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

作　　者：谭志中 

机构地区：[1]Department of Physics,Nantong University,Nantong 226019,China

出　　处：《Chinese Physics B》2017年第9期82-90,共9页中国物理B（英文版）

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

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.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 

分 类 号：O175[理学—数学]