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

Abstract

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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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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