Journal of Experimental and Theoretical Physics

, Volume 121, Issue 6, pp 1082–1095 | Cite as

Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

  • O. A. Skaldin
  • V. A. Delev
  • E. S. Shikhovtseva
  • Yu. A. Lebedev
  • E. S. Batyrshin
Statistical, Nonlinear, and Soft Matter Physics


The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.


Soliton Topological Charge Defect Core Breather Solution Anisotropic Friction 
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.
    P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1994).Google Scholar
  2. 2.
    M. Kleman, Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Ordered Media (Wiley, Chichester, 1983).Google Scholar
  3. 3.
    M. V. Kurik and O. D. Lavrentovich, Sov. Phys.—Usp. 31 (3), 196 (1988).CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Defects in Liquid Crystals: Computer Simulations, Theory and Experiments, Ed. by O. D. Lavrentovich, P. Pasini, S. Zannoni, and S. Zumer (Kluwer Academic, Dordrecht, The Netherlands, 2001).Google Scholar
  5. 5.
    P. V. Dolganov, V. M. Zhilin, V. K. Dolganov, and E. I. Kats, JETP Lett. 89 (3), 161 (2009).CrossRefADSGoogle Scholar
  6. 6.
    O. A. Skaldin and Yu. I. Timirov, JETP Lett. 90 (9), 633 (2009).CrossRefADSGoogle Scholar
  7. 7.
    E. G. Ekomasov, R. R. Murtazin, and V. N. Nazarov, Phys. Met. Metallogr. 115 (2), 117 (2014).CrossRefADSGoogle Scholar
  8. 8.
    S. A. Pikin, Structural Transformations in Liquid Crystals (Nauka, Moscow, 1981; Gordon and Breach, London, 1991).Google Scholar
  9. 9.
    Pattern Formation in Liquid Crystals, Ed. by A. Buka and L. Kramer (Springer-Verlag, New York, 1996).Google Scholar
  10. 10.
    A. Weber, E. Bodenschatz, and L. Kramer, Adv. Mater. (Weinheim) 3, 191 (1991).CrossRefGoogle Scholar
  11. 11.
    H. Yamazaki, S. Kai, and K. Hirakawa, J. Phys. Soc. Jpn. 56, 1 (1987).CrossRefADSGoogle Scholar
  12. 12.
    S. Kai, N. Chizumi, and M. Kohno, J. Phys. Soc. Jpn. 58, 3541 (1989).CrossRefADSGoogle Scholar
  13. 13.
    S. Nasuno, S. Takeuchi, and Y. Sawada, Phys. Rev. A: At., Mol., Opt. Phys. 40, 3457 (1989).CrossRefADSGoogle Scholar
  14. 14.
    S. Rasenat, V. Steinberg, and I. Rehberg, Phys. Rev. A: At., Mol., Opt. Phys. 42, 5998 (1990).CrossRefADSGoogle Scholar
  15. 15.
    E. Bodenschatz, W. Zimmermann, and L. Kramer, J. Phys. (Paris) 49, 1875 (1988).CrossRefGoogle Scholar
  16. 16.
    E. Bodenschatz, W. Pesch, and L. Kramer, Physica D (Amsterdam) 32, 135 (1988).CrossRefADSzbMATHGoogle Scholar
  17. 17.
    L. Kramer, E. Bodenschatz, W. Pesch, W. Thom, and W. Zimmermann, Liq. Cryst. 5, 699 (1989).CrossRefGoogle Scholar
  18. 18.
    L. Kramer, E. Bodenschatz, and W. Pesch, Phys. Rev. Lett. 64, 2588 (1990).CrossRefADSGoogle Scholar
  19. 19.
    E. Bodenschatz, W. Pesch, and L. Kramer, J. Stat. Phys. 64, 1007 (1991).CrossRefADSGoogle Scholar
  20. 20.
    T. A. Kontorova and Ya. I. Frenkel’, Zh. Eksp. Teor. Fiz. 8,89,1340, 1349 (1938).Google Scholar
  21. 21.
    O. M. Braun and Y. S. Kivshar, The Frenkel–Kontorova Model: Concepts, Methods, and Applications (Springer-Verlag, New York, 2004).CrossRefGoogle Scholar
  22. 22.
    A. V. Ustinov, M. Cirillo, and B. A. Malomed, Phys. Rev. B: Condens. Matter 47, 8357 (1993).CrossRefADSGoogle Scholar
  23. 23.
    H. S. J. van der Zant, T. P. Orlando, S. Watanabe, and S. H. Strogats, Phys. Rev. Lett. 74, 174 (1995).CrossRefADSGoogle Scholar
  24. 24.
    R. A. Cowley, J. D. Axe, and M. Iizumi, Phys. Rev. Lett. 36, 806 (1976).CrossRefADSGoogle Scholar
  25. 25.
    A. R. Bishop and W. F. Lewis, J. Phys. C: Solid State Phys. 12, 3811 (1979).CrossRefADSGoogle Scholar
  26. 26.
    A. C. Kovalev, Low Temp. Phys. 20 (10), 815 (1994).ADSGoogle Scholar
