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Jamming and rheology: an introduction

Fig. 1. Schematic jamming phase diagram. Here, the tem­ perature, pressure and shear stress are scaled to be dimen­ sionless. In the case where the particles have some modulus M and repel each other bv deforming each other, we have scaled shear stress by s"=s!M. inverse Dressure by 1 / p9 - M / p and temperature by T* = kT / Ma3, where a is the size of the individual particles. (The pressure could in principle be replaced by the density as was originally done [2].) When the interactions are attractive, the axes must be scaled differently; for systems with Lennard-Jones interac­ tions

for example, we use the scalings T* — kT Is and s*=sa3/e. In addition, we note that the pressure axis must be shifted because a negative pressure is required to achieve a low density, so \/ρ*=ε/οΐ(ρ+ρ0).