Theory of resistor networks: the two-point resistance

By F. Y. Wu. 2004

238 citations recorded by the source corpus.

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 Mobius 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.

Subfields: Geometry and Topology, Materials Chemistry, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d7bcc759d3b319fc5659e8a0c1b9f4967bf6b179

How researchers see this paper

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In Geometry and Topology

1. E. Esveld
2. P. Nootenboom
3. Lucas J. van Vliet
4. Gerard van Dalen
5. L. Voortman

In Materials Chemistry

1. E. Esveld
2. P. Nootenboom
3. Lucas J. van Vliet
4. Gerard van Dalen
5. L. Voortman

In Statistics and Probability

1. E. Esveld
2. P. Nootenboom
3. Lucas J. van Vliet
4. Gerard van Dalen
5. L. Voortman

Citations in the corpus

• 3-D IMAGING, ANALYSIS AND MODELLING OF POROUS CEREAL PRODUCTS USING X-RAY MICROTOMOGRAPHY (2011, methodology): “The point-to-point resistance (Ri,j) was calculated from the conduction using the resistance theorem described by Wu (2004) by using the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network.”