Uniform tiling with electrical resistors

József Cserti, Gbor Széchenyi, Gyula Dvid

Research output: Article

32 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 - máj. 27 2011

ASJC Scopus subject areas

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

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