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Intuition harnessed in the name of particle packing


This article has been updated

From avalanches to pharmaceuticals, the physics of powders relies on a much-maligned talent.

How particles jam together has implications ranging from industry to avalanche safety. Credit: Christopher Murray/EyeEm/Getty

For a cognitive skill that plays such a large part in science, intuition gets a raw deal. It is often dismissed as the irrational flipside of reasoned deduction: at best a problem-solving method engineered by evolution as a ‘good enough’ tool to deal with the mundane choices of life, at worst guesswork that proves no more reliable than random chance. But the intuition that many scientists, and anyone else making decisions in the light of experience, draws on is more a distillate from a well of implicit knowledge.

Johannes Kepler thought long and hard before formulating his 1611 conjecture that hexagonal and cubic close-packings of identical spheres are the densest possible arrangements for them. It wasn’t until 1998 that mathematicians Thomas Hales and Samuel Ferguson claimed to have proved Kepler’s intuition correct. And their formal proof was published only this May (T. Hales et al. Forum Math. Pi 5, e2; 2017).

Kepler would surely have enjoyed the verification in Nature Physics this week of another piece of intuition about geometric packing. In the late 1980s, the Welsh physicist Sam Edwards and his student R. B. S. Oakeshott suggested that, for granular materials such as powders, sand and gravel, all packing arrangements dense enough to lock the grains in place through mutual contact — a jammed state, as in the case of salt that won’t come out of the cellar unless shaken — are equally likely to occur. The assumption became a grounding principle for much theoretical work in the area of condensed-matter physics now known as granular matter.

Under this assumption, physicists can relate the number of possible configurations to a kind of entropy akin to that in thermodynamics. This allows them to treat granular media as an analogue of a fluid described using conventional Boltzmann–Gibbs statistical mechanics. The analogy is far from obvious at face value, because molecules in a fluid are in jiggling thermal motion, whereas grains in a heap are static, as if at zero temperature. Once a quantity is invoked to play the part of entropy, however, it supplies a kind of ‘effective temperature’ — the greater the entropy, the higher this ‘temperature’. 

That hypothesis helped to furnish the first theoretical framework for describing grainy systems, some time before ‘granular media’ — ubiquitous in industrial processing, food science and geomorphology — became a fashionable subject for physicists. It represents precisely the kind of foresight and imagination for which Edwards is now celebrated. But was his conjecture about granular packing correct? Using computer simulations of the configurations of discs in two dimensions, researchers have answered in the affirmative — but only for a rather special situation (S.Martinianietal.NaturePhys.;2017). Mapping all the possible configurational states of such a system is computationally demanding, even for the system of just 64 disks studied here, but that number is small enough to sample the complete landscape of distinct possible arrangements. 

That it should be only here that Edwards’ conjecture holds is surely no coincidence.

Here’s the punchline. Edwards’ conjecture about the equiprobability of jammed packings holds only at the point at which the grains are on the brink of unjamming: that is, at the jamming–unjamming transition. It’s possible to pack the grains more densely than this, but then not all such jammed states are equally likely.

This threshold is a special place in the galaxy of granular configurations. It’s the point at which the grains start to move: where a jammed powder hopper unjams, or a pile of snow slides in an avalanche. That it should be only here that Edwards’ conjecture holds is surely no coincidence. The conjecture is in effect saying something about the symmetry of the system, namely, that no configuration is privileged over the others. The implication is that the jamming transition is at root a geometrical property of all grains, just as Kepler’s closest packing is a matter of pure maths, not cannonballs. 

The possible existence of underlying deep symmetries has long been among physicists’ most valued intuitive guidelines for imagining how the Universe might be. That is what engenders a strong, if not universal, conviction in particle physics that a property called supersymmetry unites hitherto distinct classes of fundamental particles beyond the standard model. So Edwards was not just guessing about what was needed to create a working approximation of granular theory: he was listening to the best kind of intuition.

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  • 28 June 2017

    An earlier version of this article stated that Edwards and Oakeshott’s hypothesis was a grounding principle for work on soft matter. In fact, it was pertinent specifically to granular matter.

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Direct observation of dynamic shear jamming in dense suspensions 2016-Apr-04

Jamming by shear 2011-Dec-14

Dense packings of the Platonic and Archimedean solids 2009-Aug-13

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Intuition harnessed in the name of particle packing. Nature 546, 575–576 (2017).

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