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Space-time complexity in solid-state and statistical physics models

  • Session II: Nonlinear Waves - Solitons
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Book cover Trends in Applications of Pure Mathematics to Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 249))

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Abstract

Representative examples of space-time complexity motivated by solidstate and statistical physics models are discussed. The importance of competing interactions in defining classes of space-time attractors is emphasized for partial differential equations and related cellular automata or coupled-map lattices.

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References

  1. For example, Physics in One Dimension, eds. J. Bernasconi and T. Schneider Springer-Ver lag, 1981).

    Google Scholar 

  2. A. Seeger, proceedings of this conference.

    Google Scholar 

  3. J. M. Kosterlitz and D. J. Thouless, Prog. Low Temp. Phys., Vol. VII B, ed. D. F. Brewer (North-Holland, 1978).

    Google Scholar 

  4. J. F. Currie et al., Phys. Rev. B 22, 477 (1980); A. R. Bishop, in Ref. [1].

    Google Scholar 

  5. N. Theodorakopoulos, Z. Physik B 46, 367 (1982).

    Google Scholar 

  6. See articles in Solitons, eds. S. Trullinger and V. Zakharov (North-Holland, in press).

    Google Scholar 

  7. See, for example, Physica D 7 (1983), eds. D. K. Campbell and H. A. Rose.

    Google Scholar 

  8. A. R. Bishop, Proceedings of the Ninth Gwatt Workshop, Gwatt, Switzerland, October 17–19 (1985).

    Google Scholar 

  9. For example, P. Bak, Rep. Prog. Phys. 45, 587 (1982).

    Google Scholar 

  10. S. Aubry, in Ref. [7].

    Google Scholar 

  11. J. Oitmaa and A. R. Bishop, in preparation.

    Google Scholar 

  12. A. R. Bishop, in Dynamical Problems in Soliton Systems, Proceeding: of the Seventh Kyoto Summer Institute, ed. S. Tak eno Springer-Verlag, 1985); A. R. Bishop and P. S. Lomdahl, Physica D, in press.

    Google Scholar 

  13. D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).

    Google Scholar 

  14. K. Nakamura, K. Nakahara, and A. R. Bishop, Phys. Rev. Lett. 54, 861 (1985).

    Google Scholar 

  15. E. Abrahams et al., Phys. Rev. Lett. 42, 673 (1979).

    Google Scholar 

  16. Physica D 12 (1984), eds. A. R. Bishop, L. J. Campbell, and P. J. Channell.

    Google Scholar 

  17. For example, E. Ben-Jacob et al., Phys. Rev. A 29, 330 (1984); M. D. Kruskal, C. Oberman, and H. Segur, preprint (1985).

    Google Scholar 

  18. G. I. Sivashinsky, Acta Astronaut. 4, 1177 (1977); J. M. Hyman and B. Nicolaenko, preprint (1985).

    Google Scholar 

  19. M. Lowe and J. P. Gollub, Phys. Rev. A 31, 3893 (1985); P. Coullet, preprint (1985).

    Google Scholar 

  20. For example, R. P. Hall, M. Sherwin, and A. Zettl, Phys. Rev. B 29, 7076 (1984).

    Google Scholar 

  21. For example, G. Gibson and C. Jeffries, Phys. Rev. A 29, 811 (1984); L. P. Levy, Phys. Rev. B 31, 7077 (1985).

    Google Scholar 

  22. For example, M. P. Soerensen et al., Phys. Rev. Lett. 51, 1919 (1983); P. Martinoli et al., preprint (1985).

    Google Scholar 

  23. G. A. Held and C. Jeffries, Phys. Rev. Lett. 55, 887 (1985).

    Google Scholar 

  24. For example, R. Blinc et al., Phys. Rev. B 29, 1508 (1984).

    Google Scholar 

  25. For example, D. W. McLaughlin, J. V. Moloney, and A. C. Newell, Phys. Rev. Lett. 51, 75 (1983).

    Google Scholar 

  26. J. Wu and I. Rudnick, Phys. Rev. Lett. 55, 204 (1985).

    Google Scholar 

  27. J. C. Wheatley et al., preprint (1985); W. Lauterborn, J. Acoust. Soc. Am. 59, 283 (1976).

    Google Scholar 

  28. See Cellular Automata, eds. J. D. Farmer, T. Toffoli, and S. Wolfram North-Holl and, 1984).

    Google Scholar 

  29. For example, K. Kaneko, Prog. Theor. Phys. 72, 480 (1984).

    Google Scholar 

  30. N. G. van Kampen, J. Stat. Phys. 17, 71 (1977); E. Domany, Phys. Rev. Lett. 52, 871 (1984); G. Grin-stein et al., preprints (1985); E. Jen, preprint (1985).

    Google Scholar 

  31. For example, T. Schneider, M. Zannetti, and R. Badii, Phys. Rev. B 31, 2941 (1985).

    Google Scholar 

  32. For example, E. Domany and J. E. Gubernatis, Phys. Rev. B 32, 3354 (1985).

    Google Scholar 

  33. U. Frisch, B. Hasslacher, and Y. Pomeau, preprint (1985).

    Google Scholar 

  34. G. Mayer-Kress and H. Haken, preprint (1984).

    Google Scholar 

  35. D. Bennett, A. R. Bishop, and S. E. Trullinger, Z. Physik B 47, 265 (1982); A. R. Bishop et al., Phys. Rev. Lett. 50, 1095 (1983). [36] E. A. Overman, D. W. McLaughlin, and A. R. Bishop, Physica D, in press; also see K. Fesser et al., Phys. Rev. A 31, 2728 (1985). [37] 0. H. Olsen et al., J. Phys. C 18, L511 (1985).

    Google Scholar 

  36. R. K. Dodd et al., Solitons and Nonlinear Wave Equations (Academic Press, 1982).

    Google Scholar 

  37. A. R. Bishop et al., in preparation.

    Google Scholar 

  38. For example, N. Bekki and K. Nozaki, in Ref. [12].

    Google Scholar 

  39. H. T. Moon and M. V. Goldman, Phys. Rev. Lett. 53, 1821 (1984); G. Pelletier et al., Physica D, in press.

    Google Scholar 

  40. B. Horovitz, et al., preprint (1985); S. Aubry et al., in preparation.

    Google Scholar 

  41. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983); also see articles in Dimensions and Entropies in Chaotic Systems: Quantification of Complex Behavior, ed. T. G..Mayer-Kress Springer Series in Synergetics, in press).

    Google Scholar 

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Ekkehart Kröner Klaus Kirchgässner

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© 1986 Springer-Verlag

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Bishop, A.R., Eykholt, R., Overman, E.A. (1986). Space-time complexity in solid-state and statistical physics models. In: Kröner, E., Kirchgässner, K. (eds) Trends in Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016386

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  • DOI: https://doi.org/10.1007/BFb0016386

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  • Print ISBN: 978-3-540-16467-8

  • Online ISBN: 978-3-540-39803-5

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