  We present a new formulation of the jamming phase diagram for a class of
glass-forming fluids consisting of spheres interacting via finite-ranged
repulsions at temperature $T$, packing fraction $\phi$ or pressure $p$, and
applied shear stress $\Sigma$. We argue that the natural choice of axes for the
phase diagram are the dimensionless quantities $T/p\sigma^3$,
$p\sigma^3/\epsilon$, and $\Sigma/p$, where $T$ is the temperature, $p$ is the
pressure, $\Sigma$ is the stress, $\sigma$ is the sphere diameter, $\epsilon$
is the interaction energy scale, and $m$ is the sphere mass. We demonstrate
that the phase diagram is universal at low $p\sigma^3/\epsilon$; at low
pressure, observables such as the relaxation time are insensitive to details of
the interaction potential and collapse onto the values for hard spheres,
provided the observables are non-dimensionalized by the pressure. We determine
the shape of the jamming surface in the jamming phase diagram, organize
previous results in relation to the jamming phase diagram, and discuss the
significance of various limits.
