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Electrohydrodynamic Convection in Nematics

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Evolution of Spontaneous Structures in Dissipative Continuous Systems

Part of the book series: Lecture Notes in Physics ((LNPMGR,volume 55))

Abstract

The purpose of this review is to present a status report on the electrohydrodynamic convection in nematic liquid crystals. The considerable progress achieved in the past two years is emphasized.

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References

  1. P. Manneville, Dissipative Structures and Weak Turbulence, Academic Press, (New York 1990).

    MATH  Google Scholar 

  2. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).

    Article  ADS  Google Scholar 

  3. F. H. Busse, Fundamentals of thermal convection, in W. R. Peltier, editor, Mantle convection, Plate Tectonics and Global Dynamics, page 23, Gordon and Breach, (1989).

    Google Scholar 

  4. P. de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press, (NewYork 1983).

    Google Scholar 

  5. S. Chandrasekhar, Liquid Crystals, University Press, (Cambridge 1992).

    Book  Google Scholar 

  6. A. Buka and E. L. Kramer, Pattern formation in liquid crystals, Springer-Verlag, (New York 1995).

    Google Scholar 

  7. E. Dubois-Violette, G. Durand, E. Guyon, P. Manneville, and P. Pieranski, Instabilities in nematic liquid crystals, in L. Liebert, editor, Solid state physics, Suppl. 14, page 147, Academic Press, New York, (1978).

    Google Scholar 

  8. L. M. Blinov, Electrooptical and Magnetooptical Properties of Liquid Crystals, John Wiley, (New York 1983).

    Google Scholar 

  9. S. A. Pikin, Structural Transformations in Liquid Crystals, Gordon and Breach Science Publishers, (New York 1991).

    Google Scholar 

  10. I. Rehberg, B. L. Winkler, M. de la Torre, S. Rasenat, and W. Schöpf, Adv. Solid State Physics 29, 35 (1989).

    Article  Google Scholar 

  11. S. Kai and W. Zimmermann, Prog. Theor. Phys. Suppl. 99, 458 (1989).

    Article  ADS  Google Scholar 

  12. L. Kramer, E. Bodenschatz, W. Pesch, W. Thom, and W. Zimmermann, Liquid Crystals 5(2), 699 (1989).

    Article  Google Scholar 

  13. W. Zimmermann, MRS Bulletin XVI, 46 (1991).

    Google Scholar 

  14. S. Kai, Forma 7, 189 (1992).

    Google Scholar 

  15. L. Kramer and W. Pesch, Annu. Rev. Fluid Mech. 27, 515 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  16. L. Kramer and W. Pesch, Electrohydrodynamic instabilities in nematic liquid crystals, in A. Buka and L. Kramer, editors, Pattern formation in liquid crystals, Springer, (New York 1995).

    Google Scholar 

  17. E. Bodenschatz, W. Zimmermann, and L. Kramer, J. Phys.(Paris) 49, 1875 (1988).

    Google Scholar 

  18. M. Treiber, N. Eber, Á. Buka, and L. Kramer, J. Phys. France II 7, 649–661 (1997).

    Article  Google Scholar 

  19. M. Dennin, G. Ahlers, and D. Cannell, Measurement of material parameters of the nematic crystal i52, in P. Cladis and P. Palffy-Muhoray, editors, Spatio-temporal patterns in nonequilibrium complex systems, Santa Fe Institute Studies in the Sciences of Complexity XXI, Addison-Wesley, New York, (1994).

    Google Scholar 

  20. M. Dennin, D. Cannell, and G. Ahlers, Mol. Cryst. Liq. Cryst. 261, 337 (1995).

    Article  Google Scholar 

  21. M. Dennin, G. Ahlers, and D. S. Cannel, Phys. Rev. Lett. 77, 2475 (1996).

    Article  ADS  Google Scholar 

  22. H. R. Brand, C. Fradin, P. L. Finn, W. Pesch, and P. E. Cladis, Physics Lett. A 235, 508 (1997).

    Article  ADS  Google Scholar 

  23. I. Rehberg, S. Rasenat, M. de la Torre Juarez, W. Schöpf, F. Hörner, G. Ahlers, and H. Brand, Phys.Rev.Lett 67, 596 (1991).

