We examine a synthetic way of constructing the grain size distribution in the
interstellar medium (ISM). First we formulate a synthetic grain size
distribution composed of three grain size distributions processed with the
following mechanisms that govern the grain size distribution in the Milky Way:
(i) grain growth by accretion and coagulation in dense clouds, (ii) supernova
shock destruction by sputtering in diffuse ISM, and (iii) shattering driven by
turbulence in diffuse ISM. Then, we examine if the observational grain size
distribution in the Milky Way (called MRN) is successfully synthesized or not.
We find that the three components actually synthesize the MRN grain size
distribution in the sense that the deficiency of small grains by (i) and (ii)
is compensated by the production of small grains by (iii). The fraction of each
{contribution} to the total grain processing of (i), (ii), and (iii) (i.e., the
relative importance of the three {contributions} to all grain processing
mechanisms) is 30-50%, 20-40%, and 10-40%, respectively. We also show that the
Milky Way extinction curve is reproduced with the synthetic grain size
distributions.Comment: 10 pages, 6 figures, accepted for publication in Earth, Planets, and
Spac