Crack formation in two-dimensional annular networks

We used the random-fuse model to compute the topological features of Locali zed cracks in an annular two-dimensional geometry. Depending on the type of disorder in the resistivity of the fuses, the results follow the observati ons encountered in the literature for square lattices with periodic boundar y conditions or have a different behaviour explained by a small disorder in the resistivities. Finally, finite-size effects play an important role in this type of geometry.