Electrical property of an m × n apple surface network

Abstract

The circuit network model has important application value in many disciplines, and many complex problems can be simulated by establishing the network model. However, looking for the explicit solutions of the electrical property in an arbitrary resistor network is important but difficult. In this paper an arbitrary m × n apple surface network is researched by the Recursion-Transform method with voltage parameters (RT-V) for the first time, and the RT-V method consists of four rigorous basic steps. We study and derive the exact analytical expression of potential function and the equivalent resistance formula, and some special cases and applications of them are also discussed. The theoretical results obtained are concise and provide a new theoretical basis for the research of related subjects.