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Resistance between two nodes in general position on an m×n fan network.
J W Essam1, Zhi-Zhong Tan2, F Y Wu3
1Department of Mathematics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX, England.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2014
Summary
This study determines electrical resistance in fan networks. A novel method simplifies calculations for fan and cobweb networks, also revealing current distribution.
Area of Science:
- Physics
- Electrical Engineering
- Network Theory
Background:
- Fan networks and cobweb networks are common structures in various scientific fields.
- Calculating electrical resistance in these networks is crucial for understanding their behavior.
Purpose of the Study:
- To determine the electrical resistance between two nodes in a fan network.
- To reproduce and extend existing results for cobweb networks using a novel methodology.
Main Methods:
- A new analytical method is employed, avoiding the use of Kirchhoff matrices.
- The approach involves solving a single eigenvalue problem instead of two.
- The method directly yields a single summation for resistance calculation.
Main Results:
- The electrical resistance for a fan network with n radial and m transverse lines is determined.
- A simplified method for calculating resistance in m×n cobweb networks is presented.
- Explicit current distribution is derived as a byproduct of the resistance calculation.
Conclusions:
- The developed method offers a more efficient and direct approach to calculating network resistance.
- The findings extend the applicability of the method to general m values for cobweb networks.
- This work provides a foundation for further research into complex network properties.
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