Random manifolds in non-linear resistor networks: applications to varistors and superconductors

We show that current localization in polycrystalline varistors occurs on paths which are usually in the universality class of the directed polymer in a random medium. We also show that, in ceramic superconductors, voltage localizes on a surface which maps to an Ising domain wall. The emergence of these manifolds is explained and their structure is illustrated using direct solution of non-linear resistor networks.