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Theory of resistor networks: The two-point resistance | | F. Y. Wu
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14 Feb 2004 | | Journal: | Journal of Physics A 37, 6653-6673 (2004) | | Subject: | Mathematical Physics; Probability; Materials Science; Physics Education | math-ph cond-mat.mtrl-sci math.MP math.PR physics.ed-ph | | 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. | | Source: | arXiv, math-ph/0402038 | | Services: | Forum | Review | PDF | Favorites | |
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