Properties of layer-by-layer vector stochastic models of force fluctuations in granular materials

We attempt to describe the stress distributions of granular packings using lattice-based layer-by-layer stochastic models that satisfy the constraints of force and torque balance and nontensile forces at each site. The inherent asymmetry in the layer-by-layer approach appears to lead to an asymmetric force distribution, in disagreement with both experiments and general symmetry considerations. The vertical force component probability distribution is robust and in agreement with predictions of the scalar q model of Liu et al. [Science 269, 513 (1995)] and Coppersmith et al. [Phys. Rev. E 53, 4673 (1996)] while the distribution of horizontal force components is qualitatively different and depends on the details of implementation.