Recursion-transform method and potential formulae of the m×n cobweb and fan networks

doi:10.1088/1674-1056/26/9/090503

中国物理B ›› 2017, Vol. 26 ›› Issue (9): 90503-090503.doi: 10.1088/1674-1056/26/9/090503

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

收稿日期:2017-05-14 修回日期:2017-06-07 出版日期:2017-09-05 发布日期:2017-09-05
通讯作者: Zhi-Zhong Tan E-mail:tanz@ntu.edu.cn,tanzzh@163.com
基金资助:
Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161278).

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

Received:2017-05-14 Revised:2017-06-07 Online:2017-09-05 Published:2017-09-05
Contact: Zhi-Zhong Tan E-mail:tanz@ntu.edu.cn,tanzzh@163.com
Supported by:
Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161278).

摘要/Abstract

摘要：

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.

关键词: recursion-transform method, network model, potential formula, exact solution

Abstract:

Key words: recursion-transform method, network model, potential formula, exact solution

中图分类号: (Lattice theory and statistics)

05.50.+q

84.30.Bv (Circuit theory) 89.20.Ff (Computer science and technology) 41.20.Cv (Electrostatics; Poisson and Laplace equations, boundary-value problems)

谭志中. Recursion-transform method and potential formulae of the m×n cobweb and fan networks[J]. 中国物理B, 2017, 26(9): 90503-090503.

Zhi-Zhong Tan(谭志中). Recursion-transform method and potential formulae of the m×n cobweb and fan networks[J]. Chin. Phys. B, 2017, 26(9): 90503-090503.

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Recursion-transform method and potential formulae of the m×n cobweb and fan networks

Recursion-transform method and potential formulae of the m×n cobweb and fan networks

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