Hotspots in two-phase conducting media

We study electric properties of random resistor networks consisting of resistors of two kinds numerically, focusing on the power loss across each bond. Tuning the ratio of the resistances $r$ and their respective fraction $\alpha$ we find that at large $r$ the conductance of the network is dominated by a few optimal, percolation-like, conducting paths. We demonstrate that the distribution of the local power losses $P$ is exponential, $\propto \exp (-P\mathrm{/}⟨P⟩)$, and reveal the spatial distribution of hotspots concentrating the main part of the dissipated power.