Indeterminacy, Memory, and Motion in a Simple Granular Packing

We apply two theoretical and two numerical methods to the problem of a disk placed in a groove and subjected to gravity and a torque. Methods assuming rigid particles are indeterminate -- certain combinations of forces cannot be calculated, but only constrained by inequalities. In methods assuming deformable particles, these combinations of forces are determined by the history of the packing. Thus indeterminacy in rigid particles becomes memory in deformable ones. Furthermore, the torque needed to rotate the particle was calculated. Two different paths to motion were identified. In the first, contact forces change slowly, and the indeterminacy decreases continuously to zero, and vanishes precisely at the onset of motion, and the torque needed to rotate the disk is independent of method and packing history. In the second way, this torque depends on method and on the history of the packing, and the forces jump discontinuously at the onset of motion.