Statistical properties of chaos at onset of electroconvection in a homeotropically aligned nematic layer

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 3, 1999, Pages 3729-3732

  Tribelsky, Michael I ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009013036     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.3729     Document Type: Article

References (21)

1. M. I. Tribelsky, K. Hayashi, Y. Hidaka, and S. Kai, in Proceedings of the first Tokua University Statistical Physics Meeting, Fukuoka, Japan, November 1995 [Bussei Kenkyu 66, 592 (1966)].
2. S. Kai, K. Hayashi, and Y. Hidaka, J. Phys. Chem. 100, 19 007 (1996).
3. Y. Hidaka, J-H. Huh, K. Hayashi, S. Kai, and M. I. Tribelsky, Phys. Rev. E 56, R6256 (1997)
4. Y. HidakaJ-H. HuhK. HayashiS. KaiM. I. TribelskyJ. Phys. Soc. Jpn. 66, 3329 (1997).
5. H. Richter, Á. Buka, and I. Rehberg, in Spatio-Temporal Patterns in Nonequilibrium Complex Systems, edited by P. Cladis and P. Palffy-Muhoray (Addison-Wesley, New York, 1994)
6. Phys. Rev. E 51, 5886 (1995).
7. H. Richter, N. Klöpper, A. Hertrich, and Á. Buka, Europhys. Lett. 30, 37 (1995).
8. P. Tóth, Á. Buka, J. Peinke, and L. Kramer, Phys. Rev. E 58, 1983 (1998).
9. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 60, 851 (1993).
10. M. Dennin, M. Treiber, L. Kramer, G. Ahlers, and D. S. Cannell, Phys. Rev. Lett. 76, 319 (1996)
11. Phys. Rev. Lett.Y. Hu, R. E. Ecke, and G. Ahlers, 74, 5040 (1995)
12. M. Dennin, D. S. Cannell, and G. Ahlers, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 261, 337 (1995)
13. M. Dennin, G. Ahlers, and D. S. Cannell, Science 272, 388 (1996).
14. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993)
15. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, Cambridge, England, 1977).
16. Below the so-called Lifshitz point the system has an additional destabilizing mechanism supporting the rotation, namely, uncompensated torque on the director. For more details, see, e.g., A. Hertrich, W. Decker, W. Pesch, and L. Kramer, J. Phys. II 2, 1915 (1992).
17. A. G. Rossberg, A. Hertrich, L. Kramer, and W. Pesch, Phys. Rev. Lett. 76, 4729 (1996)
18. A. G. Rossberg and L. Kramer, Phys. Scr. T67, 121 (1996).
19. In this case (Formula presented) should stand for the linear rotation velocity and depend on the distance between the observation point and the rotation center.
20. It means we neglect defect generation, since A must vanish in the defect cores. The neglect would be erroneous for the planar alignment, when orientation of convective rolls is fixed by boundary conditions and the defect generation is an important mechanism for transition to chaos (the so-called defect-mediated turbulence) 7. On the contrary, the problem under consideration has an additional degree of freedom to make the pattern chaotic, viz., the mentioned undamped rotations of its different fragments with respect to each other. Regarding the defect generation, for point defects it is suppressed due to smallness of (Formula presented) 23. As for dislocation lines, which may arise at boundaries of the different pattern’s fragments, their quantitative measure is the ratio (Formula presented) which vanishes at (Formula presented) tending to zero. Thus, both the point and the line defects should not affect statistical properties of the pattern at small (Formula presented)
21. L. D. Landau and E. M. Lifshitz, Statistical Physics. Part 1 (Pergamon Press, Oxford, 1989), Sec. 118.