Biased diffusion on random networks: mean first passage time and DC conductivity

Biased diffusion on a segment with a dangling end is considered, employing a method previously developed by the authors. It is shown that a definition of the drift velocity which is different from that of White and Barma (1984) leads to non-singular behaviour as a function of bias. The two approaches to biased diffusion are compared and a critique of their validity is presented.