  We carry out overdamped simulations in a simple model of jamming - a
collection of bi-disperse soft core frictionless disks in two dimensions - with
the aim to explore the finite size dependence of different quantities, both the
relaxation time obtained from the relaxation of the energy and the
pressure-equivalent of the shear viscosity. The motivation for the paper is the
observation [Nishikawa et al., J. Stat. Phys, 182, 37 (2021)] that there are
finite size effects in the relaxation time, $\tau$, that give problems in the
determination of the critical divergence, and the claim that this is due to a
finite size dependence, $\tau\sim\ln N$, which makes $\tau$ an ill-defined
quantity. Beside analyses to determine the relaxation time for the whole system
we determine particle relaxation times which allow us to determine both
histograms of particle relaxation times and the average particle relaxation
times - two quantities that are very useful for the analyses. The starting
configurations for the relaxation simulations are of two different kinds:
completely random or taken from steady shearing simulations, and we find that
the difference between these two cases are bigger than previously noted and
that the observed problems in the determination of the critical divergence
obtained when starting from random configurations are not present when instead
starting the relaxations from shearing configurations. We also argue that the
the effect that causes the $\ln N$-dependence is not as problematic as
asserted. When it comes to the finite size dependence of the
pressure-equivalent of the shear viscosity we find that our data don't give
support for the claimed strong finite size dependence, but also that it is at
odds with what one would normally expect for a system with a diverging
correlation length, and that this calls for a novel understanding of the
phenomenon of shear-driven jamming.
