Potential formula of the nonregular m × n fan network and its application.

Abstract:

:Potential formula of an arbitrary resistor network has been an unsolved problem for hundreds of years, which is an interdisciplinary problem that involves many areas of natural science. A new progress has been made in this paper, which discovered the potential formula of a nonregular m × n fan network with two arbitrary boundaries by the Recursion-Transform method with potential parameters (simply call RT-V). The nonregular m × n fan network is a multipurpose network contains several different types of network model such as the interesting snail network and hart network. In the meantime, we discussed the semi-infinite fan network and a series of novel and special conclusions are produced, the effective resistance is educed naturally. The discovery of potential formulae of resistor network provides new theoretical tools and techniques for related scientific research.

journal_name

Sci Rep

journal_title

Scientific reports

authors

Tan Z,Tan ZZ,Chen J

doi

10.1038/s41598-018-24164-x

subject

Has Abstract

pub_date

2018-04-11 00:00:00

pages

5798

issue

1

issn

2045-2322

pii

10.1038/s41598-018-24164-x

journal_volume

8

pub_type

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