Ukrainian Antarctic Journal

No 4-5 (2006): Ukrainian Antarctic Journal

On the fractal mechanism of interactions between the genesis, size and content of atmospheric aerosoles in various areas of the Earth

V. D. Rusov
Odessa National Polytechnic University, Odessa
V. Pavlovych
Institute of Nuclear Research of NAS of Ukraine, Kyiv
R. Ilić
J.Stefan Institute, Ljubljana
R. Jaćimović
J.Stefan Institute, Ljubljana
Yu. Bondarchuk
National Polytechnic University, Odessa
V. N. Vaschenko
Taras Shevchenko National University of Kyiv, Kyiv
O. T. Mikhalus
Odessa National Polytechnic University, Odessa
S. L. Kosenko
Odessa National Polytechnic University, Odessa
Published December 15, 2006
How to Cite
Rusov, V. D., Pavlovych, V., Ilić, R., Jaćimović, R., Bondarchuk, Y., Vaschenko, V. N., Mikhalus, O. T., & Kosenko, S. L. (2006). On the fractal mechanism of interactions between the genesis, size and content of atmospheric aerosoles in various areas of the Earth. Ukrainian Antarctic Journal, (4-5), 137-159.


We discuss experimental data of the National Aerial Survey Net (NASN) of Japan in 1974-1996 and independent experiments done simultaneously in Ljubljana (Slovenia), Odessa (Ukraine) and the Ukrainian Antarctic Station Akademik Vernadskiy (64°15; 65°15) in which the traditional method of fixation of atmospheric aerosoles on nuclear filters and k0-instrumental neutron-activation analysis were used to determine the concentration composition of atmospheric air.
Comparative analysis of different pairs of experimental spectra of normalized concentrations of the elements of atmospheric aerosole measured in various areas of the Earth shows a stable linear (logarithmically) correlational dependence which suggests a power law of increase in mass (volume) of every element of the atmospheric aerosole and simultaneously the reason for the growth - the fractal nature of the genesis of the atmospheric (secondary) aerosoles.

In the framework of multifractal geometry it was shown that the distribution of the isotopic components of the secondary aerosole on the normalized masses (volumes) followed the lognormal distribution which at the logarithmic scale relative to a random variable (the isotopic component mass) is identical to a normal law. This means that the parameters of two-dimensional normal distribution relative to the corresponding isotopic component of aerosolic particles-multifractals measured in different areas are apriori linked by forward and reverse linear regression.
These linear regressions were shown to result in experimentally observed linear (at a logarithmic scale) correlations between the normalized concentrations of the same isotopic components of the experimental spectra of normalized concentrations of the atmospheric aerosole's elements registered in various locations.
It was theoretically shown how solving a system of non-linear equations uniting the first moments (the mean and the variance) of the lognormal and normal distributions can reestablish the multifractal function f(α) and the spectrum of fractal dimentions Dq of an individual aerosol particle which are global characteristics of the genesis of the atmospheric (secondary) aerosole and do not depend on where they were registered.


