Potential formula of an m × n globe network and its application

Tan, Zhi‐Zhong

doi:10.1038/s41598-018-27402-4

Cited by 32 publications

(40 citation statements)

References 37 publications

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“…This paper achieved a series of improved exact potential formulae in an m × n globe network by the RT-I method. Chebyshev polynomial of the second kind is introduced to improve the potential formula of the globe network 44 . Some applications of the new potential formula of the globe network are presented, such as some special and interesting potential formulae are given in Eqs.…”

Section: Discussionmentioning

confidence: 99%

“…Tan 44 used Kirchhoff 's law to analyze the resistor network and to establish the resistor network model. The following general matrix equation is where B m is given by Eq.…”

Section: Three Terms Recurrence Sequence and Discrete Cosine Transformmentioning

confidence: 99%

“…The potential of any node in the m × n globe network is as follows where (1) Since the potential formula (1) contains exponential function operation, it is less efficient to calculate potential of globe resistor networks by computer. The purpose of this section is to give an improved potential formula of the globe network 44 , i.e. a new formula of potential expressed by Chebyshev polynomial of the second class is given 53 .…”

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confidence: 99%

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Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Zhou

Zheng

Jiang

et al. 2022

Sci Rep

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Resistor network is widely used. Many potential formulae of resistor networks have been solved accurately, but the scale of data is limited by manual calculation, and numerical simulation has become the trend of large-scale operation. This paper improves the general solution of potential formula for an $$m\times n$$ m × n globe network. Chebyshev polynomials are introduced to represent new potential formula of a globe network. Compared with the original potential formula, it saves time to calculate the potential. In addition, an algorithm for computing potential by the famous second type of discrete cosine transform (DCT-II) is also proposed. It is the first time to be used for machine calculation. Moreover, it greatly increases the efficiency of computing potential. In the application of this new potential formula, the equivalent resistance formulae in special cases are given and displayed by three-dimensional dynamic view. The new potential formulae and the proposed fast algorithm realize large-scale operation for resistor networks.

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Section: Discussionmentioning

confidence: 99%

“…Tan 44 used Kirchhoff 's law to analyze the resistor network and to establish the resistor network model. The following general matrix equation is where B m is given by Eq.…”

Section: Three Terms Recurrence Sequence and Discrete Cosine Transformmentioning

confidence: 99%

mentioning

confidence: 99%

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Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Zhou

Zheng

Jiang

et al. 2022

Sci Rep

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“…In particular, we provide three special results when taking x x x 1 1 = = and x 0, 1 = x n. 2 = It is interesting that we established a new method to study the equivalent resistance of a 3D network, which is a very clever design that applies the results of a 2×n resistor network to a ,×n circuit network. It is necessary for us to explain that figure 2 is a new model because there are two different resistor elements on the horizontal axis, which has not been resolved before, and the general results of equations (44) and (45) are discovered for the first time.…”

Section: Summary and Discussionmentioning

confidence: 99%

Electrical characteristics of the 2 × n and □ × n circuit network

2019

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This paper presents two new fundamentals of the 2×n and ,×n circuit network. The results of a plane 2×n resistor network can be applied to a ,×n circuit network, which has not been studied before. We first study the 2×n resistor network by modeling a differential equation and obtain two equivalent resistances between two arbitrary nodes of the 2×n network. Next, the ,×n cube network is transformed to the 2×n plane network equivalently to achieve two resistance formulae between two arbitrary nodes of the ,×n cube network. By applying the resistance results to the ,×n LC cube network, the complex impedance characteristics of the LC network, which includes oscillation characteristics and resonance properties, are discovered.

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“…Subsequently, more and more scholars had been devoted to the exploration of the world of resistive networks [10][11][12][13] . In 2011, Professor Tan advanced the more widely-used Recursion-Transform method (RT) [14][15][16][17] , which is applied to solve a variety of complex m × n order networks and equivalent resistance problems with different complex boundary conditions [18][19][20][21][22][23][24][25] . Tan's method can be employed to study arbitrary circuit network, and therefore the complex boundary network problems are well addressed.…”

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confidence: 99%

Circuit network theory of n-horizontal bridge structure

Fang

Tan

2022

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This research investigates a complex n order cascading circuit network with embedded horizontal bridge circuits with the N-RT method. The contents of the study include equivalent resistance analytical formula and complex impedance characteristics of the circuit network. The research idea is as follows. Firstly the equivalent model of n-order resistance network is established, and a fractional difference equation model is derived using Kirchhoff’s law. Secondly, the equivalent transformation method is employed to transform the fractional equation into a simple linear difference equation, and its particular solution is computed. Then the solution to the difference equation is used to derive the effective resistance of the resistance network of the embedded horizontal bridge circuit, and various special cases of equivalent resistance formula are analyzed and the correctness of the analysis model gets verified. Finally, as an expanded application, the equivalent complex impedance of LC network is studied, and Matlab drawing tool is employed to offer the equivalent impedance with various variables of the graph. Our results provide new research ideas and theoretical basis for relevant scientific researches and practical applications.

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Potential formula of an m × n globe network and its application

Cited by 32 publications

References 37 publications

Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Electrical characteristics of the 2 × n and □ × n circuit network

Circuit network theory of n-horizontal bridge structure

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