Pattern Formation in Liquid Crystals pp 221-255 | Cite as
Electrohydrodynamic Instabilities in Nematic Liquid Crystals
Chapter
Abstract
We discuss various aspects of the progress in the understanding of electroconvec-tion in nematic layers achieved during the last 12 years.
Keywords
Hopf Bifurcation Nematic Liquid Crystal Normal Roll Neutral Curve Dielectric Anisotropy
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References
- [1]R. Williams, J. Chem. Phys. 39, 384 (1963).ADSCrossRefGoogle Scholar
- [2]A. Kapustin and L. Larinova, Kristallografya 9, 297 (1963).Google Scholar
- [3]R. B. Meyer, Phys. Rev. Lett. 22, 918 (1969).ADSCrossRefGoogle Scholar
- [4]N. Madhusudana and G. Durand, J. Phys. (Paris) 46, L195 (1985).Google Scholar
- [5]E. F. Carr, Mol. Crysi. Liq. Cryst. 1, 253 (1969).CrossRefGoogle Scholar
- [6]W. Helfrich, J. Chem. Phys. 51, 4092 (1969).ADSCrossRefGoogle Scholar
- [7]Orsay Liquid Crystal Group, Phys. Rev. Lett. 26, 1642 (1970).ADSCrossRefGoogle Scholar
- [8]E. Dubois-Violette, P. G. de Gennes, and O. J. Parodi, J. Phys. (Paris) 32, 305 (1971).Google Scholar
- [9]P. A. Penz and G. W. Ford, Phys. Rev. A 6, 414 (1972).ADSCrossRefGoogle Scholar
- [10]E. Bodenschatz, W. Zimmermann, and L. Kramer, J. Phys. (Paris) 49, 1875 (1988).Google Scholar
- [11]R. Ribotta and A. Joets, Defects and interactions with the structure in ehd convection in nematic liquid crystals, in Cellular Structure in Instabilities, edited by J. E. Wesfreid and S. Zaleski, Springer, Berlin (1984) p. 249.CrossRefGoogle Scholar
- [12]A. Joets and R. Ribotta, J. Phys. (Paris) 47, 595 (1986).Google Scholar
- [13]S. Kai and K. Hirakawa, Prog. Theor. Phys. Suppl. 64, 212 (1978).ADSCrossRefGoogle Scholar
- [14]S. Kai, N. Chizumi, and M. Kohno, Phys. Rev. A 40, 6554 (1989).ADSCrossRefGoogle Scholar
- [15]W. Zimmermann and L. Kramer, Phys. Rev. Lett. 55, 402 (1985).ADSCrossRefGoogle Scholar
- [16]L. Kramer, E. Bodenschatz, W. Pesch, W. Thom, and W. Zimmermann, Liquid Crystals 5(2), 699 (1989).CrossRefGoogle Scholar
- [17]L. Kramer, A. Hertrich, and W. Pesch, Electrohydrodynamic convection in nematics: the homeotropic case, in Pattern Formation in Complex Dissipitative Systems and Global Dynamics, edited by S. Kai, World scientific, (1992) p. 238.Google Scholar
- [18]E. Bodenschatz, M. Kaiser, L. Kramer, W. Pesch, A. Weber, and W. Zimmermann, Patterns and defects in liquid crystals, in New Trends in Nonlinear Dynamics and Pattern Forming Phenomena: The Geometry of Nonequilibrium, edited by P. Coullet and P. Huerre, Plenum Press, (1990). NATO ASI Series.Google Scholar
- [19]M. Kaiser, W. Pesch, and E. Bodenschatz, Physica D 59, 320 (1992).ADSMATHCrossRefGoogle Scholar
- [20]M. Kaiser and W. Pesch, Phys. Rev. E 48, 4510 (1993).ADSCrossRefGoogle Scholar
- [21]S. Sasa, Prog. Theor. Phys. 83, 824 (1990).ADSCrossRefGoogle Scholar
- [22]S. Sasa, Prog. Theor. Phys. 84, 1009 (1990).ADSCrossRefGoogle Scholar
- [23]M. Lowe and J. Gollub, Phys. Rev. Lett 55, 2575 (1985).ADSCrossRefGoogle Scholar
- [24]S. Rasenat, E. Braun, and V. Steinberg, Phys. Rev. A 42, 5728 (1991).ADSCrossRefGoogle Scholar
- [25]S. Nasuno and S. Kai, Europhys. Lett. 14(8), 779 (1991).ADSCrossRefGoogle Scholar
