 260
Copyright
Copyright © Cambridge University Press 2016 

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References

[1] da Costa, F. P., Gartland, E. C. Jr., Grinfeld, M. & Pinto, J. T. (2009) Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary condition. Eur. J. Appl. Math. 20, 269–287.Google Scholar
[2] da Costa, F. P., Grinfeld, M., Mottram, N. & Pinto, J. T. (2009) Uniqueness in the Freedericksz transition with weak anchoring. J. Differ. Equ. 246, 2590–2600.Google Scholar
[3] Fiedler, B. & Rocha, C. (1996) Heteroclinic orbits of semilinear parabolic equations. J. Differ. Equ. 125 (1), 239–281.CrossRefGoogle Scholar
[4] Freedericksz, V. & Zolina, V. (1929) On the use of a magnetic field in the measurement of the forces tending to orient an anisotropic liquid in a thin homogeneous layer. Trans. Am. Electrochem. Soc. 55, 85–96.Google Scholar
[5] Hale, J. K. (1988) Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs, Vol. 25, American Mathematical Society, Providence, RI.Google Scholar
[6] Maginu, K. (1978) Stability of stationary solutions of a semilinear parabolic partial differential equation. J. Math. Anal. Appl. 63, 224–243.Google Scholar
[7] Stewart, I. W. (2004) The Static and Dynamic Continuum Theory of Liquid Crystals, The Liquid Crystals Book Series, Vol. 2, Taylor & Francis, London.Google Scholar
[8] Yang, D.-K. & Wu, S.-T. (2015) Fundamentals of Liquid Crystal Devices, 2nd ed., Wiley-SID Series in Display Technology, John Wiley & Sons, Chichester.Google Scholar