Theory of Resistor Networks: the Two-Point Resistance
F. Wu. Journal of Physics A: Mathematical and General, 37 (26):
6653--6673(2004)
Abstract
The resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulae for two-point resistances are deduced for regular lattices in one, two and three dimensions under various boundary conditions including that of a Möbius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyse large-size expansions in two and higher dimensions.
%0 Journal Article
%1 wu04
%A Wu, F. Y.
%D 2004
%J Journal of Physics A: Mathematical and General
%K circuit effective.resistance eigenvalues laplacian matrix network resistor
%N 26
%P 6653--6673
%T Theory of Resistor Networks: the Two-Point Resistance
%U http://stacks.iop.org/0305-4470/37/i=26/a=004
%V 37
%X The resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulae for two-point resistances are deduced for regular lattices in one, two and three dimensions under various boundary conditions including that of a Möbius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyse large-size expansions in two and higher dimensions.
@article{wu04,
abstract = {The resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulae for two-point resistances are deduced for regular lattices in one, two and three dimensions under various boundary conditions including that of a Möbius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyse large-size expansions in two and higher dimensions.},
added-at = {2016-04-24T13:36:41.000+0200},
author = {Wu, F. Y.},
biburl = {https://www.bibsonomy.org/bibtex/2570d23aec6f511fe49a3604c59db2ea6/ytyoun},
interhash = {d24e403381d1d92abde1adf3d4e5e129},
intrahash = {570d23aec6f511fe49a3604c59db2ea6},
journal = {Journal of Physics A: Mathematical and General},
keywords = {circuit effective.resistance eigenvalues laplacian matrix network resistor},
number = 26,
pages = {6653--6673},
timestamp = {2016-04-27T10:03:31.000+0200},
title = {Theory of Resistor Networks: the Two-Point Resistance},
url = {http://stacks.iop.org/0305-4470/37/i=26/a=004},
volume = 37,
year = 2004
}