  We consider two (2D) and three (3D) dimensional granular systems exposed to
compression, and ask what is the influence of the number of physical dimensions
on the properties of the interaction networks that spontaneously form as these
systems evolve. The study is carried out based on discrete element simulations
of frictional disks in 2D and spheres in 3D. The main finding is that both the
number of physical dimensions and the type of particle-particle interaction
influence significantly the properties of interaction networks. These networks
play an important role in bridging the microscale (particle size) and
macroscale (system size), thus both aspects (the interaction model and
dimensionality) are carefully considered. Our work uses a combination of tools
and techniques, including percolation study, statistical analysis, as well as
algebraic topology-based techniques. In many instances we find that different
techniques and measures provide complementary information that, when combined,
allow for gaining better insight into the properties of interaction networks.
