Granular Media

photo elastic particles

Photograph of photo elastic particles placed between two cross polarizers. Courtesy of Bob Behringer.

Particulate systems consisting of a large number of particles have attracted significant attention in the last decades. Despite significant research on these systems, their properties are still not well understood and some of them appear to be rather elusive.  It is well accepted that the inter particle forces play a key role in determining the mechanical properties of static and dynamic systems.

We developed mathematical models based on persistent homology for analyzing force networks in particulate systems. These models allow us to study the time evolution of particulate systems exposed to compression, shear and other phenomena.

Our comparison of experimental data with simulations  reveals  a difference, providing insights for further improvement of the model and better understanding of the influence of  noise present  in the experiments.  We are also able to quantify  structural differences between force chains (filamentary structures shown the figure above)  depending on a friction coefficient  and polydispersisty of the system. 

Recently we studied steady states of systems subjected to tapping. It turns out that  the force networks differ considerably for different types (disks, pentagons, hexagons, … )  of particles as well as for the states obtained by different tapping intensities. By careful analysis of the persistence diagrams, we identified differences between the force  networks and started connecting them to physical properties of the systems.