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We carry out constant volume simulations of steady-state, shear driven,rheology in a simple model of bidisperse, soft-core, frictionless disks in twodimensions, using a dissipation law that gives rise to Bagnoldian rheology. Wecarry out a detailed critical scaling analysis of our resulting data forpressure $p$ and shear stress $\sigma$, in order to determine the criticalexponent $\beta$ that describes the algebraic divergence of the Bagnoldtransport coefficients, as the jamming transition is approached from below. Weshow that it is necessary, for the strain rates considered in this work, toconsider the leading correction-to-scaling term in order to achieve aself-consistent analysis of our data. Our resulting value $\beta\approx 5.0\pm0.4$ is clearly larger than the theoretical prediction by Otsuki and Hayakawa,and is consistent with earlier numerical results by Peyneau and Roux, andrecent theoretical predictions by DeGiuli et al. We have also considered themacroscopic friction $\mu\equiv \sigma/p$ and similarly find results consistentwith Peyneau and Roux, and with DeGiuli et al. Our results confirm that theshear driven jamming transition in Bagnoldian systems is well described by acritical scaling theory (as was found previously for Newtonian systems), and werelate this scaling theory to the phenomenological constituent laws fordilatancy and friction.

Critical Scaling of Bagnold Rheology at the Jamming Transition of Frictionless Two Dimensional Disks