    Article  ADS  Google Scholar 

  24. M. Treiber, Thermal fluctuations in pattern forming instabilities, in A. Buka and L. Kramer, editors, Pattern formation in liquid crystals, Springer, (New York 1995).

    Google Scholar 

  25. M. J. Stephen and J. P. Straley, Rev. Mod. Phys. 46, 617 (1974).

    Article  ADS  Google Scholar 

  26. H. Pleiner and H. Brandt, Hydrodynamics and electrohydrodynamics of liquid crystals, in A. Buka and L. Kramer, editors, Pattern formation in liquid crystals, Springer, (New York 1995).

    Google Scholar 

  27. F. M. Leslie, Quart. J. Mech. Appl. Math. 19, 357 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  28. O. Parodi, J. Phys. (Paris) 31, 581 (1970).

    Google Scholar 

  29. F. H. Busse and E. W. Bolton, J. Fluid Mech. 146, 115 (1984).

    Article  MATH  ADS  Google Scholar 

  30. R. B. Meyer, Phys. Rev. Lett. 22, 918 (1969).

    Article  ADS  Google Scholar 

  31. N. Madhusudana and G. Durand, J. Phys.Paris 46, L195 (1985).

    Google Scholar 

  32. W. Decker, PhD thesis, Universität Bayreuth, (1995).

    Google Scholar 

  33. M. Treiber and L. Kramer, Mol. Cryst. Liq. Cryst. 261, 311 (1995).

    Article  Google Scholar 

  34. A. C. Newell, T. Passot, and J. Lega, Annu. Rev. Fluid Mech. 25, 399 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  35. G. Dangelmayer and L. Kramer, in F. Busse and A. Müller, editors, this volume, Springer, (New York 1998).

    Google Scholar 

  36. W. Pesch and L. Kramer, General mathematical description of pattern forming instabilities, in A. Buka and L. Kramer, editors, Pattern formation in liquid crystals, Springer, (New York 1995).

    Google Scholar 

  37. Orsay Liquid Crystal Group, Phys. Rev. Lett. 26, 1642 (1970).

    Article  ADS  Google Scholar 

  38. E. Dubois-Violette, P. G. de Gennes, and O. J. Parodi, J. Phys.(Paris) 32, 305 (1971).

    Google Scholar 

  39. H. Haken, Synergetics, Springer-Verlag, (1978).

    Google Scholar 

  40. M. C. Cross, Phys. Fluids 23, 1727 (1980).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  41. Q. Feng, W. Pesch, and L. Kramer, Phys. Rev. A 45, 7242 (1992).

    Article  ADS  Google Scholar 

  42. Q. Feng, W. Decker, W. Pesch, and L. Kramer, J. Phys. France II, 1303 (1992).

    Google Scholar 

  43. M. Kaiser and W. Pesch, Phys. Rev. E 48, 4510 (1993).

    Article  ADS  Google Scholar 

  44. V. Ginzburg and L. Landau, Zh.Eksp.Teor.Fiz. 20, 1064 (1950).

    Google Scholar 

  45. W. Pesch and L. Kramer, Z.Phys. B 63, 121 (1986).

    Article  ADS  Google Scholar 

  46. L. Kramer, E. Bodenschatz, W. Pesch, and W. Zimmermann, in W. Güttinger and G. Dangelmayr, editors, The Physics of Structure Formation, Springer, (Berlin 1987).

    Google Scholar 

  47. E. Bodenschatz, M. Kaiser, L. Kramer, W. Pesch, A. Weber, and W. Zimmermann, Patterns and defects in liquid crystals, in P. Coullet and P. Huerre, editors, New Trends in Nonlinear Dynamics and Pattern Forming Phenomena: The Geometry of Nonequilibrium, Plenum Press, (1990). NATO ASI Series.

