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Formation of traveling waves in nematics due to material parameter ramps

Karen K. Vardanyan*

Daniel R. Spiegel

  • Department of Physics & Geology, The University of Texas-Pan American, Edinburg, Texas 78539, USA

  • Department of Physics & Astronomy, Trinity University, San Antonio, Texas 78212, USA

  • *Author to whom correspondence should be addressed.
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Phys. Rev. E 76, 031703 – Published 6 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031703

Abstract

We propose a simple one-dimensional linear model to describe the formation of localized traveling waves due to material parameter ramps in nematic liquid crystals. We assume that due to some external perturbation the material parameters (conductivity, dielectric constants, viscosity, elasticity) of the liquid crystal become slowly varying functions of position. Temperature gradient in localized regions induced by a laser beam could be one such perturbation. We obtain a 4×4 system of electrohydrodynamic equations [partial derivative equations (PDE) with respect to time and position]. At first we assume that all parameters change from their nonperturbed value by the same ramp function. Then, to reveal the parameters which slowly change are predominant in the formation of localized traveling waves, we obtain four more systems of equations. Each time we assume that just one of the material parameters changes while the others are held constant. Accordingly, by reducing 4×4 systems of equations into one equation and using a WKB-like approach for nonuniform media, we obtain the relevant dispersion relations. We show that ramps of elasticity and dielectric parameters play the dominant role in the formation of localized traveling waves in nonuniform nematic media.

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References (37)

  1. M. A. Scherer and G. Ahlers, Phys. Rev. E 65, 051101 (2002).
  2. D. Funfschilling, B. Sammuli, and M. Dennin, Phys. Rev. E 67, 016207 (2003).
  3. T. John, U. Behn, and R. Stannarius, Phys. Rev. E 65, 046229 (2002).
  4. W. I. Goldburg, Y. Y. Goldschmidt, and H. Kellay, Phys. Rev. Lett. 87, 245502 (2001).
  5. M. Scheuring, L. Kramer, and J. Peinke, Phys. Rev. E 58, 2018 (1998).
  6. N. Éber, S. Németh, A. G. Rossberg, L. Kramer, and Á. Buka, Phys. Rev. E 66, 036213 (2002).
  7. S. Komineas, H. Zhao, and L. Kramer, Phys. Rev. E 67, 031701 (2003).
  8. Á. Buka, B. Dressel, W. Otowski, K. Camara, T. Toth-Katona, L. Kramer, J. Lindau, G. Pelzl, and W. Pesch, Phys. Rev. E 66, 051713 (2002).
  9. J.-H. Huh, Y. Hidaka, A. G. Rossberg, and S. Kai, Phys. Rev. E 61, 2769 (2000).
  10. G. H. Heilmeier, L. H. Zanoni, and L. H. Barton, Proc. IEEE 56, 1162 (1968).
  11. E. F. Carr, J. Chem. Phys. 39, 1979 (1963).
  12. W. Helfrich, J. Chem. Phys. 51, 4092 (1969).
  13. P. A. Penz and G. W. Ford, Phys. Rev. A 6, 414 (1972).
  14. S. A. Pikin, Sov. Phys. JETP 33, 641 (1971).
  15. W. J. A. Goossens, in Advances in Liquid Crystals, edited by G. H. Brown (Academic Press, New York, 1978), Vol. 3.
  16. M. Dennin, G. Ahlers, and D. S. Cannell, Science 272, 388 (1996).
  17. M. Dennin, G. Ahlers, and D. S. Cannell, Phys. Rev. Lett. 77, 2475 (1996).
  18. M. Dennin, D. S. Cannell, and G. Ahlers, Phys. Rev. E 57, 638 (1998).
  19. M. Dennin, M. Treiber, L. Kramer, G. Ahlers, and D. S. Cannell, Phys. Rev. Lett. 76, 319 (1996).
  20. A. Joets and R. Ribotta, Phys. Rev. Lett. 60, 2164 (1988).
  21. H. R. Brand, C. Fradin, P. L. Finn, W. Pesch, and P. E. Cladis, Phys. Lett. A 235, 508 (1997).
  22. N. C. Giebink, E. R. Johnson, S. R. Saucedo, E. W. Miles, K. K. Vardanyan, D. R. Spiegel, and C. C. Allen, Phys. Rev. E 69, 066303 (2004).
  23. D. R. Spiegel, E. R. Johnson, and Skyler R. Saucedo, Phys. Rev. E 73, 036317 (2006).
  24. E. L. Koschmieder, Adv. Chem. Phys. 32, 109 (1975).
  25. J. P. Gollub, in Nonlinear Dynamics and Turbulence, edited by D. Joseph and G. Iooss (Pittman, New York, 1982).
  26. F. H. Busse, in Hydrodynamic Instabilities and the Transition to Turbulence (Springer-Verlag, Berlin, 1981).
  27. J. S. Langer, Rev. Mod. Phys. 52, 1 (1980).
  28. M. Flicker and J. Ross, J. Chem. Phys. 60, 3458 (1974).
  29. P. C. Fife, Mathematical Aspects of Reacting and Diffusing Systems (Springer-Verlag, Berlin, 1979).
  30. Y. Pomeau and P. Manneville, J. Phys. (Paris), Lett. 40, 609 (1979).
  31. M. C. Cross, P. G. Daniels, P. C. Hohenberg, and E. D. Siggia, Phys. Rev. Lett. 45, 898 (1980).
  32. Y. Pomeau and P. Manneville, Phys. Lett. 75A, 296 (1980).
  33. Y. Pomeau and S. Zaleski, J. Phys. (Paris) 42, 515 (1981).
  34. Y. Pomeau and P. Manneville, J. Phys. (Paris) 42, 1067 (1981).
  35. M. C. Cross, P. G. Daniels, P. C. Hohenberg, and E. D. Siggia, Phys. Rev. Lett. 45, 898 (1980).
  36. L. Kramer, E. Ben-Jacob, H. Brand, and M. C. Cross, Phys. Rev. Lett. 49, 1891 (1982).
  37. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

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Phys. Rev. E 76, 031703– Published 6 September, 2007
  • Received 21 February 2007

© 2007 American Physical Society

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