Minimal path for transport in networks.

This report examines transport through networks in which transport across each bond in the network requires exceeding a microscopic threshold potential ΔV i min . In particular, we examine the macroscopic gradient V min at which transport begins, as a function of the distribution of microscopic thresholds ΔV i min . Applications of this «minimal path» or «breakdown» problem include electrical conduction through networks of diodes and the flow of Bingham plastics through porous media. Two simple models are examined, including a solution for V min for a Bethe- (or Cayley-) tree network