Two-point resistance of a resistor network embedded on a globe

Zhi-Zhong Tan, J. W. Essam, and F. Y. Wu
Phys. Rev. E 90, 012130 – Published 28 July 2014

Abstract

We consider the problem of two-point resistance in an (m1)×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.

  • Figure
  • Figure
  • Received 16 April 2014

DOI:https://doi.org/10.1103/PhysRevE.90.012130

©2014 American Physical Society

Authors & Affiliations

Zhi-Zhong Tan*

  • Department of Physics, Nantong University, Nantong 226019, China

J. W. Essam

  • Department of Mathematics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX, England

F. Y. Wu

  • Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

  • *tanz@ntu.edu.cn; tanz@163.com
  • j.essam@rhul.ac.uk
  • fywu@neu.edu

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Issue

Vol. 90, Iss. 1 — July 2014

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