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Properties of the contact network of granular materials: jamming and mechanical equilibrium

The last few years have witnessed a rising interest in the study of the structural features
of granular media. These features may be exemplified by a number of properties. Thus, the celebrated
Edwards' statistical theory is based on the packing fraction. Developments of these and related ideas
rely on tessellations of the space, which provide information on local structure and connectivity.
Focusing on connectivity is a natural approach, given that forces propagate by contact in these materials.

In this contribution I will consider some results from topological measurements on two different types
of systems. By one hand, a granular system undergoing a jamming transition from the diluted to the dense
phase, and by other hand, a series of systems in mechanical equilibrium obtained by tapping. I will show
results from usual measurements based on a complex networks approach, and results based on a mesoscopic
extension of the concept of coordination. This involves considering not only particle-particle contacts,
but mutually connected groups of particles, in groups of three or more.

The topology of the contact network evolves across the jamming transition. Its features allow not only to
pinpoint the transition point, but to gain insight into the physical processes taking place, particularlly
the development of rigidity. Regarding systems in mechanical equilibrium, topological measurements have
been shown to be better probes of the structure than traditional tools. They can, for example, discriminate
states with the same density but different stress tensor.

And as our interest in topology rises, new techniques are introduced. As an application of the one of the
latest, persistent homology, I will show how to recover information on the topology of the contact network
from incomplete or noisy data, such as those obtained in experiments, for example.

Author(s):

Roberto Arevalo    
Nanyang Technological University, School of Physical and Mathematical Sciences, Physics and Applied Physics
Singapore