metastable states far away from a transition point. Since we were interested in the equilibrium properties, we were initiating the MD systems according the corresponding MF predictions. It meant that the density profiles were seeded according to the MF profiles and the velocities were assigned according to the Maxwell distribution. We observed that the MF density initiation virtually eliminates the transitory period, while the method of velocity assignment was practically unimportant, provided that it gave the correct value for the total kinetic energy. For example, it takes a system initialized with a flat $W({\bf u})=const$ about $\t\sim \t_r$ to evolve to the Maxwell distribution.

A typical plot of the steady state time dependence of the kinetic energy, virial variable, and the total energy is presented in Fig. \[fig\_td\].

![\[fig\_td\] Plots of time dependence of kinetic energy $e_{kin}$ (solid line), virial variable $\s$ (dashed line), and total energy $\e$ (dotted line) for a uniform system of $N=250$ particles at $e=-0.3$. ](fig3.eps){width=".45\textwidth"}

The comparison between the MD measurements and the MF results for the uniform and core-halo states is presented in Tables \[tab\_un\] and \[tab\_ch\] and reveals a perfect agreement between these two sets of data.

  --------------------------------------------------------------------
            \[tab\_un\]                        MD                MF
  ------------------------------- ---------------------------- 