Display options
Cite
Essam JW, Tan ZZ, Wu FY. Resistance between two nodes in general position on an m×n fan network. Phys Rev E Stat Nonlin Soft Matter Phys. 2014;90(3):032130doi: 10.1103/PhysRevE.90.032130.
Essam, J. W., Tan, Z. Z., & Wu, F. Y. (2014). Resistance between two nodes in general position on an m×n fan network. Physical review. E, Statistical, nonlinear, and soft matter physics, 90(3), 032130. https://doi.org/10.1103/PhysRevE.90.032130
Essam, J W, et al. "Resistance between two nodes in general position on an m×n fan network." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 90,3 (2014): 032130. doi: https://doi.org/10.1103/PhysRevE.90.032130
Essam JW, Tan ZZ, Wu FY. Resistance between two nodes in general position on an m×n fan network. Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):032130. doi: 10.1103/PhysRevE.90.032130. Epub 2014 Sep 23. PMID: 25314418.
Copy Download .nbib Format: NLM
Share it on

Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):032130. doi: 10.1103/PhysRevE.90.032130. Epub 2014 Sep 23.

Resistance between two nodes in general position on an m×n fan network.

Physical review. E, Statistical, nonlinear, and soft matter physics

J W Essam, Zhi-Zhong Tan, F Y Wu

Affiliations

  1. Department of Mathematics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX, England.
  2. Department of Physics, Nantong University, Nantong 226019, China.
  3. Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.

PMID: 25314418 DOI: 10.1103/PhysRevE.90.032130

Abstract

The resistance between two nodes in general position on a fan network with n radial lines and m transverse lines is determined. Also a similar result of Izmailian, Kenna, and Wu [J. Phys. A: Math. Theor. 47, 035003 (2014)] for an m×n cobweb network is reproduced, but the method used here is significantly different. It avoids the use of the Kirchhoff matrix, requires the solution of just one instead of two eigenvalue problems, and results directly in only a single summation. Further, the current distribution is given explicitly as a byproduct of the method. The method is the same as that used by Tan, Zhou, and Yang [J. Phys. A: Math. Theor. 46, 195202 (2013)] to find the cobweb resistance between center and perimeter for 1≤m≤3 and general n. Proof of their conjecture for general m is discussed.

MeSH terms

Publication Types