Robust propagation direction of stresses in a minimal granular packing

By employing the adaptive network simulation method, we demonstrate that th e ensemble-averaged stress caused by a local force for packings of friction less rigid beads is concentrated along rays whose slope is consistent with unity: forces propagate along lines at 45 degrees to the horizontal or vert ical. This slope is shown to be independent of polydispersity or the degree to which the system is sheared. Further confirmation of this result comes from fitting the components of the stress tensor to the null stress "consti tutive equation". The magnitude of the response is also shown to fall off w ith the -1/2 power of distance. We argue that our findings are a natural co nsequence of a system that preserves its volume under small perturbations.