    Google Scholar 

  48. A. C. Newell and J. A. Whitehead, J. Fluid Mech. 38, 279 (1969).

    Article  MATH  ADS  Google Scholar 

  49. L. A. Segel, J. Fluid Mech. 38, 203 (1969).

    Article  MATH  ADS  Google Scholar 

  50. A. Buka and L. Kramer, Theory of transient patterns in the splay freedericksz transition of nematics, in S. Kai, editor, Pattern formation in complex dissipative systems, World Scientific, (Kitakyushu, Japan 1991).

    Google Scholar 

  51. W. Decker and W. Pesch, J.Phys.II France 4, 493 (1994).

    Article  Google Scholar 

  52. A. G. Rossberg, A. Hertrich, L. Kramer, and W. Pesch, Phys. Rev. Lett. 76, 4729–4732 (1996).

    Article  ADS  Google Scholar 

  53. M. I. Tribelsky and K. Tsuboi, Phys. Rev. Lett 76, 1631 (1996).

    Article  ADS  Google Scholar 

  54. H. Riecke, Phys. Rev. Lett. 68, 301 (1992).

    Article  ADS  Google Scholar 

  55. H. Riecke and G. D. Granzow, to appear in Phys. Rev. Lett., (1998).

    Google Scholar 

  56. E. Plant and W. Pesch, to appear in Phys. Rev. E (1998).

    Google Scholar 

  57. H. Zhao and L. Kramer, in preparation, (1998).

    Google Scholar 

  58. H. Zhao, L. Kramer, I. Rehberg, and A. Rudroff. submitted to Phys. Rev. Lett, (1998).

    Google Scholar 

  59. E. F. Carr, Mol. Cryst. Liq. Cryst. 7, 253 (1969).

    Article  Google Scholar 

  60. W. Helfrich, J. Chem. Phys. 51, 4092 (1969).

    Article  ADS  Google Scholar 

  61. R. Ribotta and A. Joets, Defects and interactions with the structure in ehd convection in nematic liquid crystals, in J. E. Wesfreid and S. Zaleski, editors, Cellular Structure in Instabilities, page 249, Springer, (Berlin 1984).

    Chapter  Google Scholar 

  62. A. Joets and R. Ribotta, J. Phys.(Paris) 47, 595 (1986).

    Google Scholar 

  63. S. Kai and K. Hirakawa, Prog. Theor. Phys. Snppl. 64, 212 (1978).

    Article  ADS  Google Scholar 

  64. S. Kai, N. Chizumi, and M. Kohno, Phys. Rev. A 40, 6554 (1989).

    Article  ADS  Google Scholar 

  65. S. Kai. unpublished, (1988).

    Google Scholar 

  66. A. Joets and R. Ribotta, Phys. Rev. Letters 60, 2164 (1988).

    Article  ADS  Google Scholar 

  67. I. Rehberg, S. Rasenat, and V. Steinberg, Phys. Rev. Lett. 62, 756 1237

    Article  Google Scholar 

  68. I. Rehberg, S. Rasenat, M. de la Torre-Juarez, and V. Steinberg, Phys. Rev. Lett. 61, 2448 (1988).

    Article  ADS  Google Scholar 

  69. M. Treiber, On the Theory of the Electrohydrodynamic Instability in Nematic Liquid Crystals near Onset, PhD thesis, Universität Bayreuth, (1996).

