title: Analytic scaling function for island-size distributions.
abstract: We obtain an explicit solution for the island-size distribution described by the rate equations for irreversible growth with the simplified capture rates of the form σ(s)(Θ)∝Θ(p)(a+s-1) for all s≥1, where s is the size and Θ is the time-dependent coverage. The intrinsic property of this solution is its scaling form in the continuum limit. The analytic scaling function depends on the two parameters a and p and is capable of describing very dissimilar distribution shapes, both monomodal and monotonically decreasing. The obtained results suggest that the scaling features of the size distributions are closely related to the size linearity of the capture rates. A simple analytic scaling is obtained rigorously here and helps to gain a better theoretical understanding of possible origins of the scaling behavior of the island-size distributions.
authors.affiliation: St. Petersburg Academic University, Khlopina 8/3, 194021 St. Petersburg, Russia.|Ioffe Physical Technical Institute of the Russian Academy of Sciences, Politekhnicheskaya 26, 194021 St. Petersburg, Russia.|ITMO University, Kronverkskiy prospekt 49, 197101 St. Petersburg, Russia.
authors.forename: V G
authors.initials: VG
authors.lastname: Dubrovskii
authors.affiliation: St. Petersburg Academic University, Khlopina 8/3, 194021 St. Petersburg, Russia.|St. Petersburg State Polytechnical University, Politechnicheskaya 29, 195251 St. Petersburg, Russia.
authors.forename: N V
authors.initials: NV
authors.lastname: Sibirev