2013/11/30 by Miroslav Kramár, M. Kramar, A. Goullet +5 · 5 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #Cell Image Analysis Techniques #Topological and Geometric Data Analysis #cond-mat.soft
paper · pdf · doi:10.1016/j.physd.2014.05.009
published as Physica D, Vol. 283 (2014), 37-55
arxiv created 2014/03/18 · openalex publication_date 2014/06/09 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present mathematical models based on persistent homology for analyzing force distributions in particulate systems. We define three distinct chain complexes: digital, position, and interaction, motivated by different capabilities of collecting experimental or numerical data, e.g. digital images, location of the particles, and normal forces between particles, respectively. We describe how algebraic topology, in particular, homology allows one to obtain algebraic representations of the geometry captured by these complexes. To each complexes we define an associated force network from which persistent homology is computed. Using numerical data obtained from molecular dynamics simulations of a system of particles being slowly compressed we demonstrate how persistent homology can be used to compare the geometries of the force distributions in different granular systems. We also discuss the properties of force networks as a function of the underlying complexes, and hence, as a function of the type of experimental or numerical data provided.