ISSN 2658–5782
DOI 10.21662
Electronic Scientific Journal





© Институт механики
им. Р.Р. Мавлютова
УФИЦ РАН

Яндекс.Метрика web site traffic statistics

Delev V.A. The topological soliton decay in a linear defect of the domain structure of twisted nematic. Multiphase Systems. 17 (2022) 3–4. 135–144 (in Russian).
2022. Vol. 17. Issue 3–4, Pp. 135–144
URL: http://mfs.uimech.org/mfs2022.3.012,en
DOI: 10.21662/mfs2022.3.012
The topological soliton decay in a linear defect of the domain structure of twisted nematic
Delev V.A.
IMCP UFRC RAS, Ufa, Russia

Abstract

In this paper, the topological soliton decay in an oscillating linear defect of electroconvective structure (Williams domains) arising in π/2 twisted nematic liquid crystal are studied. In contrast to planarly oriented nematics, hydrodynamic flows in the domains of a twisted nematic have a helical character. Since, in addition to the tangential velocity component, there is also axial component, the direction of which is opposite in neighboring domains. This feature leads to the formation of stable localized extended objects — linear defects oriented normal to Williams domains. With increasing applied voltage, “zig-zag” oscillations occurs in linear defects. The boundaries between the “zig” and “zag“ states are classical dislocations. It has been found, that the dislocation, moving along the core of the defect, breaks up into an antidislocation and two dislocations. Unlike case of planarly oriented nematics, dislocations are not isolated from each other by unperturbed rolls but remain “bound” by hydrodynamic flows within the core of a linear defect. It is assumed that the splitting of the dislocation occurs as a result of the local instability of the orientational twist mode of the director n due to its strong coupling with the hydrodynamic velocity. In the framework of the sine–Gordon equation, in the presence of a dissipative term and spatial perturbations, the mechanism of a topological soliton (kink) decay into antisoliton and two solitons is considered.

Keywords

nematic liquid crystal,
nematic,
electroconvection,
Williams domains,
twist mode,
linear defect,
dislocation,
sine–Gordon equation,
kink

Article outline

The decay of a topological soliton in an oscillating linear defect of a domain structure (Williams domains) that arises in the electroconvection system of π/2 twisted nematic liquid crystal (NLC) is studied. In contrast to planarly oriented NLCs, hydrodynamic flows in the domains of a twisted nematic are helicoidal in nature, since, in addition to the tangential velocity component, there is also an axial component, the direction of which is opposite in neighboring domains. This feature leads to the formation of stable extended stationary objects — linear defects oriented normally to the Williams domains. With increasing applied voltage, zig-zag domain oscillations appear in linear defects. The boundaries between zig and zag states are classical dislocations with topological charges S = ±1 (topological solitons — kinks). It was found that a dislocation with S = +1, moving along the linear defect core of a certain length, can decay into an antidislocation with S = –1 and two dislocations with S = +1. The resulting single dislocations do not separate from each other, as in the case of a planar orientation of NLC, but remain “bound” by hydrodynamic flows within the linear defect core. It is assumed that the splitting of a dislocation occurs as a result of the local instability excitation of the orientational twist mode of the director n (n is a unit vector, indicates the direction of the predominant molecules orientation in the NLC layer) in dislocation core due to the strong coupling between director orientation and hydrodynamic flow velocity in NLC. The local instability of the orientational twist mode of the director n in the dislocation core (instability in the kink internal mode) arises when the hydrodynamic flows moving through the linear defect core become non-stationary and zig-zag domain oscillations arise. At the same time, the Williams domain structure remains stationary. The further dynamics of dislocations is set in such a way that the continuity of the helicoidal flow of an anisotropic liquid is ensured in the nonstationary linear defect core. An attempt is made to qualitatively explain the topological soliton – kink decay by the excitation of its internal mode instability in the framework of the perturbed sine-Gordon equation.

