Two-Point Resistance of a Non-Regular Cylindrical Network with a Zero Resistor Axis and Two Arbitrary Boundaries

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2017,（3）
• 页码范围: 280-288
• 页数: 9页
• 语种: 英文
• DOI: 10.1088/0253-6102/67/3/280

摘要

We study a problem of two-point resistance in a non-regular rn × n cylindrical network with a zero resistor axis and two arbitrary boundaries by means of the Recursion-Transform method.This is a new problem never solved before,the Green's function technique and the Laplacian matrix approach are invalid in this case.A disordered network with arbitrary boundaries is a basic model in many physical systems or real world systems,however looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of the arbitrary boundaries,the boundary is like a wall or trap which affects the behavior of finite network.In this paper we obtain a general resistance formula of a non-regular m × n cylindrical network,which is composed of a single summation.Further,the current distribution is given explicitly as a byproduct of the method.As applications,several interesting results are derived by making special cases from the general formula.