Loose-rigid transition in 3d packing of spheres

The classical problem of the random packing of spheres is restudied by introducing a new type of constraint among the spheres. This is done by examining the three-dimensional packing density of an open string of spherical beads as a function of the corresponding one-dimensional density along the string. The discussion stresses the peculiar behaviour of the problem as well as connections with some results in random packing of spheres and other systems.