- [26]S. Nasuno, S. Takeuchi, and Y. Sawada, Phys. Rev. A 40, 3457 (1989).ADSCrossRefGoogle Scholar
- [27a]G. Goren, I. Procaccia, S. Rasenat, and V. Steinberg, Phys. Rev. Lett. 63, 1237 (1989).ADSCrossRefGoogle Scholar
- [27b]It appears that there is no merit in the theory presented in this paper, see L. Kramer, E. Bodenschatz and W. Pesch, Phys. Rev. Lett. 64, 2588 (1990).ADSCrossRefGoogle Scholar
- [28]L. Kramer, E. Bodenschatz and W. Pesch, Phys. Rev. Lett. 64, 2588 (1990).ADSCrossRefGoogle Scholar
- [29]S. Rasenat, V. Steinberg, and I. Rehberg, Phys. Rev. A 42, 5998 (1990).ADSCrossRefGoogle Scholar
- [30]E. Braun and V. Steinberg, Europhys. Lett. 15(2), 167 (1991).ADSCrossRefGoogle Scholar
- [31]E. Braun, S. Rasenat, and V. Steinberg, Europhys. Lett. 15(6), 597 (1991).ADSCrossRefGoogle Scholar
- [32]S. Nasuno, O. Sasaki, S. Kai, and W. Zimmermann, Stability diagram in electrohy-drodynamic convection of nematics electrohydrodynamic convection in nematics: the homeotropic case, in Pattern Formation in Complex Dissipative Systems and Global Dynamics, edited by S. Kai, World Scientific, (1992) p. 275.Google Scholar
- [33]I. Rehberg, S. Rasenat, M. de la Torre Juarez, W. Schöpf, F. Hörner, G. Ahlers, and H. Brand, Phys. Rev. Lett 67, 596 (1991).ADSCrossRefGoogle Scholar
- [34]I. Rehberg, F. Hörner, L. Chiran, H. Richter, and B. Winkler, Phys. Rev. A 44, R7885 (1991).ADSCrossRefGoogle Scholar
- [35]I. Rehberg, F. Hörner, and G. Hartung, J. Stat. Phys. 64, 1017 (1991).ADSCrossRefGoogle Scholar
- [36]A. Joets and R. Ribotta, Phys. Rev. Lett. 60, 2164 (1988).ADSCrossRefGoogle Scholar
- [37]I. Rehberg, S. Rasenat, and V. Steinberg, Phys. Rev. Lett. 62, 756 (1989).ADSCrossRefGoogle Scholar
- [38]M. de la Torre Juarez and I. Rehberg, Phys. Rev. A 42, 2096 (1990).ADSCrossRefGoogle Scholar
- [39]M. Treiber and L. Kramer, Mol. Cryst. Liq. Cryst. 261, 951/311 (1995).CrossRefGoogle Scholar
- [40]M. Dennin, M. Treiber, L. Kramer, G. Ahlers, and D. Cannell, Phys. Rev. Lett 76, 319 (1995).ADSCrossRefGoogle Scholar
- [41]M. Dennin, G. Ahlers, and D. Cannell, Measurement of material parameters of the nematic crystal i52, in Spatio-Temporal Patterns in Nonequilibrium Complex Systems, edited by P. Cladis and P. Palffy-Muhoray, Santa Fe Institute Studies in the Sciences of Complexity XXI, Addison-Wesley, New York (1994).Google Scholar
- [42]M. Dennin, D. Cannell, and G. Ahlers, Mol. Cryst. Liq. Cryst. 261, 977/337 (1995).CrossRefGoogle Scholar
- [43]F. H. Busse, Fundamentals of thermal convection, in Mantle convection, Plate Tectonics and Global Dynamics, edited by W. R. Peltier, Gordon and Breach, (1989) p. 23.Google Scholar
- [44]E. Dubois-Violette, G. Durand, E. Guyon, P. Manneville, and P. Pieranski, Instabilities in nematic liquid crystals, in Solid state physics, Suppl. 14, edited by L. Liebert, Academic Press, New York, (1978) p. 147.Google Scholar
- [45]W. J. A. Goossens, in Advances in Liquid Crystals, Vol. 3, edited by G. H. Brown, Academic, New York (1978) p. 1.Google Scholar
- [46]L. M. Blinov, Electrooptical and Magnetooptical Properties of Liquid Crystals, John Wiley, New York (1983).Google Scholar
- [47]S. A. Pikin, Structural Transformations in Liquid Crystals, Gordon and Breach Science Publishers, New York (1991).Google Scholar
