Graduate School in Nonlinear Science

Sponsored by The Danish ResearchAgency

 
MIDIT                              OFD                          CATS
Modelling, Nonlinear Dynamics      Optics and Fluid Dynamics    Chaos and Turbulence Studies
and Irreversible Thermodynamics    Risø National Laboratory     Niels Bohr Institute and
Technical University of Denmark    Building 128                 Department of Chemistry
Building 321                       P.O. Box 49                  University of Copenhagen
DK-2800 Lyngby                     DK-4000 Roskilde             DK-2100 Copenhagen Ø
Denmark                            Denmark                      Denmark

FRACTAL GEOMETRY OF PERCOLATION AT CRITICALITY AND THE ALEXANDER-ORBACH CONJECTURE

Alexander V. Milovanov
Space Research Institute
Moscow, Russia

Tuesday, March 20, 2001, 14.00 h
at OFD Meeting Room, Building 130, Risų National Laboratory

Abstract: The basic ideas of the fractal geometry and percolation theory are outlined. Particular attention is paid to the universal features of the fractal geometry of percolation near the critical threshold. The topological properties of percolating sets at criticality are addressed in connection with the Alexander-Orbach conjecture on the "hyperuniversal" behavior of the spectral fractal dimension. Applications of the percolation theory to a description of various physical phenomena (e.g., transport processes in disordered media, self-organization in turbulent systems, etc.) are advocated.

References:
S. Alexander and R.L. Orbach, J. Phys. Lett. (France), 43, L625 (1982).
A.V. Milovanov, Phys. Rev. E, 56, 2437 (1997).
A.V. Milovanov and G. Zimbardo, Phys. Rev. E, 62, 250 (2000).