Modeling Geochemical Self Organization

  • Peter J. Ortoleva

Abstract

Rocks of a wide variety of origins can manifest symmetry breaking instabilities and the development of repetitive and other patterns of mineralization. Models are set forth that couple local processes (aqueous reactions, precipitation/dissolution and nucleation of mineral grains) to a variety of transport processes. Linear stability, bifurcation, matched asymptotic and numerical analysis are used.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Nicolis and I. Prigogine (1977), Self-Organization in Nonequilibrium Systems, Wiley, New York.Google Scholar
  2. 2.
    R.E. Liesegang (1913), Geologische Diffusionen, Stein Kopff, Dresden and Liepzig.Google Scholar
  3. 3.
    E. Hedges and J.E. Myers (1926), The Problem of Physico-Chemical Periodicity, Longmans, Green, New York.Google Scholar
  4. 4.
    P. Ortoleva (1978), Bordeaux Conference on Far From Equilibrium Phenomena, Springer-Verlag, New York.Google Scholar
  5. 5.
    E. Merino (1984) in Chemical Instabilities, G. Nicolis and F. Baras, eds., D. Reidel Pub. Co., Boston, p. 305.Google Scholar
  6. 6.
    A.M. Turing (1952), ‘The Chemical Basis of Morphogenesis,’ Phil. Trans. Roy. Soc. B, 237, 37.CrossRefGoogle Scholar
  7. 7.
    W. Ostwald (1925), ‘The Theory of Liesegang Rings,’ Kolloid. Z., 36, 330.Google Scholar
  8. 8.
    S. Prager (1956), ‘Periodic Precipitations,’ J. Chem. Phys. 25, 279.CrossRefGoogle Scholar
  9. 9.
    P. Ortoleva (1984), ‘From Nonlinear Waves to Spiral and Speckled Patterns: Non-Equilibrium Phenomena in Geological and Biological Systems,’ in Proceedings of the Third Annual International Conference of the Center for Nonlinear Studies on Fronts, Interfaces and Patterns, Los Alamos, New Mexico, May 2–6, 1983, edited by A. Bishop, L.J. Campbell, and P.J. Channell, Amsterdam, North-Holland Physics Publishing.Google Scholar
  10. 10.
    P. Ortoleva, G. Auchmuty, J. Chadam, E. Merino, C. Moore, ‘Redox Fronts and Their Banding Modalities,’ Physica D (to appear).Google Scholar
  11. 11.
    P. Ortoleva (1985), The Variety and Structure of Chemical Waves, a volume in the Synergetics Series, H. Haken, ed., Springer-Verlag, N.Y.Google Scholar
  12. 12.
    D. Feinn, P. Ortoleva, W. Scalf, S. Schmidt and M. Wolff (1978), ‘Spontaneous Pattern Formation in Precipitating Systems,’ J. Chem. Phys. 69, 27.CrossRefGoogle Scholar
  13. 13.
    J. Chadam, R. Feeney, P. Ortoleva, S.L. Schmidt and P. Strickholm (1983), ‘Periodic Precipitation and Coarsening Waves: Applications of the Competitive Particle Growth Model,’ J. Chem. Phys. 78, 1293.CrossRefGoogle Scholar
  14. 14.
    M. Flicker and J. Ross, ‘Mechanism of Chemical Instability for Periodic Precipitation Phenomena,’ J. Chem. Phys. 60 (1974) 3458.CrossRefGoogle Scholar
  15. 15.
    R. Sultan and P. Ortoleva (1985), ‘Cooperative Banding Patterns in Two Precipitate Systems,’ in preparation.Google Scholar
  16. 16.
    E. Merino, P. Ortoleva and P. Strickholm (1981), ‘A Kinetic Theory of Stylolite Generation and Spacing,’ Transactions, v. 62, no. 45, p. 1056.Google Scholar
  17. 17.
    P. Ortoleva, E. Merino and P. Strickholm (1982), ‘Kinetics of Metamorphic Layering in Anisotropically Stressed Rocks,’ Amer. J. of Sci. 282, 617.CrossRefGoogle Scholar
  18. 18.
    E. Merino, P. Ortoleva and P. Strickholm (1984), ‘The Self Organization of Metamorphic Layering,’ in preparation.Google Scholar
  19. 19.
    P. Ortoleva (1983), ‘Modeling Nonlinear Wave Propagation and Pattern Formation at Geochemical First Order Phase Transitions,’ an invited review for the Proceedings of the NATO Advanced Research Workshop on Chemical Instabilities: Applications in Chemistry, Engineering, Geology, and Materials Science, Austin, Texas, March 14–18, 1983.Google Scholar
  20. 20.
    T. Dewers, E. Merino and P. Ortoleva, ‘Development of Metamorphic Layering in a Three Mineral Pressure Solution Model,’ in preparation.Google Scholar
  21. 21.
    P. Ortoleva and J. Ross (1975), ‘Theory of the Propagation of Discontinuities in Kinetic Systems with Multiple Time Scales: Fronts, Front Multiplicity, and Pulses,’ J. Chem. Phys. 63, 3398.CrossRefGoogle Scholar
  22. 22.
    R. Sultan and P. Ortoleva (1985), ‘Rotating Waves in Reaction-Diffusion Systems with Folded Slow Manifolds,’ J. Chem. Phys., submitted for publication.Google Scholar
  23. 23.
    P.C. Fife (1984), ‘Propagator-Controller Systems and Chemical Patterns,’ in Nonequilibrium Dynamics in Chemistry, C. Vidal and A. Pacault, eds. (Springer, New York), pg. 76.CrossRefGoogle Scholar
  24. 24.
    R. Sultan and P. Ortoleva, ‘Rotating, Propagating and Static Structures in Reaction-Transport Systems With Folded Slow Manifolds,’ in preparation.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • Peter J. Ortoleva
    • 1
    • 2
  1. 1.Departments of Chemistry and GeologyIndiana UniversityBloomingtonUSA
  2. 2.Geo-Chem Research Assoc.BloomingtonUSA

Personalised recommendations