%0 Journal Article %1 citeulike:3338265 %A Wu, F. Y. %D 2004 %J Journal of Physics A: Mathematical and General %K 94c05-analytic-circuit-theory 65f15-numerical-eigenvalues-eigenvectors %N 26 %P 6653--6673 %R 10.1088/0305-4470/37/26/004 %T Theory of Resistor Networks: The Two-Point Resistance %U http://dx.doi.org/10.1088/0305-4470/37/26/004 %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{citeulike:3338265, 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 M\"{o}bius 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 = {2017-06-29T07:13:07.000+0200}, author = {Wu, F. Y.}, biburl = {https://www.bibsonomy.org/bibtex/2849cf7b22367db96f0b74ea2e582f44c/gdmcbain}, citeulike-article-id = {3338265}, citeulike-linkout-0 = {http://dx.doi.org/10.1088/0305-4470/37/26/004}, citeulike-linkout-1 = {http://iopscience.iop.org/0305-4470/37/26/004}, comment = {'arXiv:math-ph/0402038v2 19 Feb 2004':http://arXiv.org/abs/math-ph/0402038v2}, day = 02, doi = {10.1088/0305-4470/37/26/004}, interhash = {d24e403381d1d92abde1adf3d4e5e129}, intrahash = {849cf7b22367db96f0b74ea2e582f44c}, issn = {0305-4470}, journal = {Journal of Physics A: Mathematical and General}, keywords = {94c05-analytic-circuit-theory 65f15-numerical-eigenvalues-eigenvectors}, month = jul, number = 26, pages = {6653--6673}, posted-at = {2011-02-27 23:01:03}, priority = {2}, timestamp = {2019-02-28T23:45:33.000+0100}, title = {{Theory of Resistor Networks: The Two-Point Resistance}}, url = {http://dx.doi.org/10.1088/0305-4470/37/26/004}, volume = 37, year = 2004 }