Uniform tiling with electrical resistors

J. Cserti, Gbor Széchenyi, Gyula Dvid

Research output: Contribution to journalArticle

29 Citations (Scopus)

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 languageEnglish
Article number215201
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number21
DOIs
Publication statusPublished - May 27 2011

Fingerprint

Tiling
resistors
Resistors
Condensed matter physics
Laplacian Matrix
Lattice Structure
Triangular Lattice
Square Lattice
Green's function
Random walk
Physics
Electron
condensed matter physics
Electrons
Arbitrary
Vertex of a graph
random walk
Green's functions
Resistance
matrices

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 21, 215201, 27.05.2011.

Research output: Contribution to journalArticle

Cserti, J. ; Széchenyi, Gbor ; Dvid, Gyula. / Uniform tiling with electrical resistors. In: Journal of Physics A: Mathematical and Theoretical. 2011 ; Vol. 44, No. 21.
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