  The mechanical responses of dense packings of soft athermal spheres under a
finite-rate shear are studied by means of molecular dynamics simulations. We
investigate the volume fraction and shear rate dependence of the fluctuations
in the shear stress and the interparticle contact number. In particular, we
quantify them by defining the susceptibility as the ratio of the global to
local fluctuations. The obtained susceptibilities form ridges on the volume
fraction-shear rate plane, which are reminiscent of the Widom lines around the
critical point in an equilibrium phase transition.
