By Kabir Ramola, Ph.D

In the late 1980’s Sir Sam Edwards proposed a framework for describing the large scale properties of granular materials, such as sand or salt. In this description, similar to the well-established framework of statistical mechanics, the global properties of a complex system are determined by an average over all possible microscopic configurations consistent with a given global property. This is usually attributable to the very fast dynamics of the constituent particles making up the system. The extension of such treatments to granular systems where particles are static or ‘jammed’ represents a fundamental challenge in this field. Even so, Edwards’ conjecture postulated that for given external parameters such as volume, all possible packings of a granular material are equally likely. Such a conjecture, like Boltzmann’s hypothesis in statistical mechanics, can then be used as a starting point to develop new physical theories for such materials based on statistical principles. Indeed, several frameworks have been developed assuming this conjecture to be true.

Figure 1 : Snapshot of the system studied and illustration of the associated energy landscape at different volume fractions.

A simple illustration of this conjecture would be, if one were to pour sand into a bowl, and not bias the preparation in any way, then all the trillion trillions of configurations allowed for the grains would be equally likely. Clearly such a conjecture is utterly infeasible to test experimentally.  In a recent paper that appeared in Nature Physics, we instead performed detailed numerical computations on a theoretical system of soft disks (in two dimensions) with hard internal cores. We focused on a system of 64 disks which already pushed the limits of current computational power. We found that if one fixes the density of a given system of disks, the probability of a packing occurring depends on the pressure, violating Edwards’ proposition. However, at a critical density, where particles just begin to touch or ‘jam’, this probability remarkably becomes independent of the pressure, and all configurations are indeed equally likely to occur. This jamming point is in fact very interesting in its own right since most granular materials are found at the threshold of being jammed and ‘unjammed’. To be fair to Edwards, the hypothesis was made for ‘hard’ grains in which particles are precisely at this threshold, and therefore our numerics seem to confirm the original statement. This is the first time that this statement has been out to a direct test and will no doubt lead to many interesting directions in the future.

Links to news sources describing this article:

• Nature Materials News and Views
• Links to news articles and Cambridge press release
• Nature Physics Editorial
• Nature editorial

doi: 10.1038/nphys4168
Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming.
Stefano Martiniani, K. Julian Schrenk, Kabir Ramola, Bulbul Chakraborty & Daan Frenkel.
Nature Physics 2017