Quantifying force networks in particulate systems

Miroslav Kramár, Arnaud Goullet, Lou Kondic, Konstantin Mischaikow

    Research output: Contribution to journalArticlepeer-review

    33 Citations (Scopus)

    Abstract

    We present mathematical models based on persistent homology for analyzing force distributions in particulate systems. We define three distinct chain complexes of these distributions: digital, position, and interaction, motivated by different types of data that may be available from experiments and simulations, e.g. digital images, location of the particles, and the forces between the particles, respectively. We describe how algebraic topology, in particular, homology allows one to obtain algebraic representations of the geometry captured by these complexes. For each complex we define an associated force network from which persistent homology is computed. Using numerical data obtained from discrete element simulations of a system of particles undergoing slow compression, we demonstrate how persistent homology can be used to compare the force distributions in different systems, and discuss the differences between the properties of digital, position, and interaction force networks. To conclude, we formulate well-defined measures quantifying differences between force networks corresponding to the different states of a system, and therefore allow to analyze in precise terms dynamical properties of force networks.

    Original languageEnglish
    Pages (from-to)37-55
    Number of pages19
    JournalPhysica D: Nonlinear Phenomena
    Volume283
    DOIs
    Publication statusPublished - 2014 Aug 15

    Keywords

    • Force networks
    • Particulate systems
    • Persistence diagram

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics
    • Condensed Matter Physics
    • Applied Mathematics

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