This award supports theoretical research and educational activities focused to develop a theory that can be used to estimate the packing density of objects of arbitrary shapes in random configurations. The PI will use the theory to search for the best random packing in the space of object shapes. This research will bring together mathematical formulations from spin-glass theory such as cavity methods and belief propagation to calculate the force distribution and the coordination number, and the statistical mechanics formulation of volume fluctuations. The PI expects that this synergistic approach will produce a more comprehensive picture of the packing problem of non-spherical particles than before. The theory will estimate the optimum packing fraction for a class of shapes as an analytical continuation from the spherical point, thus paving the way for a systematic investigation of an extension of Ulam's conjecture for random packings.
The development of a theoretical framework to solve a fundamental and ancient problem in physics and mathematics will have applications in diverse industries that employ particulate matter, and is therefore of great interest to engineers, material scientists, physicists and mathematicians alike.
The PI is committed to involve students from underrepresented groups in the project. The research will also contribute to curriculum development by enriching instruction in granular matter. Data obtained from simulations will be made available to the broader research community through the project website.
NONTECHNICAL SUMMARY This award supports theoretical research and educational activities focused to study non-spherical particles pack. Finding the densest packing of objects is an outstanding materials science problem that originated with Kepler's conjecture more than 400 years ago. Almost all shapes existing in nature are non-spherical and it is believed that non-spherical particles or grains can pack more densely than spheres. This opens the exciting possibility for efficient packing optimization by shape variation. The packing problem appears in a broad range of scientific disciplines from self-assembly of nanoparticles to virus assemblies. It has also potential impact on industries involved in the processing of granular materials from concrete to nanocomposite materials.
The PI is committed to involve students from underrepresented groups in the project. The research will also contribute to curriculum development by enriching instruction in granular matter. Data obtained from simulations will be made available to the broader research community through the project website.