    Google Scholar 

  70. M. Lowe and J. Gollub, Phys.Rev.Lett 55, 2575 (1985).

    Article  ADS  Google Scholar 

  71. S. Rasenat, E. Braun, and V. Steinberg, Phys. Rev. A 42, 5728 (1991).

    Article  ADS  Google Scholar 

  72. S. Nasuno and S. Kai, Europhys. Lett. 14(8), 779 (1991).

    Article  ADS  Google Scholar 

  73. S. Nasuno, S. Takeuchi, and Y. Sawada, Phys. Rev. A40, 3457 (1989).

    ADS  Google Scholar 

  74. G. Goren, I. Procaccia, S. Rasenat, and V. Steinberg, Phys. Rev. Lett. 63, 1237 (1989). It appears that there is no merit to the theory presented in this paper, see L. Kramer, E. Bodenschatz and W. Pesch, Phys. Rev. Lett. 64, 2588 (1990)

    Article  ADS  Google Scholar 

  75. S. Rasenat, V. Steinberg, and I. Rehberg, Phys. Rev. A 42, 5998 (1990).

    Article  ADS  Google Scholar 

  76. E. Braun and V. Steinberg, Europhys. Lett. 15(2), 167 (1991).

    Article  ADS  Google Scholar 

  77. W. Pesch, W. Decker, Q. Feng, M. Kaiser, L. Kramer, and A. Weber, Weakly nonlinear analysis of pattern formation in nematic liquid crystals, in J. M. Coron, F. Helein, and J. M. Ghidaglia, editors, Nematics: Mathematical and Physical Aspects, page 291, Kluwer Academic Publishers, (Dordrecht 1991). NATO ASI Series.

    Google Scholar 

  78. M. Kaiser, W. Pesch, and E. Bodenschatz, Physica D 59, 320 (1992).

    Article  MATH  ADS  Google Scholar 

  79. S. Sasa, Prog. Theor. Phys. 83, 824 (1990).

    Article  ADS  Google Scholar 

  80. S. Sasa, Prog. Theor. Phys. 84, 1009 (1990).

    Article  ADS  Google Scholar 

  81. E. Braun, S. Rasenat, and V. Steinberg, Europhys. Lett. 15, 597 (1991).

    Article  ADS  Google Scholar 

  82. S. Nasuno, O. Sasaki, S. Kai, and W. Zimmermann, Stability diagram in electrohydrodynamic convection of nematics electrohydrodynamic convection in nematics: the homeotropic case, in S. Kai, editor, Pattern formation in complex dissipative systems and Global Dynamics, page 275, World scientific, (1992).

    Google Scholar 

  83. E. Plant, W. Decker, A. Rossberg, L. Kramer, and W. Pesch, Phys. Rev. Lett. 79, 2376, (1997).

    ADS  Google Scholar 

  84. H. Richter, A. Buka, and I. Rehberg, in P. Cladis and P. Palffy-Muhoray, editors, Spatio-temporal patterns in nonequilibrium complex systems, Santa Fe Institute Studies in the Sciences of Complexity XXI, Addison-Wesley, New York, (1994).

