Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary
Tan Zhi-Zhong
Department of Physics, Nantong University, Nantong 226019, China

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
Received: 14 November 2014
Corresponding Authors: Tan Zhi-Zhong
E-mail: tanz@ntu.edu.cn,tanzzh@163.com

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