### Abstract

The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagomé, diced and decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.

Original language | English |
---|---|

Article number | 215201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 44 |

Issue number | 21 |

DOIs | |

Publication status | Published - May 27 2011 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*44*(21), [215201]. https://doi.org/10.1088/1751-8113/44/21/215201

**Uniform tiling with electrical resistors.** / Cserti, J.; Széchenyi, Gbor; Dvid, Gyula.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 44, no. 21, 215201. https://doi.org/10.1088/1751-8113/44/21/215201

}

TY - JOUR

T1 - Uniform tiling with electrical resistors

AU - Cserti, J.

AU - Széchenyi, Gbor

AU - Dvid, Gyula

PY - 2011/5/27

Y1 - 2011/5/27

N2 - The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagomé, diced and decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.

AB - The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagomé, diced and decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.

UR - http://www.scopus.com/inward/record.url?scp=79955832061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955832061&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/44/21/215201

DO - 10.1088/1751-8113/44/21/215201

M3 - Article

VL - 44

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 21

M1 - 215201

ER -