Noise and oscillatory zoning of minerals

Geochimica et Cosmochimica Acta

Volumn 64, Issue 11, 2000, Pages 1893-1904

  Holten, Terje ^a   Jamtveit, Bjørn ^a   Meakin, Paul ^a  

^a UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTALLIZATION; OSCILLATION; ZONATION;

EID: 0034046805     PISSN: 00167037     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0016-7037(99)00444-5     Document Type: Article

References (52)

1. Bryxina N.A., Sheplev V.S. Oscillatory zoning in calcite growing from an aqueous solution (in Russian). Mathematical Modeling. 9:1997;32-38.
2. Calvert P.D., Uhlmann D.R. Surface nucleation growth theory for large and small crystal cases and the significance of transient nucleation. J. Cryst. Growth. 12:1972;291-296.
3. Gammaitoni L., Hänggi P., Jung P., Marchesoni F. Stochastic resonance. Rev. Modern Physics. 70:1998;223-287.
4. Guckenheimer J., Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. 1983;Springer-Verlag.
5. Guillouzic S., L'Heureux I. Kinetics of dichotomous noise-induced transitions in a multistable multivariable system. Phys. Rev. E. 55:1997;5060-5072.
6. Gutiérrez J.M., Iglesias A. Synchronizing chaotic systems with positive conditional Lyapunov exponents by using convex combinations of the drive and response systems. Phys. Lett. A. 239:1998;174-180.
7. Halden N.M. Determination of Lyapunov exponents to characterize the oscillatory distribution of trace elements in minerals. Can. Mineral. 34:1996;1127-1135.
8. Halden N.M., Hawthorne F.C. The fractal geometry of oscillatory zoning in crystals Application to zircon . Am. Mineral. 78:1993;1113-1116.
9. Hasler M., Maistrenko Y., Popovych O. Simple example of partial synchronization of chaotic systems. Phys. Rev. E. 58:1998;6843-6846.
10. Heagy J.F., Carroll T.L., Pecora L.M. Desynchronization by periodic orbits. Phys. Rev. E. 52:1995;R1253-R1256.
11. Helgeson H.C., Murphy W.M., Aagaard P. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. II. Rate constants, effective surface area, and the hydrolysis of feldspar. Geochim. Cosmochim. Acta. 48:1984;2405-2432.
12. Holten T., Jamtveit B., Meakin P., Cortini M., Blundy J., Austrheim H. Statistical characteristics and origin of oscillatory zoning in crystals. Am. Mineral. 82:1997;596-606.
13. Jaeger L., Kantz H. Homoclinic tangencies and non-normal Jacobians. Effects of noise in nonhyperbolic chaotic systems. Physica D. 105:1997;79-96.
14. Jamtveit B. Oscillatory zonation patterns in hydrothermal grossular-andradite garnet Nonlinear dynamics in regions of immiscibility . Am. Mineral. 76:1991;1319-1327.
15. Jamtveit B., Ragnarsdottir K.V., Wood B.J. On the origin of zoned grossular-andradite garnets in hydrothermal systems. Eur. J. Mineral. 7:1995;1399-1410.
16. Jamtveit B. Crystal growth and intracrystalline zonation patterns in hydrothermal environments. Jamtveit B., Meakin P. Growth, dissolution and pattern formation in geosystems. 1999;65-84 Kluwer Academic Publishers.
17. Jamtveit B., Meakin P. Growth, dissolution and pattern formation in geosystems. 1999;Kluwer Academic Publishers.
18. Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Physics Lett. A. 185:1994;77-87.
19. Kirkpatrick R.J., Klein L., Uhlmann D.R., Hays J.F. Rates and processes of crystal growth in the system anorthite-albite. J. Geophys. Res. 84:1979;3671-3676.
20. Lansbury A.N., Thompson J.M.T., Stewart H.B. Basin erosion in the thin well Duffing oscillator Two distinct bifurcation scenarios . Int. J. Bif. Chaos. 2:1992;505-532.
21. Lasaga A.C. Toward a master equation in crystal growth. Am. J. Sci. 282:1982;1264-1288.
22. Leung H.K. Critical slowing down in synchronizing nonlinear oscillators. Phys. Rev. E. 58:1998;5704-5709.