- [48]I. Rehberg, B. L. Winkler, M. de la Torre, S. Rasenat, and W Schöpf, Adv. Solid State Phys. 29, 35 (1989).CrossRefGoogle Scholar
- [49]S. Kai and W. Zimmermann, Prog. Theor. Phys. Suppl. 99, 458 (1989).ADSCrossRefGoogle Scholar
- [50]W. Zimmermann, MRS Bulletin XVI, 46 (1991).Google Scholar
- [51]S. Kai, Forma 7, 189 (1992).Google Scholar
- [52]L. Kramer and W. Pesch, Annu. Rev. Fluid Mech. 27, 515 (1995).MathSciNetADSCrossRefGoogle Scholar
- [53]F. H. Busse and E. W. Bolton, J. Fluid Mech. 146, 115 (1984).ADSMATHCrossRefGoogle Scholar
- [54]W. Zimmermann, On traveling waves in nematics, in Nematics: Mathematical and Physical Aspects, edited by J. M. Coron, F. Helein, and J. M. Ghidaglia, Kluwer Academic, Dordrecht (1991) pp. 401–426. NATO ASI Series.Google Scholar
- [55]A. J. Hurd, S. Fraden, F. Lonberg, and R. B. Meyer, J. Phys. France 46, 905 (1985).CrossRefGoogle Scholar
- [56]N. V. Madhusudana, V. A. Raghunathan, and K. R. Sumathy, Pramana J. Phys. 28, L311 (1987).ADSCrossRefGoogle Scholar
- [57]W. Decker, Diploma thesis, Universität Bayreuth (1990).Google Scholar
- [58]I. Smith, Y. Galerne, S. Lagerwall, E. Dubois-Violette, and G. Durand, J. Phys. Coll. 36, C1–237 (1975)Google Scholar
- [59]R de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press, (Oxford 1993).Google Scholar
- [60]P. Kishore, T. Raj, A. Iqbal, S. Sastry, and G. Satyanandam, Liquid Crystals 14, 1319 (1993).CrossRefGoogle Scholar
- [61]F. Lonberg and R. Meyer, Phys. Rev. Lett 55, 718 (1985).ADSCrossRefGoogle Scholar
- [62]A. Buka and L. Kramer, Theory of transient patterns in the splay freedericksz transition of nematics, in Pattern Formation in Complex Dissipative Systems, edited by S. Kai, World Scientific, Kitakyushu, Japan (1991).Google Scholar
- [63]M. Treiber and L. Kramer, Phys. Rev. E 49, 3184 (1994).ADSCrossRefGoogle Scholar
- [64]E. Dubois-Violette, J. Physique 33, 95 (1972).CrossRefGoogle Scholar
- [65]H. Zenginoglou, R. Rigopoulos, and I. Kosmopoulos, Mol. Cryst. Liq. Cryst. 39, 27 (1977).CrossRefGoogle Scholar
- [66]W. Thom, W. Zimmermann, and L. Kramer, Liq. Cryst. 4, 309 (1989).CrossRefGoogle Scholar
- [67]V. Raghunathan and P. N. Madhusudana, Pramana J. Phys. 131, 163 (1988).ADSCrossRefGoogle Scholar
- [68]I. Rehberg, S. Rasenat, M. de la Torre-Juarez, and V. Steinberg, Phys. Rev. Lett. 61, 2448 (1988).ADSGoogle Scholar
- [69]There is a printing error in Eq. (38) of Ref. 39. The factor (\( (1 - \frac{{{ \in_a}}}{{ \in {}_q}}{L_{{nn}}}{q^2}) \)) should be replaced by (\( ({L_{{nn}}} - \frac{{{ \in_a}}}{{{ \in_q}}}{q^2}) \)).Google Scholar
- [70]U. Schneider, M. de la Torre-Juarez, W. Zimmermann, and I. Rehberg, Phys. Rev. A 46, 1009 (1992).ADSCrossRefGoogle Scholar
- [71]S. Kai, Y. Adachi, and S. Nasuno, Stability diagram, defect turbulence, and new patterns in electroconvection in nematics, in Spatio-Temporal Patterns in Nonequi-lihrium Complex Systems, edited by P. E. Cladis and P. Palffy-Muhoray, Addison-Wesley, (1994). SFI Studies in the Sciences of Complexity.Google Scholar
- [72]F. Hoerner and I. Rehberg, Using thermal noise to measure the correlation lengths of electroconvection, in Pattern formation in complex dissipitative systems and Global Dynamics, edited by S. Kai, World Scientific p. 429 (1992).Google Scholar
