Discover
/
Article

Computational synergetics

JUL 01, 1984
As a heuristic tool, used to explore complex dynamical behavior, computers allow us to discover unexpected linkages and new concepts in nonlinear systems.

DOI: 10.1063/1.2916319

Norman J. Zabusky

Computers, used in what I shall call the “heuristic mode,” can greatly enhance our understanding of the mathematics of nonlinear dynamical processes—a field that is taking on increasing importance as we explore the complex behavior that even simple systems often exhibit. As I shall try to show, computers allow us to penetrate into unexplored regions of mathematics and to discover unforeseen linkages among ideas.

This article is only available in PDF format

References

  1. 1. H. H. Goldstine, The Computer from Pascal to von Neumann, Princeton U.P., Princeton, N.J. (1972).

  2. 2. H. H. Goldstine, J. von Neumann, in Collected Works of John von Neumann, A. Taub, ed., MacMillan, New York, (1963), volume 5, page 1.
    Another formulation is in a 1949 paper. Collected Works, volume 6, page 437.

  3. 3. S. M. Ulam, A Collection of Mathematical Problems, Wiley–Interscience, New York (1960).

  4. 4. N. J. Zabusky, J. Comput. Phys. 43, 195 (1981). This comprehensive review paper contains an extensive bibliography of papers and monographs on computational synergetics.https://doi.org/JCTPAH

  5. 5. E. Fermi, J. R. Pasta, S. M. Ulam, Los Alamos Report LA‐1940, May 1955;
    reprinted in E. Fermi, Collected Works, U. Chicago, P. Chicago (1965), volume 2, page 978.

  6. 6. N. J. Zabusky, in Proc. Conf. Mathematical Models in the Physical Sciences, S. Drobot, ed., Prentice–Hall, Englewood Cliffs, N.J. (1963), page 99.

  7. 7. M. D. Kruskal, Proc. IBM Scientific Symposium—Large Scale Problems in Physics, 9–11 December 1963, IBM, Armonk, N.Y. (1965).

  8. 8. R. M. Miura, SIAM Rev. 18, 412 (1976). https://doi.org/SIREAD
    J. W. Miles, J. Fluid Mech. 106, 131 (1981).https://doi.org/JFLSA7

  9. 9. N. J. Zabusky, M. D. Kruskal, Phys. Rev. Lett. 15, 240 (1965).https://doi.org/PRLTAO

  10. 10. M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform, SIAM Philadelphia (1981).

  11. 11. C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, Phys. Rev. Lett. 19, 1095 (1967).https://doi.org/PRLTAO

  12. 12. M. Toda, J. Phys. Soc. Japan 22, 431 (1967); https://doi.org/JUPSAU
    M. Toda, J. Phys. Soc. Japan Suppl 26, 235 (1969);
    M. Toda, Theory of Nonlinear Lattices, Springer‐Verlag, Berlin (1980) (Series in Solid State Sciences, volume 20).

  13. 13. N. J. Zabusky, in The Significance of Nonlinearity in the Natural Sciences, B. Kursunoglu, A. Perlmutter, L. F. Scott, eds., Plenum, New York (1977), page 145.

  14. 14. J. C. McWilliams, J. Fluid Mech., (1984) in press.

  15. 15. N. J. Zabusky, G. S. Deem, J. Fluid Mech. 47, 353 (1971).https://doi.org/JFLSA7

  16. 16. C.‐M. Ho, P. Huerre, Ann. Rev. Fluid Mech. 16, 365 (1984).
    F. P. Browand, C.‐M. Ho, J. Mécanique (1983) in press.

  17. 17. J. P. Christiansen, N. J. Zabusky, J. Fluid Mech. 61, 219, (1973).https://doi.org/JFLSA7

  18. 18. N. J. Zabusky, M. H. Hughes, K. V. Roberts, J. Comput. Phys. 30, 96 (1979). https://doi.org/JCTPAH
    H.‐M. Wu, E. A. Overman, II, N. J. Zabusky, J. Comput. Phys 53, 42 (1984).https://doi.org/JCTPAH

  19. 19. A. Koestler, The Act of Creation, Hutchison, London, 1964, page 454.

  20. 20. M. L. Norman, L. L. Smarr, K.‐H. A. Winkler, M. D. Smith, Astron. Astrophys. 113, 285 (1982); https://doi.org/AAEJAF
    M. L. Norman, K.‐H. A. Winkler, L. L. Smarr, in Astrophysical Jets, A. Ferrari, A. G. Pacholczyk, eds., Reidel, Boston (1983) 227;
    M. L. Norman, L. L. Smarr, K.‐H. A. Winkler, in Numerical Astrophysics, a Festschrift in Honor of James R. Wilson, J. Centrella, R. Bowers, J. Leblanc, M. Leblanc, eds. Jones and Bartlett, Boston (1984);
    M. L. Norman, K.‐H. A. Winkler, in Astrophysical Radiation Hydrodynamics, K.‐H. A. Winkler, M. L. Norman, eds., Reidel, Boston (1984).

  21. 21. Figure 5 on supersonic jets and the cover figure have not been previously published and were provided by M. L. Norman, K.‐H. A. Winkler, and L. L. Smarr. A review of their work with 30 colored panels is in L. L. Smarr, M. L. Norman, K.‐H. A. Winkler, Physica D (1984), in press. Figure 6 is from work in progress by Norman, Winkler and Zabusky.

  22. 22. For some vital thoughts on how things could be improved, see P. J. Davis, J. A. Anderson, SIAM Rev. 21, 112 (1979).https://doi.org/SIREAD

  23. 23. E. Chargaff, Science 172, 637 (1971).https://doi.org/SCIEAS

  24. 24. C. J. Jung, W. Pauli, The Interpretation of Nature and the Psyche, Pantheon, New York (1955), page 151.

More about the Authors

Norman J. Zabusky. University of Pittsburgh.

Related content
/
Article
Although motivated by the fundamental exploration of the weirdness of the quantum world, the prizewinning experiments have led to a promising branch of quantum computing technology.
/
Article
As conventional lithium-ion battery technology approaches its theoretical limits, researchers are studying alternative architectures with solid electrolytes.
/
Article
Bottom-up self-assembly is a powerful approach to engineering at small scales. Special strategies are needed to formulate components that assemble into predetermined shapes with precise sizes.
/
Article
The polymath scientist leaves behind a monumental legacy in both the scientific and political realms.
This Content Appeared In
pt-cover_1984_07.jpeg

Volume 37, Number 7

Get PT in your inbox

Physics Today - The Week in Physics

The Week in Physics" is likely a reference to the regular updates or summaries of new physics research, such as those found in publications like Physics Today from AIP Publishing or on news aggregators like Phys.org.

Physics Today - Table of Contents
Physics Today - Whitepapers & Webinars
By signing up you agree to allow AIP to send you email newsletters. You further agree to our privacy policy and terms of service.