Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

doi:10.1088/1674-1056/24/2/020503

中国物理B ›› 2015, Vol. 24 ›› Issue (2): 20503-020503.doi: 10.1088/1674-1056/24/2/020503

Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

谭志中

Department of Physics, Nantong University, Nantong 226019, China

收稿日期:2014-11-14 修回日期:2014-11-28 出版日期:2015-02-05 发布日期:2015-02-05

Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

Tan Zhi-Zhong (谭志中)

Department of Physics, Nantong University, Nantong 226019, China

Received:2014-11-14 Revised:2014-11-28 Online:2015-02-05 Published:2015-02-05
Contact: Tan Zhi-Zhong E-mail:tanz@ntu.edu.cn,tanzzh@163.com

摘要/Abstract

摘要： We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary, which has not been solved before because the Green's function technique and the Laplacian matrix approach are invalid in this case. Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network. In this paper, we give a general resistance formula that is composed of a single summation by using the recursion-transform method. Meanwhile, several interesting results are derived by the general formula. Further, the current distribution is given explicitly as a byproduct of the method.

关键词: exact solution, resistor network, matrix equation, recursion-transform, boundary conditions

Abstract: We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary, which has not been solved before because the Green's function technique and the Laplacian matrix approach are invalid in this case. Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network. In this paper, we give a general resistance formula that is composed of a single summation by using the recursion-transform method. Meanwhile, several interesting results are derived by the general formula. Further, the current distribution is given explicitly as a byproduct of the method.

Key words: exact solution, resistor network, matrix equation, recursion-transform, boundary conditions

中图分类号: (Lattice theory and statistics)

05.50.+q

84.30.Bv (Circuit theory) 01.55.+b (General physics) 02.10.Yn (Matrix theory)

谭志中. Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary[J]. 中国物理B, 2015, 24(2): 20503-020503.

Tan Zhi-Zhong (谭志中). Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary[J]. Chin. Phys. B, 2015, 24(2): 20503-020503.

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Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

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