    Google Scholar 

  85. M. Dennin, M. Treiber, L. Kramer, G. Ahlers, and D. Cannell, Phys. Rev. Lett. 76, 319 (1996).

    Article  ADS  Google Scholar 

  86. M. Treiber and L. Kramer, to appear in Phys. Rev. E (1998).

    Google Scholar 

  87. W. Zimmermann and L. Kramer, Phys. Rev. Lett. 55, 402 (1985).

    Article  ADS  Google Scholar 

  88. M. Dennin, G. Ahlers, and D. S. Cannell, Science 272, 388 (1997).

    Article  ADS  Google Scholar 

  89. E. Moses, J. Fineberg, and V. Steinberg, Phys. Rev. A 35, 2757 (1987).

    Article  ADS  Google Scholar 

  90. R. Heinrichs, G. Ahlers, and D. S. Cannell, Phys. Rev. A 35, 2761 (1987).

    Article  ADS  Google Scholar 

  91. S. Fauve, S. Douady, and O. Thual, J. Phys. (Paris) II 1,311 (1991).

    Google Scholar 

  92. R. Deissler and H. Brand, Phys. Rev. A 44, R3411 (1991).

    Article  ADS  Google Scholar 

  93. R. Deissler and H. Brand, Physica D 117, 95 (1998).

    Article  Google Scholar 

  94. Y. Tu, Phys. Rev. E 56, R6554 (1997).

    Article  ADS  Google Scholar 

  95. U. Bisang and G. Ahlers, Phys.Rev.Lett 80, 3061 (1998).

    Article  ADS  Google Scholar 

  96. M. Dennin, D. S. Cannell, and G. Ahlers, Phys. Rev. E 57, 638 (1997).

    Article  ADS  Google Scholar 

  97. H. Riecke and L. Kramer, submitted to Physica D (1998).

    Google Scholar 

  98. A. Joets and R. Ribotta, J. Stat. Phys. 64, 981 (1991).

    Article  ADS  Google Scholar 

  99. X. Yang, A. Joets, and R. Ribotta, in J. E. Wesfried, H. R. Brand, P. Manneville, G. Albinet, and N. Boccara, editors, Propagation in Systems far from Equilibrium, Springer, (Berlin 1988).

    Google Scholar 

  100. R. Ribotta, A. Joets, and L. Lin, Phys. Rev. Lett. 56, 1595 (1986).

    Article  ADS  Google Scholar 

  101. F. H. Busse, Rep. Prog. Phys. 41, 1929 (1978).

    Article  ADS  Google Scholar 

  102. S. Nasuno, O. Sasaki, S. Kai, and W. Zimmermann, Phys. Rev. A 46, 4954 (1992).

    Article  ADS  Google Scholar 

  103. H. Amm, R. Stannarius, and A. G. Rossberg, submitted to Physica D (1998).

    Google Scholar 

  104. A. Lindner, A. G. Rossberg, and L. Kramer, in preparation.

    Google Scholar 

  105. I. Smith, Y. Galerne, S. Lagerwall, E. Dubois-Violette, and G. Durand, J. Phys. Colloq. France 36, C1–237 (1975).

    Article  Google Scholar 

  106. P. Tóth, Á. Buka, J. Peinke, and L. Kramer, Phys. Rev. E (1997, submitted).

    Google Scholar 

  107. U. Schneider, M. de la Torre-Juarez, W. Zimmermann, and I. Rehberg, Phys. Rev. A 46, 1009 (1992).

    Article  ADS  Google Scholar 

  108. M. Scheuring, L. Kramer, and J. Peinke, Phys. Rev. E (1998, submitted).

    Google Scholar 

  109. S. Kai, Y. Adachi, and S. Nasuno, Stability diagram, defect turbulence, and new patterns in electroconvection in nematics, in P. E. Cladis and P. Palffy-Muhoray, editors, Spatio-Temporal Patterns in Nonequilibrium Complex Systems, Addison-Wesley Publishing Company, (1994). SFI Studies in the Sciences of Complexity.

    Google Scholar 

  110. A. G. Rossberg and L. Kramer, Physica D submitted (1997).

    Google Scholar 

  111. A. Rossberg, PhD thesis, Universität Bayreuth, (1997).

    Google Scholar 

  112. A. Hertrich, PhD thesis, Universität Bayreuth, (1995).

    Google Scholar 

  113. L. Kramer, A. Hertrich, and W. Pesch, Electrohydrodynamic convection in nematics: the homeotropic case, in S. Kai, editor, Pattern formation in complex dissipitative systems and Global Dynamics, page 238, World scientific, (1992).

