  We present experimental and numerical results for displacement response
functions in packings of rigid frictional disks under gravity. The central disk
on the bottom layer is shifted upwards by a small amount, and the motions of
disks above it define the displacement response. Disk motions are measured with
the help of a still digital camera. The responses so measured provide
information on the force-force response, that is, the excess force at the
bottom produced by a small overload in the bulk. We find that, in experiments,
the vertical-force response shows a Gaussian-like shape, broadening roughly as
the square root of distance, as predicted by diffusive theories for stress
propagation in granulates. However, the diffusion coefficient obtained from a
fit of the response width is ten times larger than predicted by such theories.
Moreover we notice that our data is compatible with a crossover to linear
broadening at large scales. In numerical simulations on similar systems (but
without friction), on the other hand, a double-peaked response is found,
indicating wave-like propagation of stresses. We discuss the main reasons for
the different behaviors of experimental and model systems, and compare our
findings with previous works.
