Graduate School in Nonlinear Science
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
Tuesday, March 20, 2001, 14.00 h
at OFD Meeting Room, Building 130, Risų National Laboratory
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.
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).