Conductance of a plane containing random cuts

In this paper we make the first careful comparison between a computer simulation and an experimental measurement of the conductance of a two-dimensional continuum random conducting medium. In the experiment horizontal and vertical slits are cut in a conducting sheet. The centers of the slits are randomly positioned, and the conductance is measured all the way to percolation. The measurements are consistent with the expected critical exponent for the conductance of t=1.3. The experimental results are compared with computer simulations of ants that are parachuted to random starting points and then diffuse with a Brownian motion. From the behavior at large times, the diffusion constant can be found and hence the conductance, using the Einstein relation. The agreement with experiment is good except near the critical point. We conclude that the analog experiment is superior to the digital computations in this continuum system. This is the reverse of the situation in discrete lattice systems.