    Google Scholar 

  114. A. Hertrich, W. Decker, W. Pesch, and L. Kramer, J. Phys. France II 2, 1915 (1992).

    Google Scholar 

  115. H. Richter, N. Klöpper, A. Hertrich, and A. Buka, Europhys. Lett. 30, 37 (1995).

    Article  ADS  Google Scholar 

  116. H. Richter, A. Buka, and I. Rehberg. unpublished.

    Google Scholar 

  117. S. Kai, K. Hayashi, and Y. Hidaka, J. Phys. Chem. 100, 19007 (1996). A

    Article  Google Scholar 

  118. S. Kai, K. Hayashi, and Y. Hidaka, preprint (1997).

    Google Scholar 

  119. G. Küppers and K. Lortz, J. Fluid Mech. 35, 609 (1996).

    Article  Google Scholar 

  120. Y. Hu, R. E. Ecke, and G. Ahlers, Phys. Rev. Lett. 74, 5040 (1995).

    Article  ADS  Google Scholar 

  121. P. Kolodner, S. Slimani, N. Aubry, and R. Lima, Physica D 85, 165 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  122. L. Kramer, E. Bodenschatz, and W. Pesch, Phys. Rev. Lett. 64, 2588 (1990).

    Article  ADS  Google Scholar 

  123. Noise in nonlinear dynamical systems, Vols. 1–3, edited by F. Moss and P. V. E. McClintock(Cambridge University Press, Cambridge, 1989).

    Google Scholar 

  124. S. Kai, T. Kai, M. Takata, and K. Hirakawa, J. Phys. Soc. Jpn. 47, 1379 (1979).

    Article  ADS  Google Scholar 

  125. T. Kawakubo, A. Yanagita, and S. Kabashima, J. Phys. Soc. Jpn. 50, 1451 (1981).

    Article  ADS  Google Scholar 

  126. H. R. Brand, S. Kai, and S. Wakabayashi, Phys. Rev. Lett. 54, 555 (1985).

    Article  ADS  Google Scholar 

  127. S. Kai, T. Tamura, S. Wakabayashi, M. Imasaki, and H. R. Brand, IEEE-IAS Conf. Records 85CH, 1555 (1985).

    Google Scholar 

  128. S. Kai, H. Fukunaga, H. R. Brand, J. Phys. Soc. Jpn. 56, 3759 (1987).

    Article  ADS  Google Scholar 

  129. S. Kai, H. Fukunaga, H. R. Brand, J. Stat. Phys 54, 1133 (1989).

    Article  ADS  Google Scholar 

  130. S. Kai, in: P. V. E. McClintock(Cambridge University Press, Cambridge, 1989). Ref. [123], 22–76.

    Google Scholar 

  131. H. R. Brand, in: P. V. E. McClintock(Cambridge University Press, Cambridge, 1989). Ref. [123], 77–89.

    Google Scholar 

  132. U. Behn and R. Müller, Phys. Lett. 113A, 85 (1985).

    ADS  Google Scholar 

  133. R. Müller and U. Behn, Z. Phys. B 69, 185 (1987).

    Article  ADS  Google Scholar 

  134. R. Müller and U. Behn, Z. Phys. B 78, 229 (1990).

    Article  ADS  Google Scholar 

  135. A. Lange, R. Müller, and U. Behn, Z. Phys. B 100, 477 (1996).

    Article  ADS  Google Scholar 

  136. H. Amm, U. Behn, N. Klöpper, and R. Stannarius, 25. Freiburger Arbeitstagung Flüssigkristalle (1996).

    Google Scholar 

  137. H. Amm, U. Behn, Th. John, and R. Stannarius, Mol. Cryst. Liq. Cryst. 304, 525 (1997).

    Article  Google Scholar 

  138. Th. John, Diploma thesis (Universität Leipzig, 1997).

    Google Scholar 

  139. U. Behn, A. Lange, and Th. John, Phys. Rev. E 58, 2047 (1998).

    Article  ADS  Google Scholar 

  140. U. Behn, Th. John, and R. Stannarius, On-off intermittency in electrohydrodynamic convection in nematics driven by multiplicative noise, in preparation.

    Google Scholar 

  141. M. Fricke, A. Kühnel, and U. Behn, preprint NTZ 47/1997.

    Google Scholar 

  142. N. Platt, E. A. Spiegel, and C. Tresser, Phys. Rev. Lett. 70, 279 (1993); J. F. Heagy, N. Platt, and S. M. Hammel, Phys. Rev. 49, 1140 (1994).

