The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

Details The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

2008-09-28

arxiv.org/abs/0809.4867v3

J. Phys. A 42 (2009) 025205

Physics

Condensed Matter

Statistical Mechanics

12 pages, re-arranged sections

Scientific paper

10.1088/1751-8113/42/2/025205

We study the corner-to-corner resistance of an M x N resistor network with
resistors r and s in the two spatial directions, and obtain an asymptotic
expansion of its exact expression for large M and N. For M = N, r = s =1, our
result is
R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).

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