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Generalized network theory of physical two-dimensional systems.

David Ormrod Morley1, Alice L Thorneywork1,2, Roel P A Dullens1

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A new generalized network theory reveals universal properties across diverse 2D materials, from atomistic systems to geopolitical regions. This framework connects ring structures to fundamental network characteristics like node degree and assortativity.

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Area of Science:

  • Materials Science
  • Network Theory
  • Computational Modeling

Background:

  • Understanding the properties of two-dimensional (2D) network materials is crucial for developing new technologies.
  • Existing theories often lack the generality to encompass diverse systems, from atomic structures to macroscopic phenomena.
  • Empirical laws like Lemaître's and Aboav-Weaire describe network properties but require a unifying theoretical framework.

Purpose of the Study:

  • To develop a generalized network theory applicable to a wide array of 2D network materials.
  • To link fundamental network descriptors (node degree distribution, assortativity) to macroscopic properties.
  • To investigate how changes in coordination, topology, and potential models affect network characteristics.

Main Methods:

  • Development of a generalized network theory.
  • Analysis of ring structures using node degree distribution and assortativity.
  • Systematic variation of coordination environments, topologies, and potential models.
  • Application to diverse systems including atomistic materials, foams, fullerenes, colloidal monolayers, and geopolitical regions.

Main Results:

  • The generalized theory successfully describes properties across diverse computational and experimental systems.
  • The ring structure is effectively characterized by node degree distribution and assortativity.
  • Established empirical laws (Lemaître's, Aboav-Weaire) are shown to be linked to these fundamental network descriptors.
  • Systematic changes in system parameters demonstrably alter network properties.

Conclusions:

  • The developed generalized network theory provides a unified approach to understanding 2D network materials.
  • Node degree distribution and assortativity are key parameters for describing network ring structures.
  • The theory's applicability across disparate fields highlights universal principles governing network behavior.