Capstone (Math 451H) Spring 2009:

Topology and Granular Materials


     Department of Mathematical Sciences 

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.