    Article  ADS  Google Scholar 

  143. W. Horsthemke and R. Lefever, Noise induced transitions (Springer-Verlag, Berlin, 1983).

    Google Scholar 

  144. R. C. Bourret, U. Frisch, and A. Pouquet, Physica 65, 303 (1973).

    Article  ADS  Google Scholar 

  145. L. Arnold and P. Kloeden, SIAM J. Appl. Math. 49, 1242 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  146. L. Arnold and R. Khasminskii, in: Stochastic Analysis, Proceedings of Symposia in Pure Mathematics, Volume 57, pp 543, edited by M.C. Cranston and M.A. Pinsky (American Mathematical Society, Providence, Rhode Island, 1995).

    Google Scholar 

  147. E. Dubois-Violette, J. Phys. (Paris) 33, 95 (1972).

    Google Scholar 

  148. W. J. A. Goossens, in: Advances in liquid crystals, Vol. 3, pp 1, edited by G.H. Brown (Academic Press, New York, 1978).

    Google Scholar 

  149. A. Crisanti, G. Paladin, and A. Vulpiani, Products of Random Matrices in Statistical Physics, Vol. 104 of Springer Series in Solid-State Sciences, edited by M. Cardona, P. Fulde, K. von Klitzing, and H.-J. Queisser (Springer-Verlag, Berlin, 1993).

    Google Scholar 

  150. V. E. Shapiro and V. M. Loginov, Physica A 91, 563 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  151. V. I. Oseledec, Trans. Moscow Math. Soc. 19, 197 (1968).

