Electrical Properties of an m × n Hammock Network

【摘要】 Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an arbitrary hammock network, which has not been resolved before, and propose the exact potential formula of an arbitrary m × n hammock network by means of the Recursion-Transform method with current parameters(RT-I) pioneered by one of us [Z. Z. Tan, Phys. Rev. E 91(2015) 052122], and the branch currents and equivalent resistance of the network are derived naturally. Our key technique is to setting up matrix equations and making matrix transformation, the potential formula derived is a meaningful discovery, which deduces many novel applications. The discovery of potential formula of the hammock network provides new theoretical tools and techniques for related scientific research.更多还原

【Abstract】 Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an arbitrary hammock network, which has not been resolved before, and propose the exact potential formula of an arbitrary m × n hammock network by means of the Recursion-Transform method with current parameters(RT-I) pioneered by one of us [Z. Z. Tan, Phys. Rev. E 91(2015) 052122], and the branch currents and equivalent resistance of the network are derived naturally. Our key technique is to setting up matrix equations and making matrix transformation, the potential formula derived is a meaningful discovery, which deduces many novel applications. The discovery of potential formula of the hammock network provides new theoretical tools and techniques for related scientific research.更多还原