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Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X		  

Kickback in nematic liquid crystals


Authors: F. P. da Costa, M. Grinfeld, M. Langer, N. J. Mottram and J. T. Pinto
Journal: Quart. Appl. Math. 70 (2012), 99-110
MSC (2000): Primary 34D15, 35Q72; Secondary 76A15, 82D30
Posted: September 7, 2011
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe a nonlocal linear partial differential equation arising in the analysis of dynamics of a nematic liquid crystal. We confirm that it accounts for the kickback phenomenon by decoupling the director dynamics from the flow. We also analyse some of the mathematical properties of the decoupled director equation.

References [Enhancements On Off] (What's this?)

  • 1. D. W. Berreman, Liquid-crystal twist cell dynamics with backflow, J. Appl. Phys. 46 (1975), 3746-3751.
  • 2. M. G. Clark and F. M. Leslie, A calculation of orientational relaxation in nematic liquid crystals, Proc. Royal Soc. Lond. A, 361 (1978), 463-485.
  • 3. S. L. Cornford, T. S. Taphouse, C. J. P. Newton, and J. R. Sambles, Determination of the director profile in a nematic cell from guided wave data: an inverse problem, New J. Phys. 9 (2007), 166-170.
  • 4. Fernando P. da Costa, Michael Grinfeld, Nigel J. Mottram, and João T. Pinto, Uniqueness in the Freedericksz transition with weak anchoring, J. Differential Equations 246 (2009), no. 7, 2590–2600. MR 2503014 (2009m:34029), http://dx.doi.org/10.1016/j.jde.2009.01.033
  • 5. Roger K. Dodd, J. Chris Eilbeck, John D. Gibbon, and Hedley C. Morris, Solitons and nonlinear wave equations, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1982. MR 696935 (84j:35142)
  • 6. C. J. Gerritsma, C. Z. van Doorn, and P. van Zanten, Transient effects in the electrically controlled light transmission of a twisted nematic layer, Phys. Lett A 48 (1974), 263-264.
  • 7. I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR 0246142 (39 #7447)
  • 8. M. Grinfeld, M. Langer and N. J. Mottram, Nematic viscosity estimation using director kickback dynamics, to appear in Liquid Crystals (2011).
  • 9. Jack K. Hale, Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs, vol. 25, American Mathematical Society, Providence, RI, 1988. MR 941371 (89g:58059)
  • 10. Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. MR 610244 (83j:35084)
  • 11. Mark H. Holmes, Introduction to perturbation methods, Texts in Applied Mathematics, vol. 20, Springer-Verlag, New York, 1995. MR 1351250 (96j:34095)
  • 12. J. R. Sambles and L. Z. Ruan, Testing the dynamic theory of nematics using fully-leaky guided modes and a convergent beam system J. Non-Newtonian Fluid Mech. 119 (2004), 39-49.
  • 13. I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: a Mathematical Introduction, The Liquid Crystals Book Series, Taylor and Francis, New York, 2004.
  • 14. C. Z. van Doorn, Dynamic behavior of twisted nematic liquid crystal layers in switched fields, J. Appl. Phys. 46 (1975), 3738-3745.
  • 15. Milton Van Dyke, Perturbation methods in fluid mechanics, Annotated edition, The Parabolic Press, Stanford, Calif., 1975. MR 0416240 (54 #4315)
  • 16. Ferdinand Verhulst, Methods and applications of singular perturbations, Texts in Applied Mathematics, vol. 50, Springer, New York, 2005. Boundary layers and multiple timescale dynamics. MR 2148856 (2006k:34001)

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Additional Information

F. P. da Costa
Affiliation: Departamento de Ciências e Tecnologia, Universidade Aberta, Rua da Escola Politécnica, 141, P-1269-001 Lisboa, Portugal, and Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, 1, P-1049-001 Lisboa, Portugal
Email: fcosta@univ-ab.pt

M. Grinfeld
Affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, United Kingdom
Email: m.grinfeld@strath.ac.uk

M. Langer
Affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, United Kingdom
Email: m.langer@strath.ac.uk

N. J. Mottram
Affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, United Kingdom
Email: n.j.mottram@strath.ac.uk

J. T. Pinto
Affiliation: Departamento de Matemática, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, 1, P-1049-001 Lisboa, Portugal, and Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, 1, P-1049-001 Lisboa, Portugal
Email: jpinto@math.ist.utl.pt

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01265-5
PII: S 0033-569X(2011)01265-5
Keywords: Nematic liquid crystals, kickback, singular perturbations, nonlocal operators
Received by editor(s): June 10, 2010
Posted: September 7, 2011
Article copyright: © Copyright 2011 Brown University



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