    MathSciNet  Google Scholar 

  152. N. V. Madhusudana, V. A. Raghunathan, and K. R. Sumathy, Pramāna, J. Phys. 28, L311 (1987).

    Google Scholar 

  153. J. M. Deutsch, Phys. Rev. E 48, 4211 (1986).

    Google Scholar 

  154. M. V. Feigel’man and I. E. Staroselsky, Z. Phys. B 62, 261 (1986).

    Article  ADS  Google Scholar 

  155. R. Müller, K. Lippert, A. Küihnel, and U. Behn, Phys. Rev. E 56, 2658 (1997).

    Article  ADS  Google Scholar 

  156. R. Graham, Phys. Rev. A 10, 1762 (1974).

    Article  ADS  Google Scholar 

  157. J. Swift and P. C. Hohenberg, Phys. Rev. A 15, 319 (1977).

    Article  ADS  Google Scholar 

  158. P. C. Hohenberg and J. Swift, Phys. Rev. A 46, 4773 (1992).

    Article  ADS  Google Scholar 

  159. G. De Nigris, G. Nicolis, and H. Frisch, Phys. Rev. A 34, 4211 (1986).

    Article  ADS  Google Scholar 

  160. M. Treiber and L. Kramer, Phys. Rev. E 49, 3184 (1994).

    Article  ADS  Google Scholar 

  161. D.R. Kurtze, Phys. Rev. Lett. 77, 63 (1996).

    Article  ADS  Google Scholar 

  162. J. Vinals, E. Hernández-García, M. San Miguel, and R. Toral, Phys. Rev. A 44, 119 (1993).

    Google Scholar 

  163. T. C. Elston and R. F. Fox, Phys. Rev. A, 44, 8403 (1991).

    Article  ADS  Google Scholar 

  164. E. Hernández-Garcia, M. San Miguel, R. Toral, and J. Vinals, Physica D 61, 159 (1992).

    Article  MATH  ADS  Google Scholar 

  165. E. Hernández-García, J. Viñals, R. Toral, and M. San Miguel, Phys. Rev. Lett. 70, 3576 (1993).

    Article  ADS  Google Scholar 

  166. J. García-Qjalvo, A. Hernández-Machado, and J. M. Sancho, Phys. Rev. Lett. 71, 1542 (1993).

    Article  ADS  Google Scholar 

  167. L. Ramirez-Piscina, A. Hernández-Machado and J. M. Sancho, Phys. Rev. B 48, 119 (1993).

    Article  ADS  Google Scholar 

  168. L. Ramírez-Piscina, A. Hernández-Machado and J. M. Sancho, Phys. Rev. B 48, 125 (1993).

    Article  ADS  Google Scholar 

  169. J. M. Sancho, A. Hernández-Machado, L. Ramírez-Piscina, and A. M. Lacasta, Acta Physica Polonica B 24, 733 (1993).

    Google Scholar 

  170. P.-M. Lam and D. Bagayoko, Phys. Rev. E 48, 3267 (1993).

    Article  ADS  Google Scholar 

  171. T. Yamada, Phys. Lett. A 161, 489 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  172. T. Yamada, K. Fukushima, and H. Fujisaka, Physica A 204, 755 (1994).

    Article  ADS  Google Scholar 

  173. C. Van den Broeck, J. M. R. Parrondo, J. Armero, and A. Hernández-Machado, Phys. Rev. E 49, 2639 (1994).

    Article  ADS  Google Scholar 

  174. A. Becker and L. Kramer, Phys. Rev. Lett. 73, 955 (1994).

    Article  ADS  Google Scholar 

  175. A. Becker and L. Kramer, Physica D 90, 408 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  176. A. Schenzle and H. Brand, Phys. Rev. A 20, 1628 (1979).

    Article  ADS  Google Scholar 

  177. R. Graham and A. Schenzle, Phys. Rev. A 25, 1731 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  178. A. Teubel, U. Behn, and A. Kühnel, Z. Phys. B 71, 393 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  179. J. Roder, H. Röder, and L. Kramer, Phys. Rev. E 55, 7068 (1997).

    Article  ADS  Google Scholar 

  180. A. Hertrich, W. Pesch, and J. T. Gleeson, Europhys. Lett. 44, 417 (1996).

    Article  ADS  Google Scholar 

  181. J. T. Gleeson, Nature, 356, 511, (1996)

    Google Scholar 

  182. R. Faller and L. Kramer, Phys. Rev. E, 57, R6249 (1998).

    Article  ADS  Google Scholar 

  183. B. J. Gluckmann, C.B. Arnold and J.P. Gollub Phys. Rev,. E, 51, 1128, (1995), I. Ning, Y. Hu, R.E. Ecke and G. Ahlers Phys. Rev. Lett. 71, 2216, 1993.

    Article  ADS  Google Scholar 

  184. S. Rudroff and I. Rehberg, Phys. Rev. E, 55, 2742 (1998).

    Article  ADS  Google Scholar 

  185. G. Ahlers, Experiments on thermally driven convection, in A. Buka and L. Kramer, editors, Pattern formation in liquid crystals, Springer, (New York 1995).

    Google Scholar 

  186. L. Thomas, W. Pesch and G. Ahlers, to appear in Phys.Rev.E, 1998.

    Google Scholar 

  187. E. Dubois-Violette and P. Manneville, Flow instabilities in Nematics, in A. Buka and L. Kramer, editors, Pattern formation in liquid crystals, Springer, (New York 1995).

    Google Scholar 

  188. A. P. Krekhov and L. Kramer, Phys. Rev. E, 53, 4925 (1996).

    Article  ADS  Google Scholar 

  189. T. Börzsönyi,A. Buka, A. P. Krekhov and L. Kramer, Phys. Rev. E, submitted (1998) (1996).

    Google Scholar 

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Authors and Affiliations

  1. Universität Bayreuth, D-95447, Bayreuth, Germany

    W. Pesch

  2. Universität Leipzig, D-04109, Leipzig, Germany

    U. Behn

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Pesch, W., Behn, U. (1998). Electrohydrodynamic Convection in Nematics. In: Evolution of Spontaneous Structures in Dissipative Continuous Systems. Lecture Notes in Physics, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49537-1_8

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