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The Multifaceted Family of the Nonlinear: Waves and Fields, Center Dynamics, Catastrophes, Rock Bands and Precipitation Patterns

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Synergetics

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 3))

Abstract

In nonlinear partial differential systems almost anything can happen. And what is beautiful is that it does. However depressing this thought might be to those who like simple generalizations, it also serves to point out the beauty and great variation of the manifestations of the nonlinear in the bio-, geo- and other spheres around us. In the following set of brief comments on studies of nonlinear phenomena done with my colleagues and students I will emphasize the cascading open endedness of the realm of the nonlinear. I would like to state here that several of these projects were direct or indirect offshoots from the very enjoyable years I spent with Professor John Ross at M.I.T.

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References

  1. S. Schmidt, P. Ortoleva: J. Chem. Phys. 67, 3771 (1977)

    Article  ADS  Google Scholar 

  2. S. Schmidt, P. Ortoleva: “Multiple Chemical Waves Induced by Applied Electrical Fields” (submitted for publication)

    Google Scholar 

  3. P. Ortoleva, J. Ross: J. Chem. Phys. 63, 3398 (1975)

    Article  ADS  Google Scholar 

  4. For a critical review see A.T. Winfree, in Adv. in Theoret. Chem., ed. H. Eyring (1978)

    Google Scholar 

  5. F.B. Gulk, A.A. Petrov: Biofizika 17, 261 (1972)

    Google Scholar 

  6. T. Erneaux, M. Herschkowitz-Kaufman: J. Chem. Phys. 66 (1977)

    Google Scholar 

  7. T. Yomada, Y. Kuramoto: Prog. Theoret. Phys. 55, 2035 (1976)

    Article  ADS  Google Scholar 

  8. P. Ortoleva, J. Ross: J. Chem. Phys. 60, 5090 (1974)

    Article  ADS  Google Scholar 

  9. P. Ortoleva: J. Chem. Phys. 69, 300 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  10. R. Thorn: Stability3 Structure and Morphogenesis (Benjamin, New York 1972)

    Google Scholar 

  11. A.E.R. Woodcock, T. Poston: A Geometric Study of the Elementary Catastrophes, Lecture Notes in Mathematics 373 (Springer, Berlin, Heidelberg, New York 1974)

    Book  Google Scholar 

  12. D. Feinn, P. Ortoleva: J. Chem. Phys. 67, 2119 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  13. M. Golubitsky, V. Guillemin: Stable Mappings and Their Singularities (Springer, Berlin, Heidelberg, New York 1973)

    MATH  Google Scholar 

  14. Y. Bottinga, Y. Kudo, D. Weill: American Mineral. 51, 792 (1966)

    Google Scholar 

  15. S. Haase, P. Ortoleva: “A Theory of Periodic Zoning in Plageoclase Feldspars” (submitted for publication)

    Google Scholar 

  16. J. Chadam, D. Feinn, S. Haase, P. Ortoleva: “Periodic Crystal Zoning of Solid Solutions” (submitted for publication)

    Google Scholar 

  17. R.E. Liesegang: Phot. Arch. 21, 221 (1896)

    Google Scholar 

  18. E. Hedges, J.E. Myers: The Problem of Physico-chemical Periodicity (Longmans Green, New York 1926)

    Google Scholar 

  19. W. Ostwald: Kolloid Z. 36, 380 (1925)

    Article  Google Scholar 

  20. S. Praeger: J. Chem. Phys. 25, 279 (1956)

    Article  ADS  Google Scholar 

  21. D. Feinn, P. Ortoleva, W. Schalf, S. Schmidt, D. Wolff: J. Chem. Phys. 69, 27 (1978)

    Article  ADS  Google Scholar 

  22. R. Lovett, P. Ortoleva, J. Ross: J. Chem. Phys. (to appear)

    Google Scholar 

  23. M.R. Flicker, J. Ross: J. Chem. Phys. 60, 3458 (1974)

    Article  ADS  Google Scholar 

  24. A. Nitzan, P. Ortoleva, J. Deutch, J. Ross: J. Chem. Phys. 61, 1056 (1974)

    Article  ADS  Google Scholar 

  25. D.A. McQuarrie: J. Appl. Prob. 4, 413.(1967)

    Article  MathSciNet  MATH  Google Scholar 

  26. aM. Maleck-Mansour, G. Nicolis: J. Stat. Phys. 13, 197 (1976)

    Article  ADS  Google Scholar 

  27. bC.W. Gardiner, K.J. McNeil, D.F. Walls, I.S. Matheson: J. Stat. Phys. 14, 307 (1976)

    Article  ADS  Google Scholar 

  28. M. Delle Donne, P. Ortoleva: J. Stat. Phys. 18, 319 (1978)

    Article  ADS  Google Scholar 

  29. P. Ortoleva, S. Yip: J. Chem. Phys. 65, 2045 (1976)

    Article  ADS  Google Scholar 

  30. M. DelleDonne, P. Ortoleva: “A Computer Molecular Dynamical Study of Critical Oscillatory Chemical Fluctuations” (in preparation)

    Google Scholar 

  31. M. DelleDonne, P. Ortoleva: “Critical Fluctuation Universality in Chemically Oscillatory Systems: A Soluble Model” (submitted for publication)

    Google Scholar 

  32. H.-S. Hahn, A. Nitzan, P. Ortoleva, J. Ross: PNAS 71, 4067 (1974)

    Google Scholar 

  33. S. Bose, P. Ortoleva: “Reacting Hard Sphere Dynamics: Liouville Equation for Condensed Media”, J. Chem. Phys. (to appear)

    Google Scholar 

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© 1979 Springer-Verlag Berlin Heidelberg

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Ortoleva, P. (1979). The Multifaceted Family of the Nonlinear: Waves and Fields, Center Dynamics, Catastrophes, Rock Bands and Precipitation Patterns. In: Pacault, A., Vidal, C. (eds) Synergetics. Springer Series in Synergetics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67262-0_20

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  • DOI: https://doi.org/10.1007/978-3-642-67262-0_20

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