- [73]B. Winkler, W. Decker, H. Richter, and I. Rehberg, Physica D 61, 284 (1992).ADSMATHCrossRefGoogle Scholar
- [74]S. Rasenat, G. Hartung, B. Winkler, and I. Rehberg, Exp. in Fluids 7, 412 (1989).ADSCrossRefGoogle Scholar
- [75]S. Rasenat, PhD thesis, Universität Bayreuth (1991).Google Scholar
- [76]L. Kramer, H. Schober, and W. Zimmermann, Physica D 31, 212 (1988).ADSMATHCrossRefGoogle Scholar
- [77]G. Tesauro and M. C. Cross, Phys. Rev. A 34, 1363 (1986).ADSCrossRefGoogle Scholar
- [78]E. D. Siggia and A. Zippelius, Phys. Rev. A 24, 1036 (1981).ADSCrossRefGoogle Scholar
- [79]E. Bodenschatz, W. Pesch, and L. Kramer, Physica D 32, 135 (1988).ADSMATHCrossRefGoogle Scholar
- [80]L. M. Pismen and J. D. Rodriguez, Phys. Rev. A 42, 2471 (1990).ADSCrossRefGoogle Scholar
- [81]E. Bodenschatz, A. Weber, and L. Kramer, J. Stat. Phys. 64, 1007 (1991).ADSCrossRefGoogle Scholar
- [82]A. Joets and R. Ribotta, Electro-hydrodynamical convective structures and transitions to chaos in liquid crystals, in Cellular Structure in Instabilities, edited by J. E. Wesfreid and S. Zaleski, Springer, Berlin (1984) p. 294.CrossRefGoogle Scholar
- [83]C. Hilsum and F. Saunders, Mol. Cry st. Liq. Cryst. 64, 25 (1980).CrossRefGoogle Scholar
- [84]W. Pesch and L. Kramer, Z. Phys. B 63, 121 (1986).ADSCrossRefGoogle Scholar
- [85]L. Kramer, E. Bodenschatz, W. Pesch, and W. Zimmermann, in The Physics of Structure Formation, edited by W. Güttinger and G. Dangelmayr, Springer, Berlin (1987).Google Scholar
- [86]L. Kramer, W. Zimmermann, E. Bodenschatz, and W. Pesch, in Propagation in Systems far from Equilibrium, edited by J. E. Wesfried, H. R. Brand, P. Manneville, G. Albinet, and N. Boccara, Springer, Berlin (1988).Google Scholar
- [87]E. Bodenschatz, PhD thesis, Universität Bayreuth, (1989).Google Scholar
- [88]M. Kaiser, PhD thesis, Universität Bayreuth, (1992).Google Scholar
- [89]W. Decker, PhD thesis, Universität Bayreuth, (1995).Google Scholar
- [90]I. Dozov, P. Martinot-Lagarde, and G. Durand, J. Phys., Paris 43, L365 (1982).Google Scholar
- [91]A. Hertrich, PhD thesis, Universität Bayreuth (1995).Google Scholar
- [92]V. Steinberg, private communication.Google Scholar
- [93]S. Sasa, Defect chaos in 2d anisotropic systems, in Pattern Formation in Complex Dis-sipitative Systems and Global Dynamics, edited by S. Kai, World Scientific, (1992) p. 336.Google Scholar
- [94]S. Morris, E. Bodenschatz, D. S. Cannell, and G. Ahlers, Phys. Rev. Lett 71, 2026 (1993).ADSCrossRefGoogle Scholar
- [95]M. Assenheimer and V. Steinberg, Phys. Rev. Lett. 70, 3888 (1993).ADSCrossRefGoogle Scholar
- [96]W. Decker, W. Pesch, and A. Weber, Phys. Rev. Lett. 73, 648 (1994).ADSCrossRefGoogle Scholar
- [97]B. B. Plapp and E. Bodenschatz, Bull. APS. 40, 765 (1995).Google Scholar
- [98]A. Hertrich, W. Decker, W. Pesch, and L. Kramer, J. Phys. France II 2, 1915 (1992).Google Scholar
- [99]F. H. Busse, in Hydrodynamic Instabilities and the Transition to Turbulence, edited by H. L. Swinney and J. P. Gollub, Springer, Berlin (1986).Google Scholar
- [100]A. Rossberg, A. Hertrich, L. Kramer, and W. Pesch, preprint (1995).Google Scholar
