  Using Newtonian and Brownian dynamics simulations, the structural and
transport properties of hard and soft spheres have been studied. The soft
spheres were modeled using inverse power potentials ($V\sim r^{-n}$, with $1/n$
the potential softness). Although the pressure, diffusion coefficient and
viscosity depend at constant density on the particle softness up to extremely
high values of $n$, we show that scaling the density with the freezing point
for every system effectively collapses these parameters for $n\geq 18$
(including hard spheres), for large densities. At the freezing points, the long
range structure of all systems is identical, when the distance is measured in
units of the interparticle distance, but differences appear at short distances
(due to the different shape of the interaction potential). This translates into
differences at short times in the velocity and stress autocorrelation
functions, although they concur to give the same value of the corresponding
transport coefficient (for the same density to freezing ratio); the microscopic
dynamics also affects the short time behaviour of the correlation functions and
absolute values of the transport coefficients, but the same scaling with the
freezing density works for Newtonian or Brownian dynamics. For hard spheres,
the short time behaviour of the stress autocorrelation function has been
studied in detail, confirming quantitatively the theoretical forms derived for
it.
