HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 56 (1976) > Number 3
| Next Article >

Prog. Theor. Phys. Vol. 56 No. 3 (1976) pp. 724-740

[ Full Text PDF : FREE ACCESS (1486K) ]

Pattern Formation in Oscillatory Chemical Reactions

Yoshiki Kuramoto and Tomoji Yamada*

Department of Physics, Kyushu University, Fukuoka
*Department of Applied Science, Kyushu University, Fukuoka

(Received March 10, 1976)

Abstract:

For the purpose of clarifying the origin of some remarkable wave phenomena arising from chemical activity, a dynamical theory of patterns for a two-component dissipative medium is developed. On two basic assumptions, namely, the existence of a stable limit-cycle oscillation and the slow spatial variation of phase, the kinetic equation is reduced to a form suitable to the analysis of patterns. On the basis of the simplified equation, target patterns, spiral waves, self-locking of phase and solitary wave propagation are discussed from a unified point of view.


URL : http://ptp.ipap.jp/link?PTP/56/724/
DOI : 10.1143/PTP.56.724

[ Full Text PDF : FREE ACCESS (1486K) ] Citation:

References:

  1. P. Glansdorff and I. Prigogine, “Thermodynamic Theory of Structure, Stability and Fluctuations” Wiley-Interscience (1971).
    G. Nicolis and J. Portnow, Chem. Rev. 73 (1973), 365.
    B. Chance et al. (ed.), Biological and Biochemical Oscillators (Acad. Press, 1973).
  2. A. M. Zhabotinsky, Doklady Akad. Nauk SSSR 157 (1964), 392; Biofizika 9 (1964), 306.
  3. R. J. Field, E. Koros and R. M. Noyes, J. Am. Chem. Soc. 94 (1972), 8646.
    R. M. Noyes, R. J. Field and E. Koros, J. Am. Chem. Soc. 95 (1972), 1394.
    R. J. Field and R. M. Noyes, Nature 237 (1962), 390[CrossRef].
  4. A. N. Zaikin and A. M. Zhabotinsky, Nature 225 (1970), 535.
  5. A. T. Winfree, Science 175 (1972), 643
  6. D. H. Sattinger, Topics in Stability and Bifurcation Theory (Springer, New York, 1973).
    G. Nicolis and J. F. G. Auchmuty, Proc. Natl. Acad. Sci. (USA) 71 (1974), 2748.
  7. P. Ortoleva and J. Ross, J. Chem. Phys. 60 (1974), 5090[CrossRef].
    N. Kopell and L. Howard, Studies in Appl. Math. 52 (1973), 291.
  8. Y. Kuramoto and T. Yamada, Prog. Theor. Phys. 55 (1976), 643[PTP].
  9. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 54 (1975), 687[PTP]; ibid. 55 (1976), 356[PTP].
  10. P. Ortoleva and J. Ross, J. Chem. Phys. 58 (1973), 5673[CrossRef].
  11. Y. Aizawa, Y. Shimatani and Y. Kobatake, Prog. Theor. Phys. 53 (1975), 305[PTP].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 60 (1991) pp. 2485-2488 :
    Target Pattern Formation in a Chaotic Medium
    Hiroyuki Nagashima
  2. Journal of the Physical Society of Japan 60 (1991) pp. 2797-2799 :
    Target Patterns and Pacemakersin a Reaction-Diffusion System
    Hiroyuki Nagashima
  3. Journal of the Physical Society of Japan 67 (1998) pp. 365-368 :
    Extinction of Oscillation in a Reaction-Diffusion System
    Hiroyuki Nagashima and Hitoshi Mahara
  4. Journal of the Physical Society of Japan 69 (2000) pp. 3552-3554 :
    “Ring-Shaped Model” of the Pacemaker in Oscillatory Reaction-Diffusion System
    Hitoshi Mahara, Takahiro Saito, Yoshimitsu Amagishi, Hiroyuki Nagashima and Tomohiko Yamaguchi
  5. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 734-745 :
    Theoretical Study of a Chemical Turbulence
    Hirokazu Fujisaka and Tomoji Yamada
  6. Progress of Theoretical Physics Vol. 60 No. 6 (1978) pp. 1935-1936 :
    Breakdown of Synchronized State in a Self-Oscillatory Chemical Reaction System
    Tomoji Yamada and Yoshiki Kuramoto
  7. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 143-153 :
    A Reductive Perturbation Approach to Hard-Mode Instabilities of Inverted-Type Bifurcations
    Kaoru Yamafuji, Kiyoshi Toko, Junsaku Nitta and Kiichi Urahama
  8. Progress of Theoretical Physics Vol. 67 No. 1 (1982) pp. 164-178 :
    Rotating Spiral Waves in Reaction-Diffusion Systems
    Shinji Koga
  9. Progress of Theoretical Physics Vol. 67 No. 2 (1982) pp. 454-463 :
    Schrödinger Equation Approach to Rotating Spiral Waves in Reaction-Diffusion Systems
    Shinji Koga
  10. Progress of Theoretical Physics Vol. 68 No. 4 (1982) pp. 1105-1121 :
    Multiperiodic Flows, Chaos and Lyapunov Exponents
    Hirokazu Fujisaka
  11. Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1104-1117 :
    Schrödinger Equation Approach to Collision Phenomena in Reaction-Diffusion Systems
    Shinji Koga
  12. Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1022-1032 :
    Obliquely Colliding Waves in Reaction-Diffusion Systems
    Shinji Koga
  13. Progress of Theoretical Physics Vol. 79 No. 5 (1988) pp. 1069-1079 :
    Mutual Entrainment in Oscillator Lattices with Nonvariational Type Interaction
    Hidetsugu Sakaguchi, Shigeru Shinomoto and Yoshiki Kuramoto
  14. Progress of Theoretical Physics Supplement No.79 (1984) pp. 223-240 :
    Cooperative Dynamics of Oscillator Community
    Yoshiki Kuramoto

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

Copyright © Progress of Theoretical Physics 2013 All rights reserved.