  27. 27.
    I. F. Lyuksyutov, A. G. Naumovets, and V. L. Pokrovskii, Two-Dimensional Crystals (Naukova Dumka, Kiev, 1988; Academic, New York, 1992).Google Scholar
  28. 28.
    J. de la Figuera, K. Pohl, O. R. de la Fuente, A. K. Schmid, N. C. Bartelt, C. B. Carter, and R. Q. Hwang, Phys. Rev. Lett. 86, 3819 (2001).CrossRefADSGoogle Scholar
  29. 29.
    A. N. Chuvyrov, O. A. O. A. Scaldin, V. A. Delev, Yu. A. Lebedev, and E. S. Batyrshin, J. Exp. Theor. Phys. 103 (6), 926 (2006).CrossRefADSGoogle Scholar
  30. 30.
    A. Hertrich, A. P. Krekhov, and O. A. Scaldin, J. Phys. II 4, 239 (1994).Google Scholar
  31. 31.
    V. A. Delev, P. Toth, and A. P. Krekhov, Mol. Cryst. Liq. Cryst. 351, 179 (2000).CrossRefGoogle Scholar
  32. 32.
    G. R. Yakupova and O. A. Skaldin, Tech. Phys. Lett. 29 (11), 892 (2003).CrossRefADSGoogle Scholar
  33. 33.
    O. A. Skaldin, G. R. Yakupova, V. A. Delev, Yu. A. Lebedev, and A. A. Nazarov, Phys. Solid State 47 (2), 374 (2005).CrossRefADSGoogle Scholar
  34. 34.
    A. Joets and R. Ribotta, J. Stat. Phys. 64, 981 (1991).CrossRefADSGoogle Scholar
  35. 35.
    O. A. Skaldin, V. A. Delev, E. S. Shikhovtseva, E. S. Batyrshin, and Yu. A. Lebedev, JETP Lett. 93 (7), 388 (2011).CrossRefADSGoogle Scholar
  36. 36.
    S. Frunza, R. Moldovan, T. Beica, M. Giurgea, and D. N. Stoenescu, Europhys. Lett. 20, 407 (1992).CrossRefADSGoogle Scholar
  37. 37.
    R. H. Kraichnan, J. Fluid Mech. 67, 155 (1975).CrossRefADSzbMATHGoogle Scholar
  38. 38.
    E. S. Shikhovtseva, Physica A (Amsterdam) 303, 133 (2002).CrossRefADSGoogle Scholar
  39. 39.
    E. S. Shikhovtseva, Physica A (Amsterdam) 349, 421 (2005).CrossRefADSGoogle Scholar
  40. 40.
    G. L. Lamb, Rev. Mod. Phys. 43, 99 (1971).CrossRefADSMathSciNetGoogle Scholar
  41. 41.
    R. Parmentier, in Solitons in Action, Ed. by K. Lonngren and E. Scott (Academic, New York, 1978; Mir, Moscow, 1981), pp. 185–209.Google Scholar
  42. 42.
    J. K. Perring and T. H. R. Skyrme, Nucl. Phys. 31, 550 (1962).CrossRefMathSciNetzbMATHGoogle Scholar
  43. 43.
    J. P. Hirth and J. Lothe, Theory of Dislocations (Willey, New York, 1982).Google Scholar
  44. 44.
    L. M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Nauka, Moscow, 1978; Wiley, New York, 1983).Google Scholar
  45. 45.
    E. S. Shikhovtsova and O. A. Ponomarev, JETP Lett. 64 (7), 509 (1996).CrossRefADSGoogle Scholar
  46. 46.
    E. S. Shikhovtseva, Phys. Low-Dimens. Struct. 11/12, 77 (1999).Google Scholar
  47. 47.
    D. W. McLauglin and A. C. Scott, Phys. Rev. A: At., Mol., Opt. Phys. 18, 1652 (1978).CrossRefADSGoogle Scholar
  48. 48.
    M. A. Shamsutdinov, I. Yu. Lomakina, V. N. Nazarov, A. T. Kharisov, and D. M. Shamsutdinov, Ferromagnetodynamics and Antiferromagnetodynamics: Nonlinear Oscillations, Waves, and Solitons (Nauka, Moscow, 2009) [in Russian].Google Scholar
  49. 49.
    O. A. Skaldin, V. A. Delev, and E. S. Shikhovtseva, JETP Lett. 97 (2), 92 (2013).CrossRefADSGoogle Scholar
  50. 50.
    M. Dennin, D. S. Cannell, and G. Ahlers, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 57, 638 (1998).CrossRefGoogle Scholar
  51. 51.
    M. Scheuring, L. Kramer, and J. Peinke, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 58, 2018 (1998).CrossRefGoogle Scholar
  52. 52.
    E. S. Shikhovtseva and O. A. Ponomarev, Phys. Low- Dimens. Struct. 5/6, 43 (1998).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  • O. A. Skaldin
    • 1
  • V. A. Delev
    • 1
  • E. S. Shikhovtseva
    • 1
  • Yu. A. Lebedev
    • 1
  • E. S. Batyrshin
    • 1
  1. 1.Institute of Molecular and Crystal Physics, Ufa Research CenterRussian Academy of SciencesUfa, BashkortostanRussia

Personalised recommendations