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

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

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.

Keywords: exact solution resistor network matrix equation recursion-transform boundary conditions

Received: 14 November 2014
Revised: 28 November 2014
Accepted manuscript online:

PACS:	05.50.+q	(Lattice theory and statistics)
	84.30.Bv	(Circuit theory)
	01.55.+b	(General physics)
	02.10.Yn	(Matrix theory)

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

Cite this article:

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

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

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