Zeitschrift für Physik B Condensed Matter

, Volume 59, Issue 2, pp 197–206 | Cite as

Diffusion and trapping on a nested fractal structure

  • F. Wegner
  • S. Grossmann


We consider the spreading of an ensemble of phase points on a nested hierarchy of levels whose spatial extension scales self-similar. In order to model turbulent pair separation, a deterministic dynamical law is defined that maps a given scale to all (infinitely many) smaller scales and also to the next larger scale. The model can be solved analytically. We find anomalous diffusion (exponential increase of the variance) or trapping (finite limiting value of low order moments) depending on the dominance of level-up or level-down mapping.


Spectroscopy Neural Network State Physics Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • F. Wegner
    • 1
  • S. Grossmann
    • 2
  1. 1.Institut für Theoretische PhysikRuprecht-Karls-Universität HeidelbergHeidelberg 1Federal Republic of Germany
  2. 2.Fachbereich PhysikPhilipps-Universität MarburgMarburgFederal Republic of Germany

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