A ‘universal’ law for jamming

30-year-old conjecture about how grains and powders pack holds up.

A computer simulation has found that all jammed arrangements of granular objects — those in which particles such as powders or sand grains are packed together densely enough to be locked in place — are equally probable.

The behaviour of particles as they become jammed and unjammed explains a wide range of phenomena, from the movement of avalanches to the most efficient ways of processing pills. Stefano Martiniani at the University of Cambridge, UK, and his colleagues modelled a material as a two-dimensional collection of circles. They found that when the grains are just dense enough to be jammed — and therefore are on the threshold of coming unjammed — all possible packings are equally likely. This is in contrast to high-density packings and, in particular, to the optimal density, for which only a regular honeycomb pattern is possible. The result supports a conjecture dating back to the 1980s.