The resistance between arbitrary two nodes in a resistor network is obtained
in terms of the eigenvalues and eigenfunctions of the Laplacian matrix
associated with the network. Explicit formulas for two-point resistances are
deduced for regular lattices in one, two, and three dimensions under various
boundary conditions including that of a Moebius 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 analyze large-size expansions of two-and-higher
dimensional lattices.
(private-note)cited by tstarke in `Fast calculation of large resistor networks'
---=note-separator=---
(private-note)subsequently published in Journal of Physics A 37, 6653-6673 (2004)
%0 Journal Article
%1 citeulike:8899537
%A Wu, F. Y.
%D 2004
%J arXiv.org:math-ph
%K 94c05-analytic-circuit-theory 65f15-numerical-eigenvalues-eigenvectors
%N 0402038
%T Theory of Resistor Networks: The Two-Point Resistance
%U http://arxiv.org/abs/math-ph/0402038v2
%X The resistance between arbitrary two nodes in a resistor network is obtained
in terms of the eigenvalues and eigenfunctions of the Laplacian matrix
associated with the network. Explicit formulas for two-point resistances are
deduced for regular lattices in one, two, and three dimensions under various
boundary conditions including that of a Moebius 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 analyze large-size expansions of two-and-higher
dimensional lattices.
%7 2
@article{citeulike:8899537,
abstract = {{The resistance between arbitrary two nodes in a resistor network is obtained
in terms of the eigenvalues and eigenfunctions of the Laplacian matrix
associated with the network. Explicit formulas for two-point resistances are
deduced for regular lattices in one, two, and three dimensions under various
boundary conditions including that of a Moebius 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 analyze large-size expansions of two-and-higher
dimensional lattices.}},
added-at = {2017-06-29T07:13:07.000+0200},
archiveprefix = {arXiv},
author = {Wu, F. Y.},
biburl = {https://www.bibsonomy.org/bibtex/2efafb0a1bfe077beec670d364f81de95/gdmcbain},
citeulike-article-id = {8899537},
citeulike-attachment-1 = {wu_04_theory_619033.pdf; /pdf/user/gdmcbain/article/8899537/619033/wu_04_theory_619033.pdf; d9b5fa912d8f56d3c93784eac9a5fb8f313b52b9},
citeulike-linkout-0 = {http://arxiv.org/abs/math-ph/0402038v2},
citeulike-linkout-1 = {http://arxiv.org/pdf/math-ph/0402038v2},
comment = {(private-note)cited by tstarke in `Fast calculation of large resistor networks'
---=note-separator=---
(private-note)subsequently published in Journal of Physics A 37, 6653-6673 (2004)},
day = 19,
edition = 2,
eprint = {math-ph/0402038v2},
file = {wu_04_theory_619033.pdf},
interhash = {d24e403381d1d92abde1adf3d4e5e129},
intrahash = {efafb0a1bfe077beec670d364f81de95},
journal = {arXiv.org:math-ph},
keywords = {94c05-analytic-circuit-theory 65f15-numerical-eigenvalues-eigenvectors},
month = feb,
number = 0402038,
posted-at = {2011-02-27 23:33:22},
priority = {2},
timestamp = {2019-02-28T23:45:33.000+0100},
title = {{Theory of Resistor Networks: The Two-Point Resistance}},
url = {http://arxiv.org/abs/math-ph/0402038v2},
year = 2004
}