Progressive nucleation mechanism for the growth behavior of items and its application to cumulative papers and citations of individual authors

A general expression based on the concepts of the progressive nucleation mechanism is proposed in the form [Formula: see text] to describe the growth behavior of items in an individual system and a collective of systems. In the above relation, α(t) is the ratio of items N(t) at time t to the maximum number C of possible items for the system, Θ is the corresponding time constant and q is the exponent. The above relation is then used to analyze: (1) the growth behavior of cumulative number N(t) of papers published by individual authors and cumulative citations L(t) of N(t) papers of an author as a function of citation duration t, and (2) the relationship between cumulative citations L(t) of papers and cumulative number N(t) of papers. The proposed approach predicts that: (1) the fraction of items produced by successive systems is additive, (2) the cumulative fraction α (sum)(t) of maximum number of sites is the sum of contributions of fractions of maximum number of items produced by different systems, and (3) the values of time constants Θ and exponent q increase with the addition of fraction of items produced by subsequent systems, but their values are the lowest for individual systems. The approach is applied to explain the growth behavior of cumulative N(t) papers and L(t) citations of four selected Polish professors.