  1. Maenhaut, W., & Zoller, W.H. (1977). Determination of the chemical composition of the South Pole aerozol by insrumental neutron activation analysis. J. Radioanal. Chem., 37, 637–650.
  2. Pushkin, S.G., & Mixajlov, V.A. (1989). Komparatorny`j nejtronno-aktivacionny`j analiz. Izuchenie atmosferny`x ae`rozolej [Comparatory neutron-activating analysis. Studying the atmospheric aerosoles]. Novosibirsk, Nauka. Sib. otdelenie.
  3. Raes, F., Van Dingenen, R., Vignati, E., Wilson, J., Putaud, J.-P., Seinfeld, J.H., & Adams, P. (2000). Formation and cycling of aerozols in the global troposphere. Atmospheric Environment, 34, 4215–4240.
  4. Rusov, V.D., Glushkov, A.V., & Vashhenko, V.N. (2003). Astrofizicheskaya model` global`nogo klimata Zemli. Kiev, Naukova dumka.
  5. Figen, Var, Yasushi, Narita, Shigeru, Tanaka. (2000). The concentration, trend and seasonal variation of metals in the atmosphere in 16 Japanese cities shown by the results of National Air Surveillance Network (NASN) from 1974 to 1996. Atmospheric Environment, 34, 2755–2770.
  6. Brownlee, K.A. (1965). Statistical theory and methodology in science and engineering. John Wiley & Sons, Inc., New York–London-Sydney.
  7. Bendat, J.S., & Piersol, A.G. (1986). Random data. Analysis and Measurement Procedures. A Wiley-Interscience Publication.
  8. Schroeder, M. (2000). Fractals, Chaos, Power Laws. Minutes from Infinite Paradise. W.H.Freeman and Company. NewYork.
  9. Witten, T.A., & Sander, L.M. (1981). Diffusion-limited aggregation: A Kinetic critical phenomenon. Phys. Rev. Lett., 47, 1400–1403.
  10. Zubarev, A. Yu., & Ivanov, A. O. (2002). Fraktal`naya struktura kolloidnogo agregata. [Fractal structure of a colloidal aggregate]. Doklady` Akademii nauk Rossiya, 383, 472–477.
  11. Maenhaut, W., Francos, F., & Cafmeyer, J. (1993). The “Gent” Stacked Filter Unit (SFU) Sampler for Collection of Atmospheric Aerosols in Two Size Fractions: Description and Instructions for Installation and Use. Report No.NAHRES-19, IAEA, Vienna. 249–263.
  12. Hopke, P.K., Hie, Y., Raunemaa, T., Biegalski, S., Landsberger, S., Maenhaut, W., Artaxo, P., & Cohen, D. (1997). Characterization of the Gent Stacked Filter Unit PM10 Sampler. Aerozol Science and Technology, 27, 726–735.
  13. Jacimovic, R., Lazaru, A., Mihajlovic, D., Ilic, R., & Stafilov, T. (2002). Determination of major and trace elements in some minerals by k0-instrumental neutron activation analysis. J. Radioanal. and Nucl. Chem., 253, 427–434.
  14. HYPERMET-PCV5.0. User’s Manual. (1977). Institute of Isotopes, Budapest, Hungary.
  15. Kauzero/Solcoi for Reactor-neutron Activation Analysis (NAA) Using the k0-Standardization Method. (1996). DSM Research, Geleen, Netherlands, Dec. 1996.
  16. Crownover, R.M. (1995). Introduction to Fractals and Chaos. Jones and Bartlett Publishers.
  17. Mandelbrot, B.B. (2002). The fractal geometry of nature. Updated and Augmented. W.H. Freeman and Co, New York.
  18. Feder, J. (1988). Fractals. Plenum Press-New York and London.
  19. Bozhokin, S. V., & Parshin, D. A. (2001). Fraktaly` i mul`tifraktaly`. [Fractals and multifractals]. Regulyarnaya i xaoticheskaya dinamika, pp. 128.
  20. Lai, F.S., Friedlander, S.K., Pich, J., & Hidy, G.M. (1972). The self-preserving particle size distribution for Brownian coagulation in the free-molecular regime. Journal of Colloid and Interface Science, 39, 395–405.
  21. Raes, F., Wilson, J., Van Dingenen, R. (1995). Aerosol dynamics and its implication for the global aerosol climatology. In: R.J. Charson, J. Heintzenberg (Eds.), Aerosol Forcing of Climate. Wiley, New York.
  22. Feller, W. (1971). An Introduction to Probability Theory and its Applications. John Wiley Sons, Inc. New York–London–Sydney–Toronto. V.2.
  23. Bote, R., Zhyul`en, R., &Kol`b, M. (1988). Agregaciya klasterov. [Cluster aggregation]. Fraktaly` v fizike. Moskva. Mir. 353–359.