It should be emphasized that the investigation of the transition from regular defect motion to highly nonstationary spatiotemporal dynamics remains a challenge in modern science. This phenomenon is related to defect-mediated turbulence. Kinks, like vortices and spirals, are particular cases of a more general phenomenon called topological defects. Although these objects may possess different origin and nature in different physical systems, they all possess very similar dynamical properties. In this work, it has been found that the transition process to weak turbulence (defects mediated turbulence) in the electroconvection system of π/2 twisted NLCs occurs not only due to the dislocations creation and annihilation, but also by their “elementary” decay into an antidislocation and two dislocations. Such instabilities as the solitons decay or breakup can adversely affect various processes in technology, medicine, etc. In particular, one possible mechanisms that is currently believed to be responsible for the transition from tachycardia to ventricular fibrillation in the heart muscle is the spontaneous breakup of a single spiral wave of electrical activity into multiple spirals leading to a turbulent wave behavior. Therefore, it is very important to understand not only all possible mechanisms of soliton decay in order to learn how to avoid them, but also, if possible, to control them.

References

  1. Coullet P., Gil L., and Lega J. Defect-mediated turbulence // Physical Review Letters. 1989. V. 62, No. 14. Pp. 1619–1622.
    DOI: 10.1103/PhysRevLett.62.1619
  2. Cross M.C., Hohenberg P.C. Pattern formation outside of equilibrium // Reviews of Modern Physics. 1993. V. 65. Pp. 851–1112.
    DOI: 10.1103/RevModPhys.65.851
  3. Getling A.V. Rayleigh-Benard convection. M.: Editorial URSS, 1999. 248 s. (In Russian)
  4. Blinov L.M. Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Nauka, Moscow, 1978; Wiley, New York, 1983). 384 p.
  5. Pikin S.A. Strukturnye prevrashcheniya v zhidkih kristallah. M.: Nauka, 1981. 336 s. (In Russian)
  6. De Gennes P.G. and Prost J. The Physics of Liquid Crystals. Oxford: Clarendon, 1994. 596 p.
  7. Buka A. and Kramer L. (editors). Pattern Formation in Liquid Crystals. N.Y.: Springer-Verlag, 1996. 339 p.
  8. Kuramoto Y. Phase dynamics of weakly unstable periodic structures // Progress of Theoretical Physics. 1984. V. 71, No. 6. Pp. 1182–1196.
    DOI: 10.1143/PTP.71.1182
  9. Toulouse G., Kléman M. Principles of a classification of defects in ordered media // Journal de Physique Lettres. 1976. V. 37, No. 6. Pp. 149– 151.
    DOI: 10.1051/jphyslet:01976003706014900
  10. Eckmann J.-P., Goren G. and Procaccia I. Nonequilibrium nucleation of topological defects as a deterministic phenomenon // Physical Review A. 1991. V. 44, No. 2. Pp. 805–808.
    DOI: 10.1103/PhysRevA.44.R805
  11. Kai S., Chizumi N., and Kohno M. Pattern formation, defect motions and onset of defect chaos in the electrohydrodynamic instability of nematic liquid crystals // Journal of the Physical Society of Japan. 1989. V. 58. Pp. 3541–3554.
    DOI: 10.1143/JPSJ.58.3541144 Multiphase Systems
  12. Rasenat S., Steinberg V., and Rehberg I. Experimental studies of defect dynamics and interaction in electrohydrodynamic convection // Physical Review A. 1990. V. 42, No. 10. Pp. 5998–6008.
    DOI: 10.1103/PhysRevA.42.5998
  13. Bodenschatz E., Weber A., and Kramer L. Interaction and dynamics of defects in convective roll patterns of anisotropic fluids // Journal of Statistical Physics 1991. V. 64, No. 5. Pp. 1007–1015.
    DOI: 10.1007/BF01048810
  14. Joets A. and Ribotta R. Localized bifurcations and defect instabilities in the convection of a nematic liquid crystal // Journal of Statistical Physics 1991. V. 64, No. 5/6. Pp. 981–1005.
    DOI: 10.1007/BF01048809
