HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 90 (1993) > Number 1
| Next Article >

Prog. Theor. Phys. Vol. 90 No. 1 (1993) pp. 1-34

[ Full Text PDF : FREE ACCESS (3540K) ]

Invited Papers

Phase Wave in a Cellular Structure

Masaki Sano, Hiroki Kokubo, Beatrice Janiaud and Katsuyoshi Sato

Research Institute of Electrical Communication, Tohoku University, Sendai 980

(Received June 8, 1993)

Abstract:

Phase waves and their stability in a cellular pattern is discussed from a viewpoint of experimentalists. When the cellular pattern exhibits oscillatory instability, rich phenomena can be observed. The prototype experimental system is the electrohydrodynamic convection of a nematic liquid crystal in which a two-dimensional cellular pattern of convection exhibits limit cycle oscillation. We observe localized target pattern of wave fronts emitted from a self-organized center. The localized structure has a life cycle: it arises from a uniform state, grows and collapses by nucleating defects at its center. They are created by a phase instability through the coupling between the oscillatory mode and the underlying cellular pattern. We experimentally determine coupled complex Ginzburg-Landau equations as well as phase equations derived from them, and we confirm that the equations quantitatively describe the instability. We also discussed mechanism and process of collapse of target which are closely related to a turbulent nature of defects in the cellular pattern.


URL : http://ptp.ipap.jp/link?PTP/90/1/
DOI : 10.1143/PTP.90.1

[ Full Text PDF : FREE ACCESS (3540K) ] Citation:

References:

