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

Area of Science:

• Physics
• Electrical Engineering
• Network Theory

Background:

• Calculating explicit potential functions in arbitrary resistor networks is a significant challenge in physics.
• Previous studies on globe resistor networks primarily focused on calculating effective resistance, leaving potential formulas unresolved.

Purpose of the Study:

• To derive an exact potential formula for arbitrary m × n globe resistor networks.
• To develop a method applicable to complex resistor network analysis.
• To facilitate practical applications by deriving potential-related results.

Main Methods:

• The study employed the Recursion-Transform method with current parameters (RT-I).
• Key steps involved setting up matrix equations and transforming 2D matrix equations into 1D.
• The general formula was used to deduce specific potential results.

Main Results:

• An exact potential formula for m × n globe resistor networks was successfully derived.
• A series of potential results were deduced from the general formula.
• The effective resistance between two nodes was naturally derived using the potential formula.

Conclusions:

• The developed Recursion-Transform method provides an effective solution for potential calculations in globe resistor networks.
• The derived potential formula offers a significant advancement for analyzing complex resistor networks.
• This work paves the way for further research in network analysis and related electrical engineering applications.