Jamming Hard-Spheres configurations through Iterative Linear Optimization

It has recently been discovered that jamming criticality of spheres-based models defines a broad universality class. Yet, computational techniques to produce jammed packings are still somewhat limited. Moreover, most of available methods are based on energy minimization algorithms, and are therefore designed for soft-spheres configurations. Consequently, generating a critical jammed packing of hard-spheres (HS) is further complicated due to the singular interaction between such type of particles. Here, we present an algorithm that allows to reach the jamming point of HS configurations in arbitrary dimensions, through a series of linear optimization problems. Within our approach, the exact, non-convex optimization problem associated to jamming of HS is replaced by a sequence of simpler linear problems. Nevertheless, in all cases the non-overlapping constraints imposed by the HS interaction are strictly satisfied. Importantly, we prove that upon convergence our algorithm produces a stable, well defined jammed state of HS, that corresponds to a (possibly local) optimum of the exact problem. We also show that our method allows to easily construct the full network of contact forces from the Lagrange multipliers associated to the non-overlapping constraints.