Microwave absorption by the Josephson network in a low field : a realistic model for ceramic high-temperature superconductor

We discuss the applied magnetic field dependence of the absorption of microwaves by a 3-dimensional array up to 30x30x30 Josephson junctions with random parameters including the resistivity, capacity and inductance of each junction. The numerical simulation results for the networks show characteristic microwave absorption anomalies observed in the ceramic samples of high temperature superconductor YBa$_{2}$Cu$_{3}$O$_{(7-x)}$. We also provide a discussion of the absorption in simple analytical terms of Josephson loop instabilities.