# The dip under the heap

## Yet unsolved is the correct description of the
distribution of static forces in a granular system
submitted to an arbitrary load. A paradigmatic example
for this has been the minimum in the pressure
exerted on the basal plane by a heap exactly below
its apex. With Jan Hemmingsson and Stéphane Roux we
have studied various cellular automata describing the
transfer of forces along the direction of gravity
and obtained the dip under the heap.

## The figure shows the network of forces inside a 2d heap
obtained by Jan Hemmingsson using the cellular automaton
described in our
paper (J. Physique I, __ 7 __, 291-302 (1997))

.

## It is interesting that one can obtain exact results
for the stress distribution in small piles despite the
non-linear nature of no-tension in the contacts. This has
been done in two dimensions for several piles in the
paper
with Gadi Oron published in Phys. Rev. E Vol. 58, p.2079-2089 (1998)
which shows that the pressure distribution on the
bottom very much depends on the orientation of the heap
packing and the nature of the bottom plate. In three dimensions
one finds similar results only that the system sizes studied
are not as big as in two dimensions as discussed in a
paper published in Physica A Vol.265,
p.336-343 (1999)