(subscript d) N-body simulations.

The choice of appropriate scaling physical units is an important aspect of N-body simulations. This is especially true in the present case, in which we want to compare MOND and Newtonian simulations having the same initial conditions. As well known, due to the scale-free nature of Newtonian gravity, a Newtonian $N$-body simulation starting from a given initial condition describes in practice $\infty^2$ systems of arbitrary mass and size. Each of them is obtained by assigning specific values to the length and mass units, ${r_*}$ and ${{M_*}}$, in which the initial conditions are expressed. Also dMOND gravity is scale free, because ${a_0}$ appears only as a multiplicative factor in equation (\[eqdMOND\]), and so a simulation in dMOND gravity represents systems with arbitrary mass and size (though in principle the results apply only to systems with accelerations much smaller than ${a_0}$). MOND simulations can also be rescaled, but, due to the presence of the characteristic acceleration ${a_0}$ in the non-linear function $\mu$, each simulation describes only $\infty^1$ systems, because ${r_*}$ and ${{M_*}}$ cannot be chosen independently of each other.

On the basis of the above discussion, we fix the physical units as follows (see Appendix \[appscal\] for a 