Topological melting in networks of granular materials

Najlaa Alalwan, Alex Arenas, Ernesto Estrada

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Abstract

Granular materials represent a vast category of particle conglomerates with many areas of industrial applications. Here we represent these materials by graphs which capture their topological organization and ordering. Then, using the communicability function—a topological descriptor representing the thermal Green function of a network of harmonic oscillators—we prove the existence of a universal topological melting transition in these graphs. This transition resembles the melting process occurring in solids. We show here that crystalline-like granular materials melts at lower temperatures and display a sharper transition between solid to liquid phases than the random spatial graphs, which represent amorphous granular materials. In addition, we show the evolution mechanism of melting in these granular materials. In the particular case of crystalline materials the process starts by melting a central core of the crystal which then growth until the whole material is in the liquid phase. We provide experimental confirmation from published literature about this process.
Original languageEnglish
Pages (from-to)875–894
Number of pages20
JournalJournal of Mathematical Chemistry
Volume57
Issue number3
Early online date3 Dec 2018
DOIs
Publication statusPublished - 31 Mar 2019

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Keywords

  • granular materials
  • melting
  • phase transition
  • graph spectrum
  • communicability function
  • matrix functions

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