Scaling behavior for the pressure and energy of shearing fluids

Recent simulation work has established that the widely accepted mode-coupling theory for the strain rate dependence of the pressure and energy of simple fluids under shear (i.e., energy and pressure are functions of strain rate to the power (3/2)) is observed in the vicinity of the triple point. Away from the triple point, the scaling exponent of the strain rate was seen to be closer to 2 than (3/2), suggesting a possible analytic behavior. In this paper, we accurately determine the scaling exponent behavior for a Lennard-Jones fluid in the dense fliud region and find that it varies continuously between ~1.2 and ~2 as a function of density and temperature, thus confirming its nonanalyticity. We furthermore find that the behavior is characterized by a simple linear function of density and temperature.