Abstract
A general Recursion-Transform method is put forward and is applied to resolving a difficult problem of the two-point resistance in a non-regular m × n cobweb network with an arbitrary longitude (or call radial), which has never been solved before as the Green’s function technique and the Laplacian matrix approach are difficult in this case. Looking for the explicit solutions of non-regular lattices is important but difficult, since the non-regular condition is like a wall or trap which affects the behavior of finite network. This paper gives several general formulae of the resistance between any two nodes in a non-regular cobweb network in both finite and infinite cases by the R-T method which, is mainly composed of the characteristic roots, is simpler and can be easier to use in practice. As applications, several interesting results are deduced from a general formula, and a globe network is generalized.
Highlights
R1), which has 7 latitudes and 14 longitudes
This paper focus on the computation of the two-point resistance between any two nodes in the non-regular m × n cobweb network, which has never been solved before, the Green’s function technique and the Laplacian matrix approach are difficult in this case because they depend on the two matrices along two directions
The boundary resistor r2 is a key parameter since the different parameter can represent different geometric structure, such as a globe is from a nearly cobweb with r2 = 0
Summary
R1), which has 7 latitudes (including boundary) and 14 longitudes. Bonds in the longitudes and latitudes directions represent, respectively, resistors r0 and r except for the resistor r1 on a longitude and the boundary resistor r2. In this paper we will study the resistances of a complex network with arbitrary resistors on the longitude line.
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