A generalised formulation of the Laplacian approach to resistor networks

Abstract

An analytic approach is presented to developing exact expressions for the two-point resistance between arbitrary nodes on certain non-regular resistor networks. This generalises previous approaches, which only deliver results for networks of more regular geometry. The new approach exploits the second minor of the Laplacian matrix associated with the given network to obtain the resistance in terms its eigenvalues and eigenvectors. The method is illustrated by application to the resistor network on the globe lattice, for which the resistance between two arbitrary nodes is obtained in the form of single summation.

17 pages, 1 figure

References in corpus (3)

• The two-point resistance of a cobweb with a superconducting boundary
• Uniform tiling with electrical resistors
• Evaluation of effective resistances in pseudo-distance-regular resistor networks

Cited by in corpus (5)

• Recursion-transform method on computing the complex resistor network with three arbitrary boundaries
• Two-point resistance of a cobweb network with a $2r$ boundary
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Anomalous fractal scaling in two-dimensional electric networks
• Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a hammock network