Abstract:
We study the uniformly weighted ensemble of
force balanced configurations on a triangular
network of nontensile contact forces. For
periodic boundary conditions corresponding to
isotropic compressive stress, we find that
the probability distribution for
single-contact forces decays faster than
exponentially. This super-exponential decay
persists in lattices diluted to the rigidity
percolation threshold. On the other hand, for
anisotropic imposed stresses, a broader tail
emerges in the force distribution, becoming a
pure exponential in the limit of infinite
lattice size and infinitely strong anisotropy.