A community-detection based approach to identification of inhomogeneities in granular matter

Interparticle interactions in granular matter are commonly represented by appropriate graphs, therefore, inhomogeneities in granular matter can be possibly reflected by community structure in the respective graphs. Approaches and algorithms for community detection are being actively developed and the achievements in this area can be utilized for analysis of granular systems, where bridging the gap from microscopic configuration to macroscopic phenomena is of great interest. we analyse applicability of graph community detection algorithms for identification of inhomogeneities of particle parameter distribution in granular matter, in order to explore the relevance of the selected approach in general. As an example application, we analyse identification of temperature distribution inhomogeneities in a simulated packed bed of fuel particles on a moving grate. We build a graph based on particle parameter similarity from the particle temperature data, available from Discrete Element/Particle Modelling, and the problem of identification of particle temperature inhomogeneities is thereby made equivalent to community detection in graphs. We apply a number of well-known community detection algorithms: Edge Betweenness, Walktrap, Infomap, Label Propagation, Spinglass and compare the resulting partitions. We apply this approach to a number of graphs, corresponding to different particle configurations, in order to identify regularities characteristic of partitions produced by different algorithms. We propose a procedure for additional postprocessing of the partitions in order to improve the quality of clusterization. In addition, we apply two alternative algorithms (not related to community detection in graphs) to identify particle distribution inhomogeneities. We also introduce a parameter to evaluate the cluster structure in particle systems.