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Topological melting in networks of granular materials

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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.

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Acknowledgements

The authors thank Dr. F. Arrigo, and Prof. D. H. Higham for useful comments and suggestions which improve the presentation of the material. NA thanks Iraqi Government for a Doctoral Fellowship at the University of Strathclyde.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow, G11HX, UK

    Najlaa Alalwan

  2. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007, Tarragona, Spain

    Alex Arenas

  3. Institute of Applied Mathematics (IUMA), Universidad de Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

    Ernesto Estrada

  4. ARAID Foundation, Government of Aragón, 50018, Zaragoza, Spain

    Ernesto Estrada

  5. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, São Carlos, São Paulo, 13560-970, Brazil

    Ernesto Estrada

Authors
  1. Najlaa Alalwan
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  2. Alex Arenas
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  3. Ernesto Estrada
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Correspondence to Ernesto Estrada.

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Alalwan, N., Arenas, A. & Estrada, E. Topological melting in networks of granular materials. J Math Chem 57, 875–894 (2019). https://doi.org/10.1007/s10910-018-0988-0

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  • DOI: https://doi.org/10.1007/s10910-018-0988-0

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