The two-point resistance of a cobweb with a superconducting boundary

Abstract

We consider the problem of two-point resistance on an m x n cobweb network with a superconducting boundary, which is topologically equivalent to a geographic globe. We deduce a concise formula for the resistance between any two nodes on the globe using a method of direct summation pioneered by one of us [Z. Z. Tan, et al, J. Phys. A 46, 195202 (2013)]. This method contrasts the Laplacian matrix approach which is difficult to apply to the geometry of a globe. Our analysis gives the result directly as a single summation.

15 pages, 3 figures

Cited by in corpus (4)

• Recursion-transform method on computing the complex resistor network with three arbitrary boundaries
• Two-point resistance of a cobweb network with a $2r$ boundary
• A generalised formulation of the Laplacian approach to resistor networks
• Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a hammock network