A generalised formulation of the Laplacian approach to resistor networks

Nikolay Izmailian, Ralph Kenna

Research output: Contribution to journalArticle

16 Citations (Scopus)

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 of 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.
Original languageEnglish
Article numberP09016
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2014
Issue number9
DOIs
Publication statusPublished - 2014

Fingerprint

resistors
formulations
Formulation
Globe
Laplacian Matrix
globes
Eigenvalues and Eigenvectors
Arbitrary
Vertex of a graph
Summation
Minor
eigenvectors
eigenvalues
Generalise
matrices
geometry
Resistance
Node

Bibliographical note

The full text is available free from the link given. The published version can be found at http://dx.doi.org/10.1088/1742-5468/2014/09/P09016 .

Keywords

  • solvable lattice models

Cite this

A generalised formulation of the Laplacian approach to resistor networks. / Izmailian, Nikolay; Kenna, Ralph.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, No. 9, P09016, 2014.

Research output: Contribution to journalArticle

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