DOI QR코드

DOI QR Code

EXISTENCE OF PERIODIC SOLUTIONS IN FERROELECTRIC LIQUID CRYSTALS

  • Park, Jinhae (PDE and Functional Analysis Research Center Seoul National University)
  • 투고 : 2010.08.09
  • 심사 : 2010.09.06
  • 발행 : 2010.09.30

초록

We introduce the Landau-de Gennes model in order to understand molecular structures in ferroelectric liquid crystals. We investigate equilibrium configurations of the governing energy functional by means of bifurcation analysis. In particular, we obtain periodic solutions of the functional, which is a signature of a rich variety of applications of ferroelectric materials.

키워드

참고문헌

  1. S. S. Antman, Nonlinear Problems of Elasticity, Applied Math. Sci. 107, Springer-Verlag, 1995.
  2. G. Barbero and L. R. Evangelista, An elementary course on the continuum theory for nematic liquid crystals, World Scientific, 2001.
  3. J. Carr, M. E. Gurtin, and M. Slemrod, Structured phase transitions on a finite interval, Arch. Ration. Mech. Anal. 86 (1984), 317-351. https://doi.org/10.1007/BF00280031
  4. M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (1971), 321-340. https://doi.org/10.1016/0022-1236(71)90015-2
  5. M. G. Crandall and P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971), 487-513. https://doi.org/10.1016/0022-1236(71)90030-9
  6. M. G. Crandall and P. H. Rabinowitz, The principle of exchange of stability, Dynamical systems, Proc. Internat. Sympos., Univ. Florida, Gainesville, Fla., (1976), 27-41.
  7. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Oxford University Press, 1993.
  8. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, New York, 1984.
  9. M. Golubitsky and D. G. Schaffer, Singularities and Groups in Bifurcation Theory Vol. I, Springer-Verlag, New York, 1985.
  10. A. Jakli, T. Kosa, A. Vajda, E. Benkler, I. Janossy, and P. Palffy-Muhoray, Optically induced periodic structures in smectic-C liquid crystals, Phys. Rev. E, 63 (2000), 011705-5. https://doi.org/10.1103/PhysRevE.63.011705
  11. H. Kielhofer, Bifurcation Theory: An introduction with applications to PDEs, Springer-Verlag, New York, 2004.
  12. S. T. Lagerwall, Ferroelectric and Antiferroelectric Liquid Crystals, Wiley- VCH, 1999.
  13. L. Modica, The Gradient Theory of Phase Transitions and the Minimal Inter- face Criterion, Arch. Ration. Mech. Anal. 98 (1987), 123-142.
  14. L. Modica and S. Mortola, Un esempio di ${\Gamma}^-$-convergenza (italian), Boll. Un. Mat. Ital. A, 14-B (1977), 285-299.
  15. N. J. Mottram and C. Newton, Introduction to Q-tensor theory, University of Strathclyde, Department of Mathematics research report, 2004:10 (2004).
  16. I. Musevic, R. Blinc, and B. Zeks, The Physics of Ferroelectric and Antifer- roelectric Liquid Crystals, World-Scientific, Singapore, New Jersey, London, Hong Kong, 2000.
  17. P. K. Mukherjee, H. R. Brand, and H. Pleiner, Landau Model of the Smectic C - Isotropic Phase Transition, Physica A, 312 (2002).
  18. J. Park and M. C. Calderer, Analysis of nonlocal electrostatic effects in chiral smectic c liquid crystals, SIAM J. Appl. Math. 66 (2006), 2107-2126. https://doi.org/10.1137/050641120
  19. S. Pikin, Structural Transformations in Liquid Crystals, Gordon and Breach Science Publishers, New York, 1991.
  20. P. Sternberg, The effect of a singular perturbation on nonconvex variational problems, Arch. Ration. Mech. Anal. 101 (1988), 206-260.
  21. F. Verhurst, Nonlinear Differential Equations and Dynamical Systems, Springer-Verlag, New York, 2000.