“…i.e., the packing fraction of a saturated random packing for spheres was found to be [ 10 ] and for disks . To obtain a higher packing fraction, an optimized packing approach is often used in modeling the particulate system [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ]; most of these works are based on mathematical modeling of the relations between geometric objects and thus reduce the optimal packing problem to a nonlinear programming problem. However, the objective of this approach is to obtain the densest packing system, regardless of considering the real physical movements of particles.…”