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Context. Laboratory experiments have shown that the initial stage of the dust growth in the protoplanetary disk starts with low-velocity hit-and-stick collisions between sub-micron grains, before the relative impact energy becomes large enough to cause the morphological restructuring of the forming aggregates. The results of these collisions are loose aggregates characterized by fractal dimensions ≤2. Numerical studies generally model this early stage with colliding clusters made of monodisperse spherical monomers.