Topology and Percolation of Particulate Systems

Supported by NSF grant 0835611

This project concentrated on the force networks that form as a system of photoelastic particles is compressed.   Photoelasticity allows to visualize these force networks and to analyze them using a variety of techniques.   This approach allows to reach an insight regarding properties of these networks, which are known to be relevant in a number of applications involving dense granular matter, from building of silos, to earthquakes, or response of Martian (or any other) surface to an impact.

In the project, the students carried out physical experiments and produced sets of images (an example is shown).   The brightness of a given particle is at least approximately proportional to the total stress exerted.  These images were then processed using image processing techniques to extract the information such as size, position, and stress of each particle.

The data obtained by image processing were then analyzed using (i) topological tools, that measured the connectivity of the force networks; and (ii) percolation theory, which was applied to discuss universal properties of force networks.  In addition, relevant fractal dimensions were computed. The results were compared to the existing theoretical models.

The instructor acknowledges help by Drs. Robert Behringer of Duke University, Miro Kramar and Konstantin Mischaikow of Rutgers University, Mark Shattuck of CCNY, and Arnaud Goullet of NJIT.     The project was in part supported by the NSF Grant No. DMS-0835611 (PI: L. Kondic).