23. L'Heureux I. Oscillatory zoning in crystal growth A constitutional undercooling mechanism . Phys. Rev. E. 48:1993;4460-4469.
24. L'Heureux I. Oscillatory zoning in plagioclase Thermal effects . Physica A. 239:1997;137-146.
25. L'Heureux I., Fowler A.D. A nonlinear dynamical model of oscillatory zoning in plagioclase. Amer. Mineral. 79:1994;885-891.
26. L'Heureux I., Fowler A.D. Isothermal constitutive undercooling as a model for oscillatory zoning in plagioclase. Can. Mineral. 34:1996;1137-1147.
27. L'Heureux I., Fowler A.D. Dynamical model of oscillatory zoning in plagioclase with nonlinear partition relation. Geophys. Res. Lett. 23:1996;17-20.
28. Longtin A. Autonomous stochastic resonance in bursting neurons. Phys. Rev. E. 55:1997;868-876.
29. Lorenz E.N. Deterministic nonperiodic flow. J. Atmos. Sci. 20:1963;130-141.
30. Malescio G. Noise and synchronization in chaotic systems. Phys. Rev. E. 53:1996;6551-6554.
31. Mandelbrot B. (1982) The fractal geometry of nature. W. H. Freeman.
32. Maritan A., Banavar J.R. Chaos, noise and synchronization. Phys. Rev. Lett. 72:1994;1451-1454.
33. Meakin P. Fractals, scaling and growth far from equilibrium. 1998;Cambridge University Press.
34. Merino E. (1984) Survey of geochemical self-patterning phenomena. In Chemical Instabilities: Applications in Chemistry, Engineering, Geology, and Materials Science (eds. G. Nicolis and F. Baras), pp. 305-328. NATO ASI series C, vol. 120.
35. Merino E. (1987) Textures of low-temperature self-organization. In Geochemistry of the Earth's Surface (eds. R. Rodriguez-Clemente and Y. Tardy), pp. 597-610. CSIC (Spain) and CNRS (France).
36. Meyer H.J. The influence of impurities on the growth rate of calcite. J. Cryst. Growth. 66:1984;639-646.
37. Ortoleva P. Geochemical self-organization. 1994;Oxford University Press.
38. Pearce T.H. Recent work on oscillatory zoning in plagioclase. Parsons I. Feldspars and their reactions. 1994;313-349 NATO ASI.
39. Pearce T.H., Kolisnik A.M. Observations of plagioclase zoning using interference imaging. Earth Sci. Rev. 29:1990;9-26.
40. Pecora L.M. Synchronization condition and desynchronization patterns in coupled limit-cycle and chaotic systems. Phys. Rev. E. 58:1998;347-360.
41. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 64:1990;821-824.
42. Pikovsky A.S., Rosenblum M.G., Osipov G.V., Kurths J. Phase synchronization of chaotic oscillators by external driving. Physica D. 104:1997;219-238.
43. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical recipes in C. 1992;Cambridge University Press.
44. Putnis A., Fernandez-Diaz L., Prieto M. Experimentally produced oscillatory zoning in plagioclase. Nature. 358:1992;743-745.
45. Reeder R.J., Fagioli R.O., Meyers W.J. Oscillatory zoning of Mn in solution-grown calcite crystals. Earth Sci. Rev. 29:1990;39-46.
46. Rosenstein M.T., Collins J.J., De Luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D. 65:1993;117-134.
47. Scott S.K. Chemical Chaos. 1991;Clarendon Press.
48. Shore M., Fowler A.D. Oscillatory zoning in minerals A common phenomenon . Can. Mineral. 34:1996;1111-1126.
49. Strogatz S. Nonlinear dynamics and chaos. 1994;Addison-Wesley.
50. Wang J.-H., Wu J.-P. Oscillatory zonation of minerals and self-organization in silicate solid-solution systems A new nonlinear dynamic model . Eur. J. Mineral. 7:1995;1089-1100.
51. Wang Y., Merino E. Dynamic model of oscillatory zoning of trace elements in calcite Double layer, inhibition, and self-organization . Geochem. Cosmochim. Acta. 56:1992;587-596.
52. Zeni A.R., Gallas J.A.C. Lyapunov exponents for a Duffing oscillator. Physica D. 89:1995;71-82.