title: Two-point resistance of a resistor network embedded on a globe.
abstract: We consider the problem of two-point resistance in an (m-1) × n resistor network embedded on a globe, a geometry topologically equivalent to an m × n cobweb with its boundary collapsed into one single point. 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, L. Zhou, and J. H. Yang, J. Phys. A: Math. Theor. 46, 195202 (2013)]. This method is contrasted with the Laplacian matrix approach formulated also by one of us [F. Y. Wu, J. Phys. A: Math. Gen. 37, 6653 (2004)], which is difficult to apply to the geometry of a globe. Our analysis gives the result in the form of a single summation.
authors.affiliation: Department of Physics, Nantong University, Nantong 226019, China.
authors.forename: Zhi-Zhong
authors.initials: ZZ
authors.lastname: Tan
authors.affiliation: Department of Mathematics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX, England.
authors.forename: J W
authors.initials: JW
authors.lastname: Essam
authors.affiliation: Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: F Y
authors.initials: FY
authors.lastname: Wu
mesh_terms: D017097:Electric Impedance; D008962:Models, Theoretical