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Mathematical simulation of complex natural systems

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Abstract

The paper presents a review of publications devoted to the mathematical simulations of natural systems whose large spatiotemporal scales make impossible their adequate experimental modeling in nature. The studies include the modeling of the mineralogy of the surface rocks of Venus and Mars, fractional condensation from the gaseous constituent of the preplanetary nebula, the genesis of chondrites and the material of the Earth’s upper mantle, and the evaporation of interstellar dust and the stratification of material in cooling planets.

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References

  1. I. L. Khodakovsky, V. P. Volkov, Yu. I. Sidorov, and M. V. Borisov, “Mineralogical Composition, Hydration, and Oxidation of the Venusian Outer Shell: A Preliminary Prediction,” Geokhimiya, No. 12, 1821–1835 (1978).

  2. I. K. Karpov, A. I. Kiselev, and F. A. Letnikov, Chemical Thermodynamics in Geochemistry and Petrology (Akad. Nauk SSSR, Irkutsk, 1971) [in Russian].

    Google Scholar 

  3. G. B. Dantzig, Programming in Linear Structures (Comptroller. USAF, Washington, 1948).

    Google Scholar 

  4. W. B. White, S. M. Johnson, and G. B. Dantzig, “Chemical Equilibrium in Complex Mixtures,” J. Chem. Phys. 28, 751–795 (1958).

    Google Scholar 

  5. Yu. V. Shvarov, Extended Abstract of Candidate’s Dissertation in Geology and Mineralogy (MGU, Moscow, 1982).

    Google Scholar 

  6. K. P. Florenskii, V. P. Volkov, and O. V. Nikolaeva, “On a Geochemical Model of the Venusian Troposphere,” Geokhimiya, No. 8, 1135–1150 (1976).

  7. I. L. Khodakovsky, V. P. Volkov, Yu. I. Sidorov, and M. V. Borisov, “Venus: Preliminary Prediction of the Mineral Composition of Surface Rocks,” Icarus 39 (3), 352–363 (1979).

    Article  Google Scholar 

  8. Yu. V. Semenov, Yu. I. Sidorov, I. L. Khodakovsky, et al., “Standard Entropy of Minerals,” in Proceedings of All-Union Conference on Mineralogy and Petrology (Kiev, 1981), pp. 96-102 [in Russian].

  9. G. G. Likhoidov, Yu. I. Sidorov, V. M. Gurevich, et al., “Thermodynamic Characteristics of Glaucophane Na2Mg3Al2Si8O22(OH)2 and Some Petrological Implications,” Geokhimiya, No. 7, 1002–1013 (1982).

  10. B. G. Gel’man, V. T. Zolotukhin, N. I. Lamonov, et al., “Gas Chromatography of the Venusian Atmosphere by the Venera-12 Spacecraft,” Kosm. Issl. 17 (5), 708–713 (1979).

    Google Scholar 

  11. U. von Zahn, S. Kumar, H. Niemann, and R. Prinn, “Composition of the Venus Atmosphere,” in Venus, Ed. by D. M. Hunten, et al. (Univ. Arizona Press, Tucson, 1983), pp. 299–430.

    Google Scholar 

  12. I. L. Khodakovsky, V. P. Volkov, Yu. I. Sidorov, et al., “The Geochemical Model of the Venusian Troposphere and Crust according to New Data,” Geokhimiya, No. 12, 1747–1758 (1979).

  13. Yu. A. Surkov, L. P. Moskaleva, O. P. Shcheglov, et al., “Determination of the Elemental Composition of Venusian Atmosphere by the Vega-2 Spacecraft: Procedure, Equipment, and Results,” Astron. Vestn., No. 4, 275–288 (1985).

  14. Yu. I. Sidorov and M. Yu. Zolotov, “Weathering of Martian Surface Rocks,” in Advances in Physical Geochemistry: Chemistry and Physics of Terrestrial Planets (Springer, New York, 1986), pp. 191–223.

    Google Scholar 

  15. A. I. Shapkin and Yu. I. Sidorov, “Thermodynamic Models in Cosmochemistry and Planetology,” Geochem. Int. 41 (Suppl. 1), S1–S144 (2003).

    Google Scholar 

  16. Yu. I. Sidorov and M. Yu. Zolotov, Martian Surface Rocks and Soil (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  17. A. E. Baird, A. J. Castro, B. C. Clark, et al., “Sampling Strategies and Ground Support for Inorganic Chemical Analyses of Mars Regolith,” J. Geophys. Res. 82, 4595–4624 (1977).

    Google Scholar 

  18. A. I. Shapkin, Extended Abstract of Candidate’tation in Technical Sciences (GEOKhI AN SSSR, Moscow, 1985).

    Google Scholar 

  19. A. I. Shapkin and Yu. I. Sidorov, “Chemical Equilibrium and Substance Condensation in the Preplanetary Nebula: Probabilistic Calculation,” Geokhimiya, No. 2, 272–285 (1994).

  20. A. I. Shapkin and Yu. I. Sidorov, “Condensation-Related Differentiation of Matter in the Preplanetary Nebula,” Geokhimiya, No. 5, 627–641 (1994).

  21. O. I. Yakovlev, V. S. Fainberg, A. I. Shapkin, and G. I. Ranendik, “Melt Evaporation under Fast Heating Conditions,” Lunar Planet. Sci. XVII, 924–925 (1985).

    Google Scholar 

  22. A. V. Ivanov, G. J. MacPherson, M. E. Zolensky, et al., “The Kaidun Meteorite: Composition and Origin of Inclusions in Metal of an Enstatite Chondrite Clast,” Meteorit. Planet. Sci. 31, 621–626 (1996).

