Growth dynamics of citations of cumulative papers of individual authors according to progressive nucleation mechanism: Concept of citation acceleration

Using data generated by progressive nucleation mechanism on the cumulative fraction of citations of individual papers published successively by a hypothetical author, an expression for the time dependence of the cumulative number Lsum(t) of citations of progressively published papers is proposed. It was found that, for all nonzero values of constant publication rate ΔN, the cumulative citations Lsum(t) of the cumulative N papers published by an author in his/her entire publication career spanning over T years may be represented in distinct regions: (1) in the region 0 < t < Θ0 (where Θ0 ≈ T/3), Lsum(t) slowly increases proportionally to the square of the citation time t, and (2) in the region t > Θ0, Lsum(t) approaches a constant Lsum(max) at T. In the former region, the time dependence of Lsum(t) of an author is associated with three parameters, viz. the citability parameter λ0, the publication rate ΔN and his/her publication career t. Based on the predicted dependence of Lsum(t) on t, a useful scientometric age-independent measure, defined as citation acceleration a = Lsum(t)/t2, is suggested to analyze and compare the scientific activities of different authors. Confrontation of the time dependence of cumulative number Lsum(t) of citations of papers with the theoretical equation reveals one or more citation periods during the publication careers of different authors.

► Equation for time dependence of cumulative citations of an author is proposed.
► Time dependence of cumulative citations of an author shows distinct regions.
► Conceptual basis of a scientometric age-independent measure is suggested.
► Analysis of real citation data of authors reveals one or more citation periods.