My work at Princeton focuses on issues related to the mechanical properties of networks, commonly called rigidity theory among mathematicians. One of the main subjects of interest is the mechanical properties of jammed particle packings, particularly focusing on packings of ellipsoids, and in particular, spheres.
Jamming in Hard Sphere Packings
During my first year at Princeton I focused on algorithms for testing for jamming in hard-sphere packings. Look at our paper ``A Linear Programming Algorithm to Test for Jamming in Hard-Sphere Packings'' [by Aleksandar Donev, Salvatore Torquato, Frank H. Stillinger, and Robert Connelly] as a 1 MB gzipped PostScript file or a high-quality 2 MB PDF, and some related VRML animations. Even smaller (but with lower-quality images) are the files produced by ArXiv. You can also look at a presentation I gave at Cornell (slides PDF, printable PS) during Fall 2002.
Extensions are now underway to packings of ``soft'' spheres, i.e. spheres which interact with a non-singular, but still very stiff, interaction potential. I am developing a Fortran 95 library to deal with such networks of nonlinear springs, a direct but major extension of my SSCNO library. The major challenge is the parallelization of the library, using MPI; also, the codes are Fortran-2002-aware. Some Fortran tools I am developing along the way are useful to other programmers as well and can be downloaded in raw form.
Finally, there are some AMPL models related to hard-sphere packings that you can look at in this directory (here is a tar gzipped file). Look at the Instructions.txt for instructions on how to run this under a bash Unix shell. The output are some VRML animations that you can look at directly. I use Linux and LOQO locally or the Kestrel interface to the NEOS server to try different optimization techniques/solvers for some packing problems. Only a few sample packing data files are included, but I have plenty more if you need them...
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