Packing things into a crowded place
Predicting the geometry and behaviour of densely packed objects in the natural and man-made worlds, from rocks to foams to spheres.
Densely packed objects of a similar shape, from rocks to foams to spheres, have intrigued mathematicians since the ancients. The mechanical properties of these materials are determined by how big the gaps are between them—in particular, how close they are to their maximum random-packed density. Predicting this maximum, and how the material properties vary around it, is a geometric and physics challenge.
In this project we investigate the packing of spheres of the same size and mixtures of spheres with a range of sizes. While simulating packing is easy to program, the running time scales poorly with system size. To overcome this obstacle, we develop new mathematical techniques for determining the properties of dense packings using a simplified 1d model. This powerful approach captures essential features of higher-dimensional systems.
Understanding how objects fit closely together under pressure or by design is at the heart of materials science and branches of fluid dynamics. Predicting the behaviour of dense packings also sets the stage for reverse-engineering new composite materials to have desired properties.
Journal of Chemical Physics
P. Lopez-Sanchez, V. Chapara, S. Schumm, R. Farr
R. Farr, E. Griffiths
Physical Review E