Interstitial single resistor in a network of resistors application of the lattice Green's function

Abstract

The resistance between two arbitrary nodes of a network of resistors is studied when the network is perturbed by connecting an extra resistor between two arbitrary nodes in the perfect lattice. The lattice Green's function and the resistance of the perturbed network are expressed in terms of those of the perfect lattice by solving Dyson's equation. A comparison is carried out between numerical and experimental results for a square lattice.

Theory on resistance of m × n cobweb network and its application

“…A classic problem in electric circuit theory studied by numerous authors over 160 years is the computation of the resistance between two nodes in a resistor network , yet some basic problem in m × n cobweb network is still not solved ideally . Now the research on resistor network model is no longer confined to the circuit field; it has expanded into the basic model in the application of various disciplines . Human beings have solved many abstract and complex scientific problems through modeling resistor network since the German scientist Kirchhoff (1824–1887) founded the node current law and the circuit voltage law in 1845.…”

“…Past efforts have been focused mainly on m × n rectangle network (including infinite lattices and finite lattices), where the resistance of the infinite lattices are researched in terms of use of Green's function technique . The infinite resistor network is an ideal model; however, the practical problems are always finite resistor networks occurring in real life.…”

“…This structure of m × n cobweb model determines its meaning of owning many potential applications. Although the researchers have made brilliant achievements in the field of rectangular network, the research for the cobweb network has only just begun not only in results but also in methods. In addition, there have been very few studies on the impedance between two arbitrary nodes in an m × n RLC cobweb network.…”

“…Many previous studies (including infinite lattices and finite lattices) give us some new inspiration; recently, we investigated the equivalent resistance of the m × n cobweb network ; the equivalent resistance of 3 × n and 4 × n cobweb network are given respectively in , in which we proposed two conjectures on the resistance of m × n cobweb network. In this paper, we not only proved its correctness but also extended its research results.…”

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

“…18 Based on this approach, several interesting applications were presented. [9][10][11][12][13][14][15][16][17][18] The problem of computing the two-node resistance on finite resistor networks was considered by Wu. 19 He obtained a general expression for the resistance of a finite resistor graph in terms of the eigenvalues and the eigenvectors of the Kirchhoff matrix.…”