Application of progressive nucleation mechanism for the citation behavior of individual papers of different authors

The basic concepts and equations of the progressive nucleation mechanism (PNM) are presented first for the growth and decay of items. The mechanism is then applied to describe the cumulative citations L and citations ΔL per year of the individual most-cited papers i of four selected Polish professors as a function of citation duration t. It was found that the PNM satisfactorily describes the time dependence of cumulative citations L of the papers published by different authors with sufficiently high citations ΔL, as represented by the highest yearly citations ΔL (max) during the entire citation period t (normal citation behavior). The citation period for these papers is less than 15 years and it is even 6–8 years in several cases. However, for papers with citation periods exceeding about 15 years, the growth behavior of citations does not follow the PNM in the entire citation period (anomalous citation behavior), and there are regions of citations in which the citation data may be described by the PNM. Normal and anomalous citation behaviors are attributed, respectively, to the occurrence and nonoccurrence of stationary nucleation of citations for the papers. The PNM also explains the growth and decay of citations ΔL per year of papers exhibiting normal citation behavior.