Zeitschrift für Physik B Condensed Matter

, Volume 78, Issue 2, pp 229–234 | Cite as

EHD instabilities in nematics driven by dichotomous noise: Stability criteria and influence of free boundary conditions

  • R. Müller
  • U. Behn


Different criteria for the onset of EHD instabilities in nematic liquid crystals driven by dichotomous stochastic electric fields are compared within a 1d linear model. Sample stability gives always higher, energetic stability always lower thresholds than the first moment's stability investigated in a previous paper, showing the same qualitative behaviour. Especially the direct transition towards chaos above a critical strength of the noise and the change from stabilizing to destabilizing effect of the noise with increasing correlation time can be explained. The influence of free boundary conditions is investigated analyzing first moment's stability of a 2d linear model. The thresholds are slightly higher but behave qualitatively like in the 1d model. The Williams strip pattern becomes more narrow both with increasing strength and mean frequency of the noise.


Neural Network Linear Model Liquid Crystal Nonlinear Dynamics Lower Threshold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Noise in nonlinear dynamical systems. Moss, F., McClintock, P.V.E. (eds.), Vols 1–3. Cambridge; Cambridge University Press 1989Google Scholar
  2. 2.
    Proceedings of the Workshop on external noise and its interaction with spatial degrees of freedom in nonlinear dissipative systems. In: J. Stat. Phys.54, Nos. 5/6 (1989)Google Scholar
  3. 3.
    Brand, H.R., Doering, C.R., Ecke, R.E.: J. Stat. Phys.54, 1111 (1989)Google Scholar
  4. 4.
    Zippelius, A., Lücke, M.: J. Stat. Phys.24, 345 (1981)Google Scholar
  5. 5.
    Benzi, R., Sutera, A.: J. Phys. A17, 2551 (1984)Google Scholar
  6. 6.
    Satchell, J.S., Sarkar, S.: J. Phys. A20, 1333 (1987)Google Scholar
  7. 7.
    Wulbrand, W., Kagerman, H.: Physica131A, 182 (1985)Google Scholar
  8. 8.
    Niemela, J.J., Donnelly, R.J.: Phys. Rev. Lett.57, 2524 (1986)Google Scholar
  9. 9.
    deNigris, G., Nicolis, G., Frisch, H.: Phys. Rev. A34, 4211 (1986)Google Scholar
  10. 10.
    Ecke, R., Haucke, H.: J. Stat. Phys.54, 1153 (1989)Google Scholar
  11. 11.
    Moss, F., Welland, G.V.: Phys. Rev. A25, 3389 (1982)Google Scholar
  12. 12.
    Griswold, D., Lorenson, C.P., Tough, J.T.: Phys. Rev. B35, 3149 (1987)Google Scholar
  13. 13.
    Schumaker, M.F., Horsthemke, W.: Phys. Rev. A36, 354 (1987)Google Scholar
  14. 14.
    Griswold, D., Tough, J.T.: Phys. Rev. A36, 1360 (1987)Google Scholar
  15. 15.
    Tough, J.: J. Stat. Phys.54, 1173 (1989)Google Scholar
  16. 16.
    Horthemke, W., Schumaker, M.: J. Stat. Phys.54, 1175 (1989)Google Scholar
  17. 17.
    Schumaker, M., Horsthemke, W.: J. Stat. Phys.54, 1189 (1989)Google Scholar
  18. 18.
    Dissler, R.J., Brand, H.R.: Phys. Lett.130A, 293 (1988)Google Scholar
  19. 19.
    Brand, H.R., Deissler, R.J.: Phys. Rev. A39, 462 (1989)Google Scholar
  20. 20.
    Brand, H.R., Deissler, R.J.: Phys. Rev. A39, 462 (1989)Google Scholar
  21. 20a.
    Deissler, R.J.: J. Stat. Phys54, 1459 (1989)Google Scholar
  22. 21.
    Kai, S., Kai, T., Takata, M., Hirakawa, K.: J. Phys. Soc. Jpn.47, 1379 (1979)Google Scholar
  23. 22.
    Brand, H., Schenzle, A.: J. Phys. Soc. Jpn.48, 1382 (1980)Google Scholar
  24. 23.
    Kawakubo, T., Yanagita, A., Kabashima, S.: J. Phys. Soc. Jpn.50, 1451 (1981)Google Scholar
  25. 24.
    Lefever, R., Horsthemke, W.: In: Nolinear phenomena in chemical dynamics. Vidal, C., Pacault, A. (eds.), pp 120. Berlin, Heidelberg, New York: Springer 1981Google Scholar
  26. 25.
