Hotspots in two-phase conducting media

TL;DR

This study investigates the electric behavior of two-phase resistor networks, revealing that at high resistance ratios, conductance is dominated by a few paths, with hotspots where most power is dissipated.

Contribution

It numerically analyzes the power loss distribution and spatial hotspots in two-phase resistor networks, highlighting the exponential distribution of local power losses.

Findings

Power loss distribution is exponential.

Conductance is dominated by a few optimal paths at high resistance ratios.

Hotspots concentrate the majority of dissipated power.

Abstract

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, $\propto\exp(-P/\langle P\rangle)$, and reveal the spatial distribution of hotspots concentrating the main part of the dissipated power.