### Abstract

Original language | English |
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Article number | P09016 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2014 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2014 |

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### 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.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2014, no. 9, P09016. https://doi.org/10.1088/1742-5468/2014/09/P09016

}

TY - JOUR

T1 - A generalised formulation of the Laplacian approach to resistor networks

AU - Izmailian, Nikolay

AU - Kenna, Ralph

N1 - 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 .

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - solvable lattice models

U2 - 10.1088/1742-5468/2014/09/P09016

DO - 10.1088/1742-5468/2014/09/P09016

M3 - Article

VL - 2014

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 9

M1 - P09016

ER -