particles. We notice that the stress σ is not the kinetic pressure, p , measured in the LS packings which diverges at the end of the LS protocol. Here σ refers to the mechanical pressure related to the trace of the stress tensor σ$_{ij}$ via σ = σ$_{ii}$/ 3, where where the sum is over all the contact forces, f c i denotes the i -th component of the contact force, ˆ n c is the unit vector joining the center of two spheres of radius R in contact and V is the system volume. The system is then compressed isotropically by a constant compression rate until a given nonzero stress σ is reached. Next, we turn off the compression and allow the system to relax with constant volume. If the system eventually reaches a jammed state with a fixed nonzero σ and coordination number, the system pressure will remain unchanged over a large period of time (usually ∼ 10 7 MD steps); otherwise, if the system is not stable, the pressure will relax to zero very fast [7]. Previous studies show that there exists a jamming transition for granular matter as and Here, σ$_{j}$ is zero for frictionless packings. However, it could has nonzero value for frictional packings, in general. The exponent α = 3 / 2 is trivially related to the Hertz-law of in- terparticle contact force and β = 1 / 2 seems to be universal over different force laws [4]. In practice, it is difficult to reach a jammed packing exactly at the transition point φ$_{j}$ while it is much easier to get a stable packing with slightly higher pressure. In order to approach the transition point, a jammed packing at higher pressure than σ$_{j}$ in Eq. (4) obtained using the above protocol is decompressed with a negative compression rate until certain lower pressure is reached. Then the system is allowed to relax again to check for mechanical stability. If it is stable, then the system is decompressed further to an even lower pressure, and we check its stability again. By this process (called the split algorithm in [7]) we are able to approach the density φ$_{j}$ at the jamming transition point as close as possible 17 σ$_{ij}$ = R 2 V ∑ contacts f c i n c j + f c $_{j}$n c $_{i}$, (3) σ ( φ ) − σ$_{j}$ ∼ ( φ − φ$_{j}$ ) $^{α}$, (4) Z ( φ ) − Z$_{j}$ ∼ ( φ − φ$_{j}$ ) $^{β}$. (5)