  We carry out constant volume simulations of steady-state, shear driven,
rheology in a simple model of bidisperse, soft-core, frictionless disks in two
dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We
carry out a detailed critical scaling analysis of our resulting data for
pressure $p$ and shear stress $\sigma$, in order to determine the critical
exponent $\beta$ that describes the algebraic divergence of the Bagnold
transport coefficients, as the jamming transition is approached from below. We
show that it is necessary, for the strain rates considered in this work, to
consider the leading correction-to-scaling term in order to achieve a
self-consistent analysis of our data. Our resulting value $\beta\approx 5.0\pm
0.4$ is clearly larger than the theoretical prediction by Otsuki and Hayakawa,
and is consistent with earlier numerical results by Peyneau and Roux, and
recent theoretical predictions by DeGiuli et al. We have also considered the
macroscopic friction $\mu\equiv \sigma/p$ and similarly find results consistent
with Peyneau and Roux, and with DeGiuli et al. Our results confirm that the
shear driven jamming transition in Bagnoldian systems is well described by a
critical scaling theory (as was found previously for Newtonian systems), and we
relate this scaling theory to the phenomenological constituent laws for
dilatancy and friction.
