Topology and Granular Materials
Supported by NSF grants No. 0511514 and 0835611
Students: Paul Accisano, Matthew Albano, Temitope Brotherson, Andrew Christie, Kelly Cosman, Michael Lam, Arif Patel, Matthew Peragine, Thomas Perrella, Andrew Pskowski, Alexander Sheppard
Laboratory Assistant: Daniel Cargill
Instructor: Lou Kondic
Project Description
This
project explored the use of computational homology in understanding
structure formation in dense granular materials. Experimental,
theoretical, modeling, and computational components were
implemented. The experimental group set up and carried out
table-top experiments with photo-elastic cylindrical particles and
explored their response to applied pressure. Figure 1 shows a
snapshot of an experiment. This group has been also involved in
developing software for image processing, leading to grey scale images,
such as Fig. 2, which were consequently processed by the computational
group.
Figure 1: Image of force chains. Figure 2: Processed image.
Main effort of the computational group consisted of analyzing the images using computational homology
and in particular extracting the quantities describing their
topological properties. In addition to the experimental images,
this group has analyzed the results of molecular dynamics simulations
images, such as Figure 3.
Figure 3: An image from molecular dynamics simulations.
Theoretical
group learned about the background beyond the tools implemented in
computational homology and supported other groups by providing
theoretical background for the computational analysis. The
modeling group worked on relating the topological methods to other
approaches used in analysis of granular matter, such as correlation
functions and the tools developed within the framework of percolation
theory. More about these projects can be found in the final presentations and reports linked below.
Experimental Group
Computational Group
Topology Group
Modeling Group