    SanMiguel, M., Sancho, J.M.: Z. Phys. B-Condensend Matter43, 361 (1981)Google Scholar
  27. 26.
    Horsthemke, W., Lefever, R.: Noise induced transitions. Berlin, Heidelberg, New York: Springer 1983Google Scholar
  28. 27.
    Kus, M., Wódkiewicz, K.: Phys. Lett.99A, 223 (1983)Google Scholar
  29. 28.
    Brand, H.R., Kai, S., Wakabayashi, S.: Phys. Rev. Lett.54, 555 (1985)Google Scholar
  30. 29.
    Behn, U., Müller, R.: Phys. Lett.113A, 85 (1985)Google Scholar
  31. 30.
    Kai, S., Tamura, T., Wakabayashi, S., Imasaki, M., Brand, H.R.: IEEE-IAS Conf. Records85 CH, 1555 (1985)Google Scholar
  32. 31.
    Horsthemke, W., Doering, C.R., Lefever, R., Chi, A.S.: Phys. Rev. A31, 1123 (1985)Google Scholar
  33. 32.
    Kai, S., Wakabayashi, S., Imasaki, M.: Phys. Rev. A.33, 2612 (1986)Google Scholar
  34. 33.
    Müller, R., Behn, U.: Z. Phys. B-Condensed Matter69, 185 (1987)Google Scholar
  35. 34.
    Kai, S., Fukumaga, H., Brand, H.R.: J. Phys. Soc. Jpn.56, 3759 (1987)Google Scholar
  36. 35.
    Kai, S., Fukunaga, H., Brand, H.R.: J. Stat. Phys.54, 1133 (1989)Google Scholar
  37. 36.
    Kai, S.: In Ref. 1, pp 22Google Scholar
  38. 37.
    Brand, H.R.: In Ref. 1, pp 77Google Scholar
  39. 38.
    Buka, A., Behn, U.: Budapest 1988 (unpublished)Google Scholar
  40. 39.
    Müller, R.: Thesis. KMU Leipzig 1989 (unpublished)Google Scholar
  41. 40.
    Hoffmann, K.H.: Z. Phys. B-Condensed Matter49, 1465 (1985)Google Scholar
  42. 41.
    Lücke, M., Schank, F.: Phys. Rev. Lett.54, 1465 (1985)Google Scholar
  43. 42.
    Lücke, M., Schank, F.: Phys. Rev. Lett.54, 1465 (1985)Google Scholar
  44. 42.
    Feigel'mann, M.V., Staroselsky, I.E.: Z. Phys. B-Condensed Matter62, 261 (1986)Google Scholar
  45. 43.
    Bourret, R.C., Frisch, U., Pouquet, A.: Physica64, 303 (1973)Google Scholar
  46. 44.
    Arnold, L., Kloeden, P.: Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise, to appear in: SIAM J. Appl. Math. (1989)Google Scholar
  47. 45.
    Dubois-Violette, E., deGennes, P.G., PArodi, O.: J. Phys. (Paris)32, 305 (1971); Dubois-Violette, E: J. Phys. (Paris)33 95 (1972) Smith, I.W., Galerne, Y., Lagerwall, S.T., Dubois-Violette, E., Durand, G.: J. Phys. (Paris)36, C1-237 (1975)Google Scholar
  48. 46.
    Tsuchiya, Y., Horie, S.: J. Phys. Soc. Jpn.55, 2945 (1986)Google Scholar
  49. 47.
    Shapiro, V.E., Loginov, V.M.,: Physica91 A 563 (1978)Google Scholar
  50. 48.
    Goossens, W.J.A.: In: Advances in liquid crystals. Brown, G.H. (ed.), Vol. 3, p 1. New York, SanFrancisco, London: Academic Press 1978Google Scholar
  51. 49.
    Oseledec, V.I.: Trans. Moscow Math Soc.19, 197 (1986)Google Scholar
  52. 50.
    Bateman, H., Erdélyi, A.: Higher transcendental functions. Vol. 1. New York, Toronto, London: McGraw-Hill 1953Google Scholar
  53. 51.
    Bodenschatz, E., Zimmermann, W., Kramer, L.: J. Phys. (Paris)49, 1875 (1988)Google Scholar
  54. 52.
    Klosek-Dygas, M.M., Matkowsky, B.J., Schuss, Z.: Phys. Lett.130 A, 11 (1988)Google Scholar
  55. 53.
    Meunier, C., Verga, A.D.: J. Stat. Phys.50, 345 (1988)Google Scholar
  56. 54.
    Meron, E.: Phys. Rev. A35, 4892 (1987)Google Scholar
  57. 55.
    Barbero, G., Durand, G.: Phys. Rev. A35, 1294 (1987)Google Scholar
  58. 56.
    Madhusudana, N.V., Raghunathan, V.A.: Mol. Cryst. Liq. Cryst. Lett.5, 201 (1988)Google Scholar
  59. 57.
    Thom, W., Zimmermann, W., Kramer, L.: The influence of the flexoelectric effect on the electrohydrodynamic instability in nematics, preprint. Bayreuth 1988Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • R. Müller
    • 1
  • U. Behn
    • 1
  1. 1.Sektion PhysikKarl-Marx-Universität LeipzigLeipzigGerman Democratic Republic

Personalised recommendations