Self-organization of the critical state in granular superconductors

The critical state in granular superconductors is studied using two mathema tical models: systems of differential equations for the gauge-invariant pha se difference and a simplified model that is described by a system of coupl ed mappings and in many cases is equivalent to the standard models used for studying self-organized criticality. It is shown that the critical state o f granular superconductors is self-organized in all cases studied. In addit ion, it is shown that the models employed are essentially equivalent, i.e., they demonstrate not only the same critical behavior, but they also lead t o the same noncritical phenomena. The first demonstration of the existence of self-organized criticality in a system of nonlinear differential equatio ns and its equivalence to self-organized criticality in standard models is given in this paper. (C) 2000 MAIK "Nauka/Interperiodica".