Scale invariance and invariant scaling in a mixed hierarchical system.
We consider a mixed hierarchical model with heterogeneous and monotone conditions of destruction. We investigate how scaling properties of defects in the model are related with heterogeneity of rules of destruction, determined by concentration of the mixture. The system demonstrates different kinds of criticality as a general form of system behavior. The following forms of critical behavior are obtained: stability, catastrophe, scale invariance, and invariant scaling. Different slopes of the magnitude-frequency relation are realized in areas of critical stability and catastrophe. A simple relation between the slope of magnitude-frequency relation and parameters of the mixture is established.
Shnirman
M G
MG
International Institute for Earthquake Prediction Theory and Mathematical Geophysics, Warshavskoye sh 79, korp 2, Moscow 113556, Russia.
Blanter
E M
EM