**
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.