Hi Jim, To have a realistic model of friction, you need static and kinetic coefficients along with an idea of the normal forces at all points of contact. Then rate of change for the velocity vectors depends on weighing of the frictional forces against the gravitational forces, by Newton's Law. Say that you hold two rolls adjacent with longitudinal axes parallel to Earth's surface. Then place a third roll into the crevice between the two so that it rests in stable equilibrium. Tilting the whole configuration toward vertical, you should find a critical angle where the third roll begins to slip down the fixed two. This is the old problem of the block and the inclined plane, where inevitability of slipping is explained by the fact that increasing the angle toward vertical takes a limit toward zero normal force from the ramp on the block. How do normal forces get distributed in yr cording problem? Draw a graph whose vertices are the rolls, and whose edges indicate contact points. Then label all the edges with values for the force, by requiring zero sums on each vertex (static equilibrium). Don't forget that the cord is an elastic medium that stretches uniformly, and puts on an external force to any of the tubes it touches. At the detail level, this picture looks complicated, but maybe the details aren't necessary. The edge set divides the region interior to the cord into disjoint tiles. We can go from stable configuration to unstable by adding a small-enough tube somewhere on a region interior to any one tile. What is "small enough"? Given a set of radii on the vertices of the tiles, this can be calculated explicitly. However, I think we already know that the rattlers have to be pretty small relative to their boundary. I would think that the best strategy is to start off going for a smoothly varying gradient of radii. If this doesn't work at first, it seems plausible that a recursive procedure of letting the rattlers fall out and then putting them back into the configuration on the boundary should, after so many iterations, reach a stable configuration. --Brad