FINITE SIZE EFFECT ON THE CURRENT ENHANCEMENT AT THE TIP OF A LONG DEFECT IN A RESISTOR NETWORK

The current at the tip of a long defect in a resistor network has been investigated as a function of the defect length and of the network size. Numerical simulations show that noticeable size effects influence the tip current. In particular, the tip current as a function of the defect length is shown to converge very slowly toward the asymptotic square root law previously predicted for large defects in an infinite network. The nature of the corrections to this asymptotic law is exhibited with a finite size scaling analysis. For practical use, an empirical formula for the tip current is proposed.