Construction of velocity similarity graph for velocity field analysis in
granular intruder motion
Abstract
We present a method based on graph community detection algorithms to
analyse velocity fields induced by an intruder particle impinging upon a
stationary bed of particles. Based on velocity relations between the
pairs of adjacent particles, the “velocity similarity” graphs are
built where the graph vertices represent the particles and the edge
weights are calculated according to the velocities of the respective
particle pairs. A few different expressions for the edge weights are
tested. Based on the graph, a Louvain community detection algorithm with
the “geographic” null model is used to identify the goups of particles
moving in a coordinated manner, represented in the graph as a community
of vertices, for which the community detection algorithms developed for
graph analysis can be applied. Selection of the expression of the graph
edge weights based on the velocities of the respective particles
influences the resulting graph structure and thereby has an influence on
the community detection results.