generate MRJ packings of convex superdisks in two dimensions and superballs in three dimensions. The DTS algorithm generalizes the Lubachevsky-Stillinger (LS) sphere-packing algorithm [38] to the case of other centrally symmetric convex bodies (e.g., ellipsoids and superballs). Initially, small particles are randomly distributed and randomly oriented in the simulation box (fundamental cell) with periodic boundary conditions and without any overlap. The particles are then given translational and rotational velocities randomly and their motion followed as they collide elastically and also expand uniformly with an expansion rate γ , while the fundamental cell deforms to better accommodate the configuration. After some time, a jammed state with a diverging collision rate is reached and the density reaches a local maximum value. To generate random jammed packings, initially large γ are employed to prevent the system following the equilibrium branch of the phase diagram that leads to crystallization. Near the jamming point, sufficiently small expansion rate is necessary for the particles to establish contacting neighbor networks and to form a truly jammed packing. On the basis of our experience with spheres [17] and ellipsoids [31], we believe that our algorithm with rapid particle expansion produces final states that represent the MRJ state well. Here we use the largest possible initial γ ∈ (0 . 1 − 0 . 5) that is numerically feasible to ensure the generated superdisk and superball packings are maximally random jammed. We mainly focus on superdisks and superballs with deformation parameters p within the range 0 . 85 − 3 . 0, since extreme values of p associated with polyhedron-like shapes present numerical difficulties. 

All of the generated packings used in the subsequent analyses are verified to be at least collectively jammed using an “infinitesimal shrinkage” method [13], i.e., the particles in the packing are shrunk by a very small amount [39] and given random velocities. If no significant structural changes occur after the system “relaxes” after a sufficiently long enough time, the packing is considered to be collectively jammed. It is well established that the “infinitesimal shrinkage” method is robust, i.e., it always gives the same results for sphere packings as those obtained from a rigorous linear programming jamming test algorithm provided the amount of shrinkage from the jammed state is sufficiently small for a given number of particles within the periodic cell [40]. 

