fluctuations are visible as small amplitude waves, which cause departure from perfect axisymmetry. Despite the existence of the local density fluctuations for both versions there are no significant changes happening on scales comparable to the scale length during the isolation run. Moreover, the analysis of the global mass distribution including the dominant dark matter component as shown by the circular velocity curves in figure \[fig:figure5\] along with the radial distribution of the cumulative mass present in figure \[fig:figure6\], do not show any appreciable changes. We conclude that the stability of the models is satisfactory.

Replacement method and numerical simulations
--------------------------------------------

At the end of their evolution in isolation the galactic models replace the original objects in four steps. All bound particles of the original objects are removed after measuring their centre of mass (COM) velocity and position from the cosmological box at redshift 2.87. The particles of the newly created pairs of galaxies have their residual COM velocities and positions removed. Afterwards their individual positions and velocities are rotated with random matrices generated with the [@arvo1991]. Finally the COM phase space coordinates are translated to match the COM phase space coordinates of the original objects that they replace. The resulting 