HR: 0800h
AN: NG31A-0857    [Abstracts]
TI: Hierarchical Description of Evolution of an Inverse Cascade in Percolation Model
AU: Gabrielov, A
EM: agabriel@math.purdue.edu
AF: Departments of Mathematics and Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907 United States
AU: Zaliapin, I
EM: zal@ess.ucla.edu
AF: Institute of Geophysics and Planetary Physics, 3845 Slichter Hall, University of California, Los Angeles, CA 90095 United States
AU: * Wong, H
EM: hlwong@ess.ucla.edu
AF: Institute of Geophysics and Planetary Physics, 3845 Slichter Hall, University of California, Los Angeles, CA 90095 United States
AB: The dynamics of a 2D site percolation model on a square lattice is studied using the hierarchical approach introduced by Gabrielov, Newman, and Turcotte [{\it Phys. Rev. E}, {\bf 60}, 5293-5300, 1999]. The central role in this approach is played by the Horton-Strahler rule for ranking elements within a hierarchical structure. In percolation model a hierarchy is created by the temporal evolution of the system that allows one to represent an inverse cascade of particle aggregation as a time-oriented tree. Our main results are the following: A) The time-dependent scaling laws for cluster ranks are derived using the Tokunaga branching constraint and the classical results on percolation in terms of cluster masses. Remarkably, at percolation these laws coincide with the corresponding laws obtained by Gabrielov, Newman, and Turcotte [{\it Phys. Rev. E}, {\bf 60}, 5293-5300, 1999] in a steady-state approximation to a general aggregation process. B) The three-exponent time-dependent scaling for the cluster rank distribution is reported in deviation from the two-exponent scaling well-known for the mass distribution. C) Deviations from the pure scaling at percolation and their time-dependent evolution are described. In addition, an empirical constraint on the dynamics of a rank population is reported based on extensive numerical simulations.
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3299 General or miscellaneous
SC: Nonlinear Geophysics [NG]
MN: 2004 AGU Fall Meeting