中国物理B ›› 2020, Vol. 29 ›› Issue (8): 80503-080503.doi: 10.1088/1674-1056/ab96a7

• SPECIAL TOPIC—Ultracold atom and its application in precision measurement • 上一篇    下一篇

Electrical properties of m×n cylindrical network

Zhi-Zhong Tan(谭志中), Zhen Tan(谭震)   

  1. 1 Department of Physics, Nantong University, Nantong 226019, China;
    2 School of Information Science and Technology, Nantong University, Nantong 226019, China
  • 收稿日期:2020-02-26 修回日期:2020-05-18 出版日期:2020-08-05 发布日期:2020-08-05
  • 通讯作者: Zhi-Zhong Tan E-mail:tanz@ntu.edu.cn
  • 基金资助:

    Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161278).

Electrical properties of m×n cylindrical network

Zhi-Zhong Tan(谭志中)1, Zhen Tan(谭震)2   

  1. 1 Department of Physics, Nantong University, Nantong 226019, China;
    2 School of Information Science and Technology, Nantong University, Nantong 226019, China
  • Received:2020-02-26 Revised:2020-05-18 Online:2020-08-05 Published:2020-08-05
  • Contact: Zhi-Zhong Tan E-mail:tanz@ntu.edu.cn
  • Supported by:

    Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161278).

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摘要：

We consider the problem of electrical properties of an m×n cylindrical network with two arbitrary boundaries, which contains multiple topological network models such as the regular cylindrical network, cobweb network, globe network, and so on. We deduce three new and concise analytical formulae of potential and equivalent resistance for the complex network of cylinders by using the RT-V method (a recursion-transform method based on node potentials). To illustrate the multiplicity of the results we give a series of special cases. Interestingly, the results obtained from the resistance formulas of cobweb network and globe network obtained are different from the results of previous studies, which indicates that our research work creates new research ideas and techniques. As a byproduct of the study, a new mathematical identity is discovered in the comparative study.

关键词: cylindrical network, complex boundaries, RT-V method, electrical properties, Laplace equation

Abstract:

We consider the problem of electrical properties of an m×n cylindrical network with two arbitrary boundaries, which contains multiple topological network models such as the regular cylindrical network, cobweb network, globe network, and so on. We deduce three new and concise analytical formulae of potential and equivalent resistance for the complex network of cylinders by using the RT-V method (a recursion-transform method based on node potentials). To illustrate the multiplicity of the results we give a series of special cases. Interestingly, the results obtained from the resistance formulas of cobweb network and globe network obtained are different from the results of previous studies, which indicates that our research work creates new research ideas and techniques. As a byproduct of the study, a new mathematical identity is discovered in the comparative study.

Key words: cylindrical network, complex boundaries, RT-V method, electrical properties, Laplace equation

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
84.30.Bv (Circuit theory) 89.20.Ff (Computer science and technology) 02.10.Yn (Matrix theory)