Early stages of generation of two-dimensional structures by the Hastings-Levitov method of conformal mapping dynamics

  • T. A. Rostunov
  • L. N. Shchur
Nonlinear Physics


Two-dimensional structures obtained by the Hastings-Levitov conformal mapping were studied for a relatively small number of mappings n. The fractal dimension D of these structures is computed by the recent Davidovitch-Procaccia technique [6] as a function of n. For small n < n0 (where n0 is the number of particles at the first layer), D exponentially decreases, which should have supported the conclusion made in [6] about the possibility of determining the fractal dimension with an arbitrary accuracy using a relatively small number of mappings nn0. On the other hand, it turned out that D irregularly deviates from a certain quantity D0 depending on the initial size of the bump \(\sqrt {\lambda _0 } \), which contradicts the main assertion of


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  1. 1.
    T. C. Halsey, B. Duplantier, and K. Honda, Phys. Rev. Lett. 78, 1719 (1997).CrossRefADSGoogle Scholar
  2. 2.
    T. A. Witten and L. M. Sanders, Phys. Rev. Lett. 47, 1400 (1981).CrossRefADSGoogle Scholar
  3. 3.
    T. C. Halsey, Phys. Today 53, 36 (2000).Google Scholar
  4. 4.
    M. B. Hastings and L. S. Levitov, Physica D (Amsterdam) 116, 244 (1998).ADSGoogle Scholar
  5. 5.
    M. B. Hastings, Phys. Rev. E 55, 135 (1997).CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    B. Davidovitch and I. Procaccia, Phys. Rev. Lett. 85, 3608 (2000).CrossRefADSGoogle Scholar
  7. 7.
    P. Ossadnik, Physica A (Amsterdam) 195, 319 (1993).ADSGoogle Scholar
  8. 8.
    L. Nimeyer, L. Pietronero, and H. J. Wiessmann, Phys. Rev. Lett. 52, 1033 (1984).ADSMathSciNetGoogle Scholar
  9. 9.
    Fractals and Disordered Systems, Ed. by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1996).Google Scholar
  10. 10.
    S. Wiseman and E. Domany, Phys. Rev. Lett. 81, 22 (1998); Phys. Rev. E 58, 2938 (1998).ADSGoogle Scholar
  11. 11.
    E. Somfai, L. M. Sander, and R. C. Ball, Phys. Rev. Lett. 83, 5523 (1999).CrossRefADSGoogle Scholar
  12. 12.
    B. Kol and A. Aharony, Phys. Rev. E 63, 046117 (2001).Google Scholar
  13. 13.
    M. G. Stepanov and L. S. Levitov, Phys. Rev. E 63, 061102 (2001).Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • T. A. Rostunov
    • 1
  • L. N. Shchur
    • 1
    • 2
    • 3
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  2. 2.Laboratoire de Physique des MatériauxUniversité Henri PoincaréVandoevre les Nancy CedexFrance
  3. 3.MilanoItaly

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