We study a problem of two-point resistance in a non-regular m × 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...We study a problem of two-point resistance in a non-regular m × 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.展开更多
基金Supported by the Natural Science Foundation of Jiangsu Province under Grant No.BK20161278
文摘We study a problem of two-point resistance in a non-regular m × 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.
