Uniform tiling with electrical resistors
Megjelenés dátuma: 2011
MTMT: 1804737
WoS ID: 000290231700002
Scopus ID: 79955832061
Absztrakt:
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 Kagome, 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.