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).