  1. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Claredon Press, Oxford, 1961).
  2. R. Feynmann, Lectures on Physics, Vol. II, chap. 41 (Addison-Weslay, 1964).
  3. F. H. Busse, Rep. Prog. 41 (1978), 1929.
    R. M. Clever and F. H. Busse, J. Fluid. Mech. 65 (1974), 625[CrossRef].
  4. Y. Pomeau and P. Manneville, J. de Phys. Lett. 40 (1979), 609.
  5. Y. Kuramoto, Prog. Theor. Phys. 71 (1984), 182[PTP].
  6. V. Croquette and A. Pocheau, in Cellular Structures in Instabilities, ed. J. E. Wesfreid and S. Zaleski, Lecture Notes in Phys. 210 (Springer, 1984).
  7. M. Lowe and J. P. Gollub, Phys. Rev. Lett. 55 (1985), 2575[APS].
  8. C. D. Andereck, S. S. Liu and H. L. Swinney, J. Fluid Mech. 164 (1986), 155[CrossRef].
  9. J. M. Flesselles, A. J. Simon and A. Libchaber, Adv. in Phys. 40 (1991), 1.
  10. B. Janiaud, A. Pumir, D. Bensimon, V. Croquette, H. Richter and L. Kramer, Physica D55 (1992), 269.
  11. P. Kolodner, J. A. Glazier and H. Williams, Phys. Rev. Lett. 65 (1990), 1579[APS].
  12. S. Ciliberto and P. Bigazzi, Phys. Rev. Lett. 60 (1988), 286[APS].
  13. F. Daviaud, M. Dubois and P. Berge, Europhys. Lett. 9 (1989), 441[CrossRef].
  14. K. Kaneko, Prog. Theor. Phys. 74 (1985), 1033[PTP].
  15. H. Chate and P. Manneville, Phys. Rev. Lett. 58 (1987), 112[APS]; Physica D32 (1988), 402.
  16. P. Coullet and G. Iooss, Phys. Rev. Lett. 64 (1990), 866[APS].
  17. S. Nasuno, M. Sano and Y. Sawada, J. of Phys. Soc. Jpn. 58 (1989), 1875.
  18. H. Sakaguchi, Prog. Theor. Phys. 87 (1992), 241, [PTP]1049; 89 (1993), 1123.
  19. P. Manneville, Dissipative Structures and Weak Turbulence (Academic Press, San Diego, 1989).
  20. E. Dubois-Violette, P. G. de Gennes and O. Parodi, J. de Phys. 32 (1971), 305.
    P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1973).
  21. A. Pocheau, V. Croquette and P. LeGal, Phys. Rev. Lett. 55 (1985), 1094[APS].
  22. F. Heslo, B. Casting and A. Libchaber, Phys. Rev. A36 (1987), 5870[APS].
  23. E. Bodenschatz, J. R. de Bruyn, G. Ahlers and D. S. Cannel, Phys. Rev. Lett. 67 (1991), 3078[APS].
  24. See, e.g., E. Bodenschatz, W. Zimmermann and L. Krammer, J. de Phys. 49 (1988), 1875, and references therein.
  25. K. Kondo, M. Arakawa, A. Fukuda and E. Kuze, Jpn. J. Appl. Phys. 22 (1983), 394.
  26. P. Bloomfield, Fourier Analysis of Time Series: An Introduction (John Wiley, 1976).
  27. S. Kai and K. Hirakawa, Prog. Theor. Phys. Suppl. No. 64 (1978), 212[PTP].
  28. A. Joets and R. Ribbota, J. de Phys. 47 (1986), 595.
  29. L. M. Blinov, J. de Phys. C3 (1979), 247.
  30. A. N. Chuvyrov and V. G. Chigrinov, Sov. Phys.-JETP 60 (1984), 101.
  31. S. Nasuno, O. Sasaki, S. Kai and W. Zimmermann, Phys. Rev. A46 (1992), 4954[APS].
  32. S. Sasa, Prog. Theor. Phys. 83 (1990), 824[PTP].
  33. F. H. Busse and R. M. Clever, J. Fluid Mech. 91 (1979), 319[CrossRef].
  34. U. Frish, Z. S. She and O. Thual, J. Fluid. Mech. 168 (1986), 221[CrossRef].
  35. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
  36. M. Sano, K. Sato, S. Nasuno and H. Kokubo, Phys. Rev. A15. 46 (1992), 3540.
  37. M. Sano, K. Sato and B. Janiaud, in Pattern Formation in Complex Dissipative Systems, ed. S. Kai (World Scientific, Singapore, 1992).
  38. F. Daviaud, J. Lega, P. Berge, P. Coullet and M. Dubois, Physica 55D (1992), 287[Elsevier].
  39. J. Guckenheimer and P. Holms, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields (Springer, Berlin, 1983).
  40. B. Janiaud, H. Kokubo and M. Sano, Phys. Rev. E47 (1992), 2237[APS].
  41. H. Kokubo, M. Sano, B. Janiaud and Y. Sawada, to appear in J. Phys. Soc. Jpn.
  42. G. Goren, I. Procaccia, S. Rasenat and V. Steinberg, Phys. Rev. Lett. 63 (1989), 1237[APS].
  43. H. Meinhardt and A. Gierer, J. Cell. Sci. 15 (1974), 321.
  44. S. Fauve and O. Thual, Phys. Rev. Lett. 64 (1990), 282[APS].
  45. L. Tuckermann and D. Barkley, Physica D46 (1990), 57.
  46. W. Eckhaus, Studies in Nonlinear Stability Theory (Springer-Verlag, New York, 1965).
  47. H. Sakaguchi, Prog. Theor. Phys. 85 (1991), 927[PTP].
  48. L. Kramer, private communications.
  49. S. Nasuno, Doctral Thesis, Tohoku University (1990).
  50. S. Sasa, T. Mizuguchi and M. Sano, Europhys. Lett. (1992).

Citing Article(s) :

  1. Journal of the Physical Society of Japan 63 (1994) pp. 895-903 :
    Generation Mechanism of a Localized Target Pattern in Electrohydrodynamic Convection
    Hiroki Kokubo, Masaki Sano, Beatrice Janiaud and Yasuji Sawada
  2. Journal of the Physical Society of Japan 64 (1995) pp. 1081-1084 :
    Simple Model for Target Patterns and Spiral Waves
    Osamu Moriyama and Mitsugu Matsushita
  3. Journal of the Physical Society of Japan 71 (2002) pp. 650-656 :
    Dynamical Properties of Transient Spatio-Temporal Patterns in Bacterial Colony of Proteus mirabilis
    Kazuhiko Watanabe, Jun-ichi Wakita, Hiroto Itoh, Hirotoshi Shimada, Sayuri Kurosu, Takemasa Ikeda, Yoshihiro Yamazaki, Tohey Matsuyama and Mitsugu Matsushita
  4. Journal of the Physical Society of Japan 78 (2009) 084801 (4 pages) :
    Synchronization of Two Target Patterns
    Yusuke Yoshida and Yasuyuki Kimura
  5. Progress of Theoretical Physics Vol. 99 No. 1 (1998) pp. 33-43 :
    Pattern Formation in a System with Spontaneously-Broken Rotational Symmetry
    Hidetsugu Sakaguchi

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.