The seminar will focus on the distribution of contact forces in a two-dimensional granular pile. For hard grains, these forces can fluctuate greatly. Studies in the literature so far have focussed on either the distribution of local forces, or on the spatial distribution of the mean force. It has been noted however that the contact forces form spatial structures as the result of the balance condition on each grain. We have attempted to describe the distribution of these so called force chains. We discovered that by suitably defining the termination of the force chains their size has a power law distribution. By studying these system via finite size scaling we could measure the scaling properties of the force chain distribution. These appear to be universal, independent of the physical details of the granular pile. The observation of universality invites the use of simplified models open to mathematical analysis. One such model, which has been observed to be in the correct universality class is solvable by Bethe Ansatz, and allows one to calculate the entropy of the force network. It is naturally interpreted as a 1+1 dimensional gas of two species of fermions permitting a bound state between the two species, but having no other interaction. The space in which these particles move is made by the forces between the original grains.

Université d’Amsterdam