On the resistive function measured between two points on a grid or a lattice of similar non-linear resistors

摘要

The known problem of the resistance measured between two closest nodes on a grid of similar resistors, often considered in a linear version in physics and electrical engineering textbooks, is considered in a non-linear version. An estimation, based on a simple polynomial model, shows that with increase in the number of the dimensions of the grid (or a lattice), the non-linearity of the characteristic of a single resistor is expressed more and more weakly in the input resistive function, and that the input resistive function has the same (in the sense of the degrees involved and polarities of the coefficients) polynomial structure as the individual characteristic of the single resistor. (C) 1998 John Wiley Sons, Ltd. References: 9