Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a hammock network

2014/11/07 by John W. Essam, Essam, John W., Nikolay Sh. Izmailyan +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1411.1916

17 pages, 5 figures

arxiv created 2014/11/07 · arxiv updated 2014/11/10

Abstract

Considerable progress has recently been made in the development of techniques to exactly determine two-point resistances in networks of various topologies. In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. The second method is based on a recurrence relation associated with the distribution of currents in the network. Here, these methods are compared and used to determine the resistance distances between any two nodes of a network with topology of a hammock.

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