What determines force chains in granular media?

The determination of the normal and transverse (frictional) inter-particle forces within a granular medium is a long standing, taunting, and yet unresolved problem. We present a new formalism which employs the knowledge of the external forces and the orientations of contacts between particles (of any given sizes), to compute all the inter-particle forces. Having solved this problem we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.