title: Structure of force networks in tapped particulate systems of disks and pentagons. I. Clusters and loops.
abstract: The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the companion paper [Kondic et al., Phys. Rev. E 93, 062903 (2016)10.1103/PhysRevE.93.062903], we consider two-dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network's topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Such differences in network properties are expected to lead to different macroscale response of the considered systems, despite the fact that averaged measures (such as force probability density function) do not show any obvious differences. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.
authors.affiliation: Dpto. de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, Av. 60 Esq. 124, 1900 La Plata, Argentina.|Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina.
authors.forename: Luis A
authors.initials: LA
authors.lastname: Pugnaloni
authors.affiliation: Instituto de Física de Líquidos y Sistemas Biológicos (CONICET La Plata, UNLP), Calle 59 Nro 789, 1900 La Plata, Argentina.|Universidad Tecnológica Nacional-FRBA, UDB Física, Mozart 2300, C1407IVT Buenos Aires, Argentina.
authors.forename: C Manuel
authors.initials: CM
authors.lastname: Carlevaro
authors.affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
authors.forename: M
authors.initials: M
authors.lastname: Kramár
authors.affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
authors.forename: K
authors.initials: K
authors.lastname: Mischaikow
authors.affiliation: Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
authors.forename: L
authors.initials: L
authors.lastname: Kondic