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Symbolic Simulation of Nonlinear Random Resistor Networks by Mathematica

K. Yu
Journal / Anthology

Computers in Physics
Year: 1994
Volume: 8
Issue: 6
Page range: 735-740

Symbolic simulation is a technique, which combines symbolic and numerical solutions of a system of linear or nonlinear algebraic equations. One parameter is left in symbolic form and all quantities of interest are computed in a series expansion with respect to this parameter. As an example of considerable current interest, the computer algebra system Mathematica is used to study the effective response of a nonlinear random resistor network. A system of nonlinear circuit equations is solved and the effective response is computed as a series expansion. We also find that due to geometric effects near the percolation threshold, the ohmic region in the current-voltage characteristics shrinks. The present approach is shown to have many advantages over purely numerical techniques while the required computing effort is quite modest. Applications of symbolic simulations to other related problems and the extension to more parameters are also discussed.

*Engineering > Electrical Engineering