    Google Scholar 

  23. A. I. Shapkin and Yu. I. Sidorov, “’solar Chondrite’: A Product of the Post-condensation Transformation of Preplanetary Nebula Matter,” Geokhimiya, No. 6, 771–770 (1994).

  24. D. N. C. Lin and J. Papaloizou, “On the Structure and Evaluation of the Primordial Solar Nebula,” Month. Not. R. Soc. 191 (1), 37–48 (1980).

    Google Scholar 

  25. H. B. Wiik, “The Chemical Composition of Some Stony Meteorites,” Geochim. Cosmochim. Acta 9, 279–289 (1956).

    Article  Google Scholar 

  26. A. I. Shapkin and Yu. I. Sidorov, “The Condensation of Solar Gas and the Formation of Preplanetary Nebula,” Geokhimiya, No. 8/9, 1147–1160 (1994).

  27. A. V. Vityazev, Yu. F. Makagon, and G. V. Pechernikova, The Origin of the Solar System: Kinetic and Thermodynamic Aspects (Nauka, Moscow, 1994) [in Russian].

    Google Scholar 

  28. R. T. Dodd, Meteorites: A Petrologic-Chemical Synthesis (Cambridge Univ. Press, New York, 1981; Mir, Moscow, 1986) [in Russian].

    Google Scholar 

  29. A. N. Simonenko and B. Yu. Levin, “A Possible Mechanism of the Mass Transer within the Protoplanetary Nebula,” Meteoritika, No. 42, 23–27 (1983).

  30. O. L. Kuskov, Yu. I. Sidorov, and A. I. Shapkin, “A Composition Model of the Earth’s Mantle Formed from the ’solar Chondrite’ Matter,” Geokhimiya, No. 8/9, 1140–1146 (1994).

  31. A. E. Ringwood, Origin of the Earth and Moon (Springer, New York, 1979; Nedra, Moscow, 1982).

    Google Scholar 

  32. A. P. Vinogradov, “The Atomic Distribution of Chemical Elements in the Sun and Stony Meteorites,” Geokhimiya, No. 4, 292–295 (1962).

  33. A. P. Vinogradov, “Meteoritic Matter,” Geokhimiya, No. 11, 1275–1312 (1965).

  34. A. P. Vinogradov, “The Chemistry of Planets in the Solar System,” in Plenary Reports to the 11th Mendeleyev Conference on General and Applied Chemistry (Nauka, Alma-Ata, 1975), pp. 139–169 [in Russian].

    Google Scholar 

  35. A. E. Ringwood, Composition and Origin of the Earth Res. School Earth Sci. A.N.U., no. 1299 (1977).

  36. J. W. Morgan and E. Anders, “Chemical Composition of Earth, Venus, and Mercury,” Proc. Natl. Acad. Sci. USA 77, 6973–6977 (1980).

    Google Scholar 

  37. H. Wanke, “Constitution of Terrestrial Planets,” Phil. Trans. R. Soc. London, 303, 287–302 (1981).

    Google Scholar 

  38. S. K. Saxena and G. Eriksson, “Chemistry of the Formation of the Terrestrial Planets,” inChemistry and Physics of Terrestrial Planets (Springer, New York, 1986), pp. 30–105.

    Google Scholar 

  39. A. Dziewonski and D. L. Anderson, “Preliminary References Earth Model,” Phys. Earth Planet. Int. 25, 297–356 (1981).

    Google Scholar 

  40. J.-P. Montagner and D. L. Anderson, “Constrained Reference Mantle Model,” Phys. Earth Planet. Int. 58, 205–227 (1989).

    Google Scholar 

  41. A. I. Shapkin and Yu. I. Sidorov, “Physicochemical Evolution of the Interstellar Dust Material in the Process of Heating,” Geokhimiya, No. 5, 423–426 (1996) [Geochem. Int. 34 (5), 378–383 (1996)].

  42. E. K. Jessberger, A. Christoforidis, and J. Kissel, “Aspects of the Major Element Composition of Halley’s Dust,” Nature 332, 691–695 (1988).

    Article  Google Scholar 

  43. A. I. Shapkin and Yu. I. Sidorov, “P-T Dependence of the Density of the Nebular Condensate,” Geokhimiya, No. 12, 1196-1207 (1997) [Geochem. Int. 35 (12), 1060–1070 (1997)].

  44. A. I. Shapkin and Yu. I. Sidorov, “Evolution of Mineral Composition of Interstellar Dust Particles,” Exp. Geosci. 6 (2), 79–80 (1997).

    Google Scholar 

  45. A. I. Shapkin and Yu. I. Sidorov, “Stratification in Cooled Planets,” Geokhimiya, No. 12, 1226-1240 (1998) [Geochem. Int. 36 (12), 1109–1122 (1998)].

  46. Y. Nakamura, “Seismic Velocity Structure of the Lunar Mantle,” J. Geophys. Res. 88, 677–686 (1983).

    Google Scholar 

  47. Yu. I. Sidorov and A. I. Shapkin, “Internal Structure of Mars: A Gravitational-Thermodynamic Model,” Geochem. Int. 38 (Suppl. 3), S375–S382 (2000).

    Google Scholar 

  48. A. I. Shapkin and Yu. I. Sidorov, Thermodynamic Models in Cosmochemistry and Planetology (Editorial URSS, Moscow, 2004) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, ul. Kosygina 19, Moscow, 119991, Russia

    Yu. I. Sidorov

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Original Russian Text © Yu.I. Sidorov, 2006, published in Geokhimiya, 2006, No. 1, pp. 103–116.

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Sidorov, Y.I. Mathematical simulation of complex natural systems. Geochem. Int. 44, 94–107 (2006). https://doi.org/10.1134/S0016702906010095

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  • DOI: https://doi.org/10.1134/S0016702906010095

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