Litcius/Paper detail

Theory of an <i>m</i> × <i>n</i> apple surface network with special boundary

Zhi‐Zhong Tan

2023Communications in Theoretical Physics16 citationsDOIOpen Access PDF

Abstract

Abstract As is well known, any condition change in a network model will affect the research method and result. This paper studies an arbitrary m × n apple surface network with a pair of non-uniform boundary resistors, which is a complex network that has not been solved before. The research process of this paper consists of four strict basic steps according to RT-V theory. With the breakthrough of matrix transformation and eigenvector solution, two exact potential function formulae and two equivalent resistance formulae are derived. A series of applications and special cases are given to help readers understand the results. In particular, we have drawn eight visualized potential function images, which can intuitively understand the changing characteristics of potential function. The establishment of theoretical results provides a new theoretical basis for related interdisciplinary research.

Topics & Concepts

Transformation (genetics)Eigenvalues and eigenvectorsFunction (biology)Boundary (topology)ResistorSurface (topology)Computer scienceBasis (linear algebra)Series (stratigraphy)Matrix (chemical analysis)Transformation matrixApplied mathematicsMathematicsMathematical analysisGeometryPhysicsClassical mechanicsQuantum mechanicsComposite materialChemistryVoltageEvolutionary biologyMaterials scienceBiologyPaleontologyBiochemistryGeneKinematicsGraph theory and applicationsGraph Labeling and Dimension ProblemsAdvanced Graph Theory Research
Theory of an <i>m</i> × <i>n</i> apple surface network with special boundary | Litcius