- [101]H. Richter, A. Buka, and I. Rehberg, Phys. Rev. E 51, 5886 (1995).ADSCrossRefGoogle Scholar
- [102]H. Richter, N. Klöpper, A. Hertrich, and A. Buka, Europhys. Lett. 30 37 (1995).ADSCrossRefGoogle Scholar
- [103]Q. Feng, W. Decker, W. Pesen, and L. Kramer, J. Phys. France II 2, 1303 (1992).Google Scholar
- [104]M. Barnik, L. Blinov, M. Grebenkin, S. Pikin, and V. Chigrinov, Zh. Eksp. Tear. Fiz. 69, 1080 (1975).Google Scholar
- [105]J. Gleeson and D. Todorovic-Marinic, Mol. Cryst. Liq. Cryst. 261, 327 (1995).CrossRefGoogle Scholar
- [106]A. Hertrich, W. Pesch. and J. Gleeson, preprint (1995).Google Scholar
- [107]M. Silber, H. Riecke, and L. Kramer, Physica D 61, 260 (1992).MathSciNetADSMATHCrossRefGoogle Scholar
- [108]H. Riecke and L. Kramer, unpublished (1995).Google Scholar
- [109]M. Low, B. Albert, and J. Gollub, J. Fluid. Mech. 173, 253 (1986).ADSCrossRefGoogle Scholar
- [110]P. Coullet, Phys. Rev. Lett. 56, 724 (1986).MathSciNetADSCrossRefGoogle Scholar
- [111]P. Coullet and P. Huerre, Physica D 63, 123 (1986).Google Scholar
- [112]W. Zimmermann, A. Ogawa, S. Kai, K. Kawasaki, and T. Kawakatsu, Europhys. Lett. 24, 217 (1993).ADSCrossRefGoogle Scholar
- [113]H. Riecke, J. Crawford, and E. Knobloch, Phys. Rev. Lett. 61, 1942 (1988).MathSciNetADSCrossRefGoogle Scholar
- [114]D. Walgraef, Europhys. Lett. 7, 495 (1988).ADSCrossRefGoogle Scholar
- [115]H. Riecke, M. Silber, and L. Kramer, Phys. Rev. E 49, 4100 (1994).ADSCrossRefGoogle Scholar
- [116]R. Müller and U. Behn, Z. Phys. B—Condensed Matter 69, 185 (1987).ADSCrossRefGoogle Scholar
- [117]U. Behn and A. Lange, preprint (1995).Google Scholar
- [118]S. Kai, in Noise in Nonlinear Dynamical Systems, Vol. 3, edited by S. Moss and P. McClintock, Cambridge University, (1989) p. 22.Google Scholar
- [119]U. Behn, A. Buka, and N. Kloepper, unpublished (1995).Google Scholar
- [120]L. Gil, J. Lega, and J. Meunier, Phys. Rev. A 41, 1138 (1990).ADSCrossRefGoogle Scholar
- [121]S. Kai, M. Kohno, M. Andoh, M. Imizaki, and W. Zimmermann, Mol. Cryst. Liq. Cryst. 198, 247 (1991).CrossRefGoogle Scholar
- [122]M. Sano, H. Kokubo, H. Janiaud, and K. Sato, Prog. Theor. Phys. 90, 1 (1993).ADSCrossRefGoogle Scholar
- [123]V. Delev, O. Scaldin, and A. Chuvyrov, Liquid Crystals 12, 441 (1992).CrossRefGoogle Scholar
- [124]A. Hertrich, A. P. Krekhov, and W. Pesch, J. Phys. II France 5, 773 (1995).CrossRefGoogle Scholar
- [125]V. Raghunathan, P. M. Murthy, and N. Madhusudana, MoL Cryst. Liq. Cryst. 199, 48 (1992).Google Scholar
- [126]K. Babcock, G. Ahlers, and D. Cannell, Phys. Rev. Lett. 67, 3388 (1991).ADSCrossRefGoogle Scholar
- [127]A. Tsameret and V. Steinberg, Phys. Rev. Lett. 67, 3392 (1991).ADSCrossRefGoogle Scholar
- [128]S. Frunza, R. Moldovan, T. Beica, M. Giurgea, and D. Stoenescu, Europhys. Lett. 20, 407 (1992).ADSCrossRefGoogle Scholar
- [129]A. Hertrich, A. P. Krekhov, and O. A. Scaldin, J. Phys. II France 4, 239 (1994).CrossRefGoogle Scholar
- [130]S. Morris, J. de Bruyn, and A. May, Phys. Rev. A 44, 8146 (1991).ADSCrossRefGoogle Scholar
- [131]S. S. Mao, J. R. de Bruyn, and S. W. Morris, preprint (1995).Google Scholar
- [132]Z. A. Daya, S. W. Morris, and J. R. de Bruyn, unpublished (1995).Google Scholar
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