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Chin. Phys. B, 2017, Vol. 26(9): 090503    DOI: 10.1088/1674-1056/26/9/090503
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Recursion-transform method and potential formulae of the m×n cobweb and fan networks

Zhi-Zhong Tan(谭志中)
Department of Physics, Nantong University, Nantong 226019, China
Abstract  

In this paper, we made a new breakthrough, which proposes a new Recursion-Transform (RT) method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m×n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

Keywords:  recursion-transform method      network model      potential formula      exact solution  
Received:  14 May 2017      Revised:  07 June 2017      Accepted manuscript online: 
PACS:  05.50.+q (Lattice theory and statistics)  
  84.30.Bv (Circuit theory)  
  89.20.Ff (Computer science and technology)  
  41.20.Cv (Electrostatics; Poisson and Laplace equations, boundary-value problems)  
Fund: 

Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161278).

Corresponding Authors:  Zhi-Zhong Tan     E-mail:  tanz@ntu.edu.cn,tanzzh@163.com

Cite this article: 

Zhi-Zhong Tan(谭志中) Recursion-transform method and potential formulae of the m×n cobweb and fan networks 2017 Chin. Phys. B 26 090503

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