  15. Delev V.A., Toth P., and Krekhov A.P. Electroconvection in twisted nematic liquid crystals // Molecular Crystals and Liquid Crystals. 2000. V. 351. Pp.179–186.
    DOI: 10.1080/10587250008023267
  16. Tatsumi S., Sano M., and Rossberg A.G. Observation of stable phase jump lines in convection of a twisted nematic liquid crystal // Physical Review E. 2006. V. 73. Pp. 011704-1–8.
    DOI: 10.1103/PhysRevE.73.011704
  17. Hertrich A., Krekhov A.P., and Scaldin O.A. The electrohydrodynamic instability in twisted nematic liquid crystals // Journal de Physique II (France). 1994. V. 4. Pp. 239–252.
    DOI: 10.1051/jp2:1994126
  18. Braun O.M., Kivshar’ YU.S. Model’ Frenkelya-Kontorovoj. Koncepcii, metody, prilozheniya. M.: Fizmatlit, 2008. 536 s. (In Russian)
  19. Dodd R., Ejlbek Dzh., Gibbon Dzh., Morris H. Solitony i nelinejnye volnovye uravneniya. M.: Mir, 1988. 694 s. (In Russian)
  20. Zabusky N.J., Kruskal M.D. Interaction of solitons in a collisionless plasma and recurrence of initial states // Physical Review Letters. 1965. V. 15, No. 6. P. 240–243.
    DOI: 10.1103/PhysRevLett.15.240
  21. Kerner B.S., Osipov V.V. Autosolitons // Uspehi Fizicheskih Nauk. 1989. V. 157, No. 2. Pp. 201–266. (In Russian)
  22. Rosanov N.N. Spatial hysteresis and optical patterns. Berlin: Springer, 2002. 308 p.
  23. Lam L., Prost J (editors). Solitons in liquid crystals. N.Y.: Springer Science & Business Media, 1992. 338 p.
  24. Shen Yu. and Dierking I. Recent progresses on experimental investigations of topological and dissipative solitons in liquid crystals // Crystals. 2022. V. 12, No. 1. Pp. 1–17.
    DOI: 10.3390/cryst12010094
  25. CHuvyrov A.N., Skaldin O.A., Delev V.A., Lebedev YU.A., Batyrshin E.S. Struktura i dinamika dislokacij Frenkelya-Kontorovoj pri elektrokonvekcii v zhidkih kristallah // ZHurnal Eksperimental’noj i Teoreticheskoj Fiziki. 2006. T. 130, № 6. S. 1072–1081. (In Russian)
    eLIBRARY ID: 9430706
  26. Skaldin O.A., Delev V.A., Shikhovtseva E.S., Lebedev Yu.A., and Batyrshin E.S. Breatherlike defects and their dynamics in the one- dimensional roll structure of twisted nematics // Journal of Experimental and Theoretical Physics. 2015. V. 121, No. 6. Pp. 1082–1095.
    DOI: 10.1134/S1063776115120158
  27. Delev V.A., Nazarov V.N., Scaldin O.A., Batyrshin E.S., and Ekomasov E.G. Complex dynamics of the cascade of kink–antikink interactions in a linear defect of the electroconvective structure of a nematic liquid crystal // Journal of Experimental and Theoretical Physics. 2019. V. 110, No. 9. Pp. 607–612.
    DOI: 10.1134/S0021364019210069
  28. Delev V.A. Inelastic interactions of solitons in a linear defect of the electroconvective structure of a nematic liquid crystal // Letters to Journal of Experimental and Theoretical Physics. 2021. Vol. 113, No. 1. Pp. 23–29.
    DOI: 10.1134/S0021364021010021
  29. González J.A., Bellorín A., Guerrero L.E. Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations // Physical Review E. 2002. V. 65. Pp. 065601-1-4.
    DOI: 10.1103/PhysRevE.65.065601
  30. González J.A., Bellorín A., Guerrero L.E. Kink-soliton explosions in generalized Klein–Gordon equations // Chaos. Solitons & Fractals. 2007. V. 33. Pp. 143–155.
    DOI: 10.1016/j.chaos.2006.10.047
  31. Kivshar Yu.S. and Malomed B.A. Dynamics of solitons in nearly integrable systems // Reviews of Modern Physics. Vol. 61, No. 4. 1989. Pp. 763–915.
    DOI: 10.1103/RevModPhys.61.763
  32. Bak P. and Brazovsky .A. Theory of quasi-one-dimensional conductors: Interaction between chains and impurity effects // Physical Review B. 1978. V. 17, No. 8. Pp. 3154–3164.
    DOI: 10.1103/PhysRevB.17.3154
  33. Zipes D.P., Jalife J, and Stevenson W.G. Cardiac electrophysiology: from cell to bedside. E-Book, 2017. 1120 p.
  34. González J.A., Bellorín A., Guerrero L.E. Controlling soliton explosions // Physics Letters A. 2005. V. 338. Pp. 60–65.
    DOI: 